Kazimir Majorinc http://kazimirmajorinc.blogspot.com http://instprog.com Lot of Reduced Lambda Expressions ------ 175001/19985592. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 175002/19985619. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175003/19985646. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 175004/19986033. ------ 1. ==[ start ]==> ((a (b (^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(b (a a))) REDUCED to normal form. ------ 175005/19986123. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.b) c)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b) c)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b) c)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175006/19986312. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(a a))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175007/19986348. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((b c)((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> ((b c)((^x.b)(a (^y.y)))) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 175008/19986375. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 175009/19986420. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 175010/19986483. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 175011/19986501. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^y1.(a a)))) REDUCED to normal form. ------ 175012/19986510. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(a a))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 175013/19986582. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((a a) a) c)) 3. ==[ beta ]==> (b (((a a) a) c)) REDUCED to normal form. ------ 175014/19986591. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 175015/19986618. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 175016/19986699. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 175017/19986726. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((b (^x.a))(^z.(a a))) 6. ==[ alpha ]==> ((b (^x.a))(^y.(a a))) REDUCED to normal form. ------ 175018/19986816. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y) a)) 7. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 175019/19986843. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 175020/19986870. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a b)(((^y.y) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a b)(a ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a b)(a ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((a b)(a (^y.y))) 10. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 175021/19986897. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 175022/19986924. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a a)(a b))) 3. ==[ beta ]==> (((^y.y)(b a))((a a)(a b))) 4. ==[ alpha ]==> (((^x.x)(b a))((a a)(a b))) 5. ==[ beta ]==> ((b a)((a a)(a b))) REDUCED to normal form. ------ 175023/19987365. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a) b)) 3. ==[ beta ]==> (b ((^x1.a) b)) 4. ==[ alpha ]==> (b ((^x.a) b)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175024/19987590. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> (a ((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> (a ((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> (a (((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> (a (((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> (a (a ((^y.y) a))) 10. ==[ alpha ]==> (a (a ((^x.x) a))) 11. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 175025/19987608. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(z z)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(z z))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(y y))) 9. ==[ beta ]==> (a (^y.(y y))) 10. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 175026/19987635. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 175027/19987689. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((a a) a) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((a a) a) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((a a) a) a)) 5. ==[ beta ]==> ((b ((^y.y) b))(((a a) a) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))(((a a) a) a)) 7. ==[ beta ]==> ((b b)(((a a) a) a)) REDUCED to normal form. ------ 175028/19987698. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 175029/19987725. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175030/19987779. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 175031/19987806. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 175032/19987833. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.a)) REDUCED to normal form. ------ 175033/19987878. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175034/19987941. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (^y.(y y)))) REDUCED to normal form. ------ 175035/19988013. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 175036/19988247. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (a (a a)))) REDUCED to normal form. ------ 175037/19988301. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (a a))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a))(a a))) REDUCED to normal form. ------ 175038/19988328. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)(a (^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a)(a (^y.y)))) 5. ==[ beta ]==> ((b (a (a a)))(a (a (^y.y)))) 6. ==[ alpha ]==> ((b (a (a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 175039/19988355. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a (^x.x)) a)) REDUCED to normal form. ------ 175040/19988427. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a a))) 5. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 175041/19988445. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((^z.z) a)(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175042/19988832. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.z))) 5. ==[ beta ]==> (b ((^y.a)(^z.z))) 6. ==[ alpha ]==> (b ((^x.a)(^y.y))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175043/19988850. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1)) b)) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z)) b)) 5. ==[ beta ]==> ((^y.y)((a (^z.z)) b)) 6. ==[ alpha ]==> ((^x.x)((a (^y.y)) b)) 7. ==[ beta ]==> ((a (^y.y)) b) 8. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 175044/19988859. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 175045/19988886. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.a)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.a)) REDUCED to normal form. ------ 175046/19988904. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a) a)) 3. ==[ beta ]==> ((^y.y)((^y1.a) a)) 4. ==[ alpha ]==> ((^x.x)((^y.a) a)) 5. ==[ beta ]==> ((^y.a) a) 6. ==[ alpha ]==> ((^x.a) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175047/19988994. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 7. ==[ beta ]==> ((^y.(^z.z))(a a)) 8. ==[ alpha ]==> ((^x.(^y.y))(a a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175048/19989021. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 175049/19989039. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y)) a)) 3. ==[ beta ]==> (b ((a (^y.y)) a)) 4. ==[ alpha ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 175050/19989102. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (^z.z))) REDUCED to normal form. ------ 175051/19989147. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175052/19989183. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175053/19989210. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 175054/19993146. ------ 1. ==[ start ]==> ((^a.(b a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.((a a)(a a)))) 3. ==[ eta ]==> (b (^y.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 175055/20000238. ------ 1. ==[ start ]==> ((^a.b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 175056/20000508. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175057/20000778. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(a a))(^z.(^x1.x1)))(((^y.(a a))(^z.(^x1.x1)))((^y.(a a))(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(^z.z)))(((^x1.(a a))(^y1.(^z1.z1)))((^x2.(a a))(^y2.(^z2.z2))))) 5. ==[ beta ]==> ((a a)(((^x1.(a a))(^y1.(^z1.z1)))((^x2.(a a))(^y2.(^z2.z2))))) 6. ==[ alpha ]==> ((a a)(((^x.(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a a)((a a)((^x1.(a a))(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((a a)((a a)((^x.(a a))(^y.(^z.z))))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 175058/20000979. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 175059/20001003. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175060/20002074. ------ 1. ==[ start ]==> ((^a.(a b))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((^y.a)(^z.a)) b) 4. ==[ alpha ]==> (((^x.a)(^y.a)) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 175061/20002461. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (^y.((((a a) a)((a a)(^z.z)))(((a a) a)((a a)(^z.z))))) 4. ==[ alpha ]==> (^x.((((a a) a)((a a)(^y.y)))(((a a) a)((a a)(^z.z))))) REDUCED to normal form. ------ 175062/20002986. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175063/20003382. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 175064/20004099. ------ 1. ==[ start ]==> ((^a.(b a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)((a a)(a a)))) 3. ==[ eta ]==> (b ((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 175065/20004102. ------ 1. ==[ start ]==> ((a (b a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 175066/20004462. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((y y)(y y)))) 3. ==[ beta ]==> (((a b)(a b))(^y.((y y)(y y)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.((x x)(x x)))) REDUCED to normal form. ------ 175067/20004648. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a) a)(a b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 175068/20004936. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^x1.(a a))((^y1.y1)(^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(a a))((^y.y)(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((a a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 175069/20005539. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175070/20005776. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 175071/20005854. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175072/20006667. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175073/20006853. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(y y))(a b))) 3. ==[ beta ]==> ((((^y.(y y))(a b))((^y.(y y))(a b)))(((^y.(y y))(a b))((^y.(y y))(a b)))) 4. ==[ alpha ]==> ((((^x.(x x))(a b))((^y.(y y))(a b)))(((^z.(z z))(a b))((^x1.(x1 x1))(a b)))) 5. ==[ beta ]==> ((((a b)(a b))((^y.(y y))(a b)))(((^z.(z z))(a b))((^x1.(x1 x1))(a b)))) 6. ==[ alpha ]==> ((((a b)(a b))((^x.(x x))(a b)))(((^y.(y y))(a b))((^z.(z z))(a b)))) 7. ==[ beta ]==> ((((a b)(a b))((a b)(a b)))(((^y.(y y))(a b))((^z.(z z))(a b)))) 8. ==[ alpha ]==> ((((a b)(a b))((a b)(a b)))(((^x.(x x))(a b))((^y.(y y))(a b)))) 9. ==[ beta ]==> ((((a b)(a b))((a b)(a b)))(((a b)(a b))((^y.(y y))(a b)))) 10. ==[ alpha ]==> ((((a b)(a b))((a b)(a b)))(((a b)(a b))((^x.(x x))(a b)))) 11. ==[ beta ]==> ((((a b)(a b))((a b)(a b)))(((a b)(a b))((a b)(a b)))) REDUCED to normal form. ------ 175074/20007216. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(^y.(b y))) 3. ==[ eta ]==> (((^x.x)((a a)(a a))) b) 4. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 175075/20007720. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 175076/20007933. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175077/20008854. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 175078/20009043. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(a y))) 3. ==[ eta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 175079/20010042. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^z.(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175080/20010312. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175081/20010336. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z))(a a))) 3. ==[ beta ]==> (((^z.(z z))(a a))(((^z.(z z))(a a))(^y.y))) 4. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.(y y))(a a))(^z.z))) 5. ==[ beta ]==> (((a a)(a a))(((^y.(y y))(a a))(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.(x x))(a a))(^y.y))) 7. ==[ beta ]==> (((a a)(a a))(((a a)(a a))(^y.y))) 8. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 175082/20010807. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^z1.z1)) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.y1)) 5. ==[ beta ]==> ((^y.y)(^y1.y1)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175083/20010942. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.c)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.c)) 3. ==[ beta ]==> (b (^y.c)) 4. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 175084/20011086. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 175085/20011113. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 175086/20011161. ------ 1. ==[ start ]==> (((^a.a) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x) a)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> (a (((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> (a (((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 175087/20011188. ------ 1. ==[ start ]==> (((a a) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) a)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 175088/20011197. ------ 1. ==[ start ]==> ((a b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 175089/20011242. ------ 1. ==[ start ]==> (((^a.a) b)((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x) b)((b a)(^y.b))) 3. ==[ beta ]==> (b ((b a)(^y.b))) 4. ==[ alpha ]==> (b ((b a)(^x.b))) REDUCED to normal form. ------ 175090/20011269. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 175091/20011296. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 175092/20011350. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 175093/20011377. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 175094/20011413. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 175095/20011440. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 175096/20011467. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175097/20011512. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (a (^y.y))) a)) REDUCED to normal form. ------ 175098/20011539. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> ((a a)((^y.y) b)) 6. ==[ alpha ]==> ((a a)((^x.x) b)) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 175099/20011566. ------ 1. ==[ start ]==> (((a a)(^b.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.a))((b (^y.y)) c)) REDUCED to normal form. ------ 175100/20011737. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 175101/20011935. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(a (a (a (^y.y))))) 3. ==[ beta ]==> (((a a)(a a))(a (a (a (^y.y))))) 4. ==[ alpha ]==> (((a a)(a a))(a (a (a (^x.x))))) REDUCED to normal form. ------ 175102/20011944. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.y))) REDUCED to normal form. ------ 175103/20011962. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175104/20012097. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175105/20012124. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))(a b)) 6. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 175106/20012178. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)((a a)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a b)((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 7. ==[ beta ]==> ((a b)((a a)(^y.y))) 8. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 175107/20012232. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 11. ==[ beta ]==> (a (^y.(^z.z))) 12. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 175108/20012259. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 175109/20012313. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 175110/20012466. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(a (a a))) REDUCED to normal form. ------ 175111/20012493. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 175112/20012646. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 10. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175113/20012673. ------ 1. ==[ start ]==> ((((a a) a) a)((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a) a)((a (a a))(^x.x))) REDUCED to normal form. ------ 175114/20012781. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z) a)) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y) a)) 5. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 175115/20012808. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b (^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b (^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175116/20012871. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.(y y))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(x x))) REDUCED to normal form. ------ 175117/20012898. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 175118/20012979. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 175119/20013006. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 175120/20013033. ------ 1. ==[ start ]==> ((a (a b))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((a (a b))((^x.a)(^y.a))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 175121/20013204. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((b (^z.z))(a a))) 3. ==[ beta ]==> (b ((b (^z.z))(a a))) 4. ==[ alpha ]==> (b ((b (^x.x))(a a))) REDUCED to normal form. ------ 175122/20013231. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> ((a b)(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> ((a b)(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 175123/20013240. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a)) c)) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 175124/20013258. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> (((^y.y) b)((^z.z) a)) 6. ==[ alpha ]==> (((^x.x) b)((^y.y) a)) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175125/20013312. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((b a)(^y.y))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)(^x.x))) REDUCED to normal form. ------ 175126/20013393. ------ 1. ==[ start ]==> (((^a.b)(a a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (b ((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 175127/20013420. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 175128/20013591. ------ 1. ==[ start ]==> (((^a.b) b)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) b)((b (^y.y))(^z.z))) 3. ==[ beta ]==> (b ((b (^y.y))(^z.z))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 175129/20013807. ------ 1. ==[ start ]==> (((a b) b)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 175130/20013861. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175131/20013888. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (^z.z))) REDUCED to normal form. ------ 175132/20013969. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z)) a)) 5. ==[ beta ]==> ((^y.(y y))((b (^z.z)) a)) 6. ==[ alpha ]==> ((^x.(x x))((b (^y.y)) a)) 7. ==[ beta ]==> (((b (^y.y)) a)((b (^y.y)) a)) 8. ==[ alpha ]==> (((b (^x.x)) a)((b (^y.y)) a)) REDUCED to normal form. ------ 175133/20013996. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(a a)) b)) REDUCED to normal form. ------ 175134/20014023. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b c)) REDUCED to normal form. ------ 175135/20014113. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 175136/20014140. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(a a))(^z.b))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(a a))(^y.b))) 5. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 175137/20014167. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 175138/20014248. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a b)(a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 175139/20014275. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.y))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 175140/20014338. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(a (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(a (b (^y.y)))) 5. ==[ beta ]==> (a (b (^y.y))) 6. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 175141/20014473. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 175142/20014554. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(((a a) a)(a a))) REDUCED to normal form. ------ 175143/20014581. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175144/20014635. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a (a (^y.(^z.z))))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 175145/20014725. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 175146/20014752. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 175147/20014779. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 175148/20014869. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))((a a) a))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))((a a) a))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))((a a) a))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 175149/20014896. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.b)(a b))) 3. ==[ beta ]==> (((a (a a))((a a) a)) b) REDUCED to normal form. ------ 175150/20014950. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 175151/20014977. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a b) a)((^y.(y y))(b a))) 4. ==[ alpha ]==> (((a b) a)((^x.(x x))(b a))) 5. ==[ beta ]==> (((a b) a)((b a)(b a))) REDUCED to normal form. ------ 175152/20015004. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a (^x.x))) a) REDUCED to normal form. ------ 175153/20015031. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 175154/20015058. ------ 1. ==[ start ]==> ((a (b a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.x)((a a)(a a)))) 3. ==[ beta ]==> ((a (b a))((a a)(a a))) REDUCED to normal form. ------ 175155/20015418. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(a ((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(a ((a a)(a a)))) REDUCED to normal form. ------ 175156/20015427. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 175157/20015481. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175158/20015499. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((b a)((^y.y) a))) 3. ==[ beta ]==> (b ((b a)((^y.y) a))) 4. ==[ alpha ]==> (b ((b a)((^x.x) a))) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 175159/20015607. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(a b))) REDUCED to normal form. ------ 175160/20015706. ------ 1. ==[ start ]==> (((a (a a))(a b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a b))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 175161/20015733. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(b (^z.z))) 3. ==[ beta ]==> (((^y.y)((a a) a))(b (^z.z))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(b (^y.y))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 175162/20015787. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(a a))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 175163/20015814. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(a (^x1.x1)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 175164/20015886. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175165/20015895. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 175166/20016363. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(c (b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(c (b a))) 3. ==[ beta ]==> (b (c (b a))) REDUCED to normal form. ------ 175167/20016426. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 175168/20016471. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((b a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175169/20016498. ------ 1. ==[ start ]==> ((a (^b.b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 175170/20016678. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(c (^d.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(c (^z.a))) 3. ==[ beta ]==> (((a b)(^y.y))(c (^z.a))) 4. ==[ alpha ]==> (((a b)(^x.x))(c (^y.a))) REDUCED to normal form. ------ 175171/20016705. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a (a a)))(b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 175172/20016732. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(a (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(a (^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(a (^y.y))) REDUCED to normal form. ------ 175173/20016777. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175174/20016813. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 175175/20017101. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a)(^z.z)) c)) REDUCED to normal form. ------ 175176/20017308. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(b (b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(b (b a))) 3. ==[ beta ]==> (b (b (b a))) REDUCED to normal form. ------ 175177/20017344. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175178/20017416. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^y1.y1)(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175179/20017623. ------ 1. ==[ start ]==> ((((a a) a)(a b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 175180/20017704. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 175181/20017785. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 175182/20017812. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(a b))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a b)(a b))) REDUCED to normal form. ------ 175183/20018172. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(a (b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(a (b a))) 3. ==[ beta ]==> (((a a)(a a))(a (b a))) REDUCED to normal form. ------ 175184/20018199. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a a))) 5. ==[ beta ]==> (((a a)(^y.y))(a a)) 6. ==[ alpha ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 175185/20018208. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 175186/20018235. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(a a)) c)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(a a)) c)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a)) c)) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 175187/20018253. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a b)((^y.y) a))) 3. ==[ beta ]==> (((b a)(b a))((a b)((^y.y) a))) 4. ==[ alpha ]==> (((b a)(b a))((a b)((^x.x) a))) 5. ==[ beta ]==> (((b a)(b a))((a b) a)) REDUCED to normal form. ------ 175188/20018334. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (a a))((a a) a))) 3. ==[ beta ]==> (b ((a (a a))((a a) a))) REDUCED to normal form. ------ 175189/20018451. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a)(^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 175190/20018478. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 175191/20018505. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a b)(^y.a))) REDUCED to normal form. ------ 175192/20018568. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 175193/20018595. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))((a a) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(((a a) a)((a a) a))) REDUCED to normal form. ------ 175194/20018622. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(a b))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 175195/20018649. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175196/20018676. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(^y.y))) 6. ==[ alpha ]==> ((((a a) a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 175197/20018703. ------ 1. ==[ start ]==> (((a b)(a b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 175198/20018730. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 175199/20018757. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 175200/20018811. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 175201/20018838. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.a)(^z.a))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.a))) 7. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 175202/20018865. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.a)(^y.b))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 175203/20018892. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 175204/20018982. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a b)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b)(a (^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(a (^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(a (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175205/20019063. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((a (a a))(^y.y))) 6. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 175206/20019207. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((b c)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 175207/20019234. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((a a) a)(^x.a))) REDUCED to normal form. ------ 175208/20019342. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 175209/20019369. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^x1.(a a)))) REDUCED to normal form. ------ 175210/20019450. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a) a) c)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a) a) c)) REDUCED to normal form. ------ 175211/20019612. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175212/20019783. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b (^z.b))) 3. ==[ beta ]==> (((^y.y)(b a))(b (^z.b))) 4. ==[ alpha ]==> (((^x.x)(b a))(b (^y.b))) 5. ==[ beta ]==> ((b a)(b (^y.b))) 6. ==[ alpha ]==> ((b a)(b (^x.b))) REDUCED to normal form. ------ 175213/20019810. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 175214/20019837. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.b)(a a))) 3. ==[ beta ]==> (((a b)(a a))((^y.b)(a a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.b)(a a))) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 175215/20019864. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a b))((^y.a)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 175216/20019891. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 175217/20019945. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 175218/20019972. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))((a a) a))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))((a a) a))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 175219/20019999. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(a b))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a b)) REDUCED to normal form. ------ 175220/20020143. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(c ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(c ((^y.y)(^z.z)))) 7. ==[ beta ]==> (c ((^y.y)(^z.z))) 8. ==[ alpha ]==> (c ((^x.x)(^y.y))) 9. ==[ beta ]==> (c (^y.y)) 10. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 175221/20020224. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(a a))) 3. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 175222/20020332. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175223/20020449. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (a a))(^z.a))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x) a)((a (a a))(^y.a))) 5. ==[ beta ]==> (a ((a (a a))(^y.a))) 6. ==[ alpha ]==> (a ((a (a a))(^x.a))) REDUCED to normal form. ------ 175224/20020557. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((a a) a) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a) a)) REDUCED to normal form. ------ 175225/20020584. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1)) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1)) b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1)) b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175226/20020638. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a) d)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a d)) REDUCED to normal form. ------ 175227/20020737. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1)(^x2.x2))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175228/20020746. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 175229/20020773. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z)) c)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z)) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y)) c)) 5. ==[ beta ]==> ((b (^x.(x x)))(c c)) REDUCED to normal form. ------ 175230/20020890. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175231/20020917. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a (^x1.x1))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 175232/20020944. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 175233/20020971. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 175234/20020998. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175235/20021025. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 175236/20021052. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 175237/20021079. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.a))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 175238/20021106. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 175239/20021268. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(a (^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 175240/20021286. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (a a))(^z.z))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 175241/20021295. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y))(a a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a a)(a a))) REDUCED to normal form. ------ 175242/20021691. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a) a)) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a) a)) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a) a)) 5. ==[ beta ]==> (b (((^y.y) a) a)) 6. ==[ alpha ]==> (b (((^x.x) a) a)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175243/20021718. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y)) b)) REDUCED to normal form. ------ 175244/20021736. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b (a (^z.z)))) 3. ==[ beta ]==> ((a (a (^y.y)))(b (a (^z.z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (a (^y.y)))) REDUCED to normal form. ------ 175245/20021763. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(a ((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(a ((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a))) 5. ==[ beta ]==> (a ((^y.y) a)) 6. ==[ alpha ]==> (a ((^x.x) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175246/20021817. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a)(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)(a (^x.x)))) REDUCED to normal form. ------ 175247/20021853. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z))) 7. ==[ beta ]==> ((a (^y.y))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 175248/20021880. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175249/20021898. ------ 1. ==[ start ]==> (((^a.b)(b a))(a c)) 2. ==[ alpha ]==> (((^x.b)(b a))(a c)) 3. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 175250/20021961. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 175251/20022006. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b a)) 3. ==[ beta ]==> ((^y.(^z.z))(b a)) 4. ==[ alpha ]==> ((^x.(^y.y))(b a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175252/20022042. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 175253/20022069. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 175254/20022095. ------ 1. ==[ start ]==> (^a.((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (^x.((b (^y.y))(^z.x))) REDUCED to normal form. ------ 175255/20022096. ------ 1. ==[ start ]==> (a ((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (a ((b (^x.x))(^y.a))) REDUCED to normal form. ------ 175256/20026014. ------ 1. ==[ start ]==> ((^a.(b a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(^z.(a a)))) 3. ==[ eta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 175257/20033061. ------ 1. ==[ start ]==> ((^a.a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((b (^y.y))(^z.a)) 4. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 175258/20033088. ------ 1. ==[ start ]==> ((^a.(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a))(^y.(y y)))(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 175259/20033115. ------ 1. ==[ start ]==> ((^a.b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 175260/20033151. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175261/20033196. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^z.z))(^x1.(a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 175262/20033313. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175263/20033424. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(a (a (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^y1.(a (a (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 175264/20033556. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 175265/20033856. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 175266/20033865. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 175267/20034438. ------ 1. ==[ start ]==> ((^a.((a a) a))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.((x x) x))((b a)(^y.a))) 3. ==[ beta ]==> ((((b a)(^y.a))((b a)(^y.a)))((b a)(^y.a))) 4. ==[ alpha ]==> ((((b a)(^x.a))((b a)(^y.a)))((b a)(^z.a))) REDUCED to normal form. ------ 175268/20034693. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a a)(^y.((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> ((a a)(^x.((^y.(^z.z)) a))) 9. ==[ beta ]==> ((a a)(^x.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 175269/20034771. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 175270/20035107. ------ 1. ==[ start ]==> ((((a a) a) b)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> ((((a a) a) b)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 175271/20035545. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((((a a)(a a))(^z.(^x1.x1)))(((a a)(a a))(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((((a a)(a a))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a)(a a))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175272/20036976. ------ 1. ==[ start ]==> ((^a.(b a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((a a)(^y.(a a)))) 3. ==[ eta ]==> (b ((a a)(^y.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 175273/20036979. ------ 1. ==[ start ]==> ((a (b a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 175274/20037339. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 175275/20037348. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.((y y)(y y)))) REDUCED to normal form. ------ 175276/20037813. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^x1.x1)(a a))(^y1.(^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175277/20038347. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^z.b)) REDUCED to normal form. ------ 175278/20038731. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175279/20039238. ------ 1. ==[ start ]==> (((a b)(^c.a))(^d.(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(b a))) REDUCED to normal form. ------ 175280/20039265. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 175281/20039730. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a (a a))(^y.b))) 3. ==[ beta ]==> ((((a (a a))(^y.b))((a (a a))(^y.b)))(((a (a a))(^y.b))((a (a a))(^y.b)))) 4. ==[ alpha ]==> ((((a (a a))(^x.b))((a (a a))(^y.b)))(((a (a a))(^z.b))((a (a a))(^x1.b)))) REDUCED to normal form. ------ 175282/20041533. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 175283/20041971. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((a a) a) b)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((a a) a) b)) 3. ==[ eta ]==> ((^y.(^z.z))(((a a) a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175284/20042469. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((a a) a))) 7. ==[ beta ]==> ((b b)(^y.((a a) a))) 8. ==[ alpha ]==> ((b b)(^x.((a a) a))) REDUCED to normal form. ------ 175285/20043213. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a))(^z.z))) 3. ==[ beta ]==> (((a (a a))(^z.z))(((a (a a))(^z.z))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((a (a a))(^y.y))(^z.z))) REDUCED to normal form. ------ 175286/20043684. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 5. ==[ beta ]==> (^y.(^z.a)) 6. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 175287/20043819. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(a (^z.z)))) 3. ==[ beta ]==> (b (^y.(a (^z.z)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 175288/20043882. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 175289/20043927. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175290/20043963. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 175291/20043990. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 175292/20044029. ------ 1. ==[ start ]==> ((a a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 175293/20044056. ------ 1. ==[ start ]==> ((a (a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a a))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 175294/20044083. ------ 1. ==[ start ]==> ((a b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 175295/20044092. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175296/20044119. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175297/20044137. ------ 1. ==[ start ]==> (((a a)(a a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(a a))((b a)(^x.b))) REDUCED to normal form. ------ 175298/20044164. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 175299/20044200. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175300/20044227. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(b a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(b a))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 175301/20044281. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 175302/20044362. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 175303/20044389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (a (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a (a (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 175304/20044524. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 175305/20044632. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.(a a))(^z.(^x1.x1)))((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a a)((^x1.(a a))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 175306/20044713. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175307/20044776. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(c (b (^z.z)))) REDUCED to normal form. ------ 175308/20044803. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 175309/20044821. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(y (^z.z))))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y (^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 175310/20044830. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (a (a (^y.y))))) REDUCED to normal form. ------ 175311/20044938. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((b b)(((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> ((b b)(((^x.x) b)(a (a a)))) 5. ==[ beta ]==> ((b b)(b (a (a a)))) REDUCED to normal form. ------ 175312/20045073. ------ 1. ==[ start ]==> (((a (a a)) b)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 175313/20045100. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(b a))) 5. ==[ beta ]==> (a (((a a) a)(b a))) REDUCED to normal form. ------ 175314/20045127. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 175315/20045154. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a (a a)) b)) REDUCED to normal form. ------ 175316/20045181. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 175317/20045208. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 175318/20045235. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 8. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175319/20045271. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175320/20045298. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175321/20045325. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))(^y.a))) 5. ==[ beta ]==> ((a a)(((a a)(a a))(^y.a))) 6. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 175322/20045352. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(b (^y.(y y)))) REDUCED to normal form. ------ 175323/20045379. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175324/20045406. ------ 1. ==[ start ]==> ((a ((a a) a))((b a)(^c.a))) 2. ==[ alpha ]==> ((a ((a a) a))((b a)(^x.a))) REDUCED to normal form. ------ 175325/20045442. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))(a b)) 6. ==[ alpha ]==> ((^x.(^y.y))(a b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175326/20045496. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> (a ((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.b)((a a)(^y.y)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 175327/20045577. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> (((a a) a)(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> (((a a) a)(b ((^y.y) b))) 8. ==[ alpha ]==> (((a a) a)(b ((^x.x) b))) 9. ==[ beta ]==> (((a a) a)(b b)) REDUCED to normal form. ------ 175328/20045604. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)((a a)(a a))) 6. ==[ alpha ]==> ((^x.a)((a a)(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175329/20045658. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a a)((^y.y)((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> ((a a)((^x.x)((^y.(^z.z)) a))) 9. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 10. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 11. ==[ beta ]==> ((a a)(^y.y)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175330/20045739. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 175331/20045928. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((^y.b)((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((^x.b)((^y.a)(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175332/20046009. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)(^x1.(a a)))) IRREDUCIBLE: cycle. ------ 175333/20046072. ------ 1. ==[ start ]==> ((((a a) a) b)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) b)(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((((a a) a) b)(a (^y.y))) 4. ==[ alpha ]==> ((((a a) a) b)(a (^x.x))) REDUCED to normal form. ------ 175334/20046099. ------ 1. ==[ start ]==> (((a b) a)((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a b) a)((b (^x.x))(a a))) REDUCED to normal form. ------ 175335/20046126. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 175336/20046180. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 175337/20046207. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((b a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b a)(^y.y))) REDUCED to normal form. ------ 175338/20046234. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.a)(((a a)(^z.z))((a a) a))) 6. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))((a a) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175339/20046261. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 175340/20046288. ------ 1. ==[ start ]==> (((a b)(^a.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.x))((a b)(a a))) REDUCED to normal form. ------ 175341/20046486. ------ 1. ==[ start ]==> (((a b)(a a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a a))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 175342/20046513. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a a))(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 175343/20046522. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175344/20046549. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 175345/20046684. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> (b ((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175346/20046738. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(b a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(b a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175347/20046765. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.(y y))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 175348/20046819. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((a a)(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 11. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 12. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175349/20046900. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175350/20047368. ------ 1. ==[ start ]==> (((a b) c)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((a a)(^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b) c)(((a a)(^x.x))(^z.z))) 4. ==[ alpha ]==> (((a b) c)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 175351/20047395. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> (((a a) b)((a a)((a a) a))) REDUCED to normal form. ------ 175352/20047422. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)(a b))) REDUCED to normal form. ------ 175353/20047476. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a a)(^z.z))) REDUCED to normal form. ------ 175354/20047503. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (a a))(b a))) 3. ==[ beta ]==> ((a (^y.b))((a (a a))(b a))) 4. ==[ alpha ]==> ((a (^x.b))((a (a a))(b a))) REDUCED to normal form. ------ 175355/20047557. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175356/20047584. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 175357/20047701. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 175358/20047728. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175359/20047755. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> ((a (a b))((a a)(^y.a))) 6. ==[ alpha ]==> ((a (a b))((a a)(^x.a))) REDUCED to normal form. ------ 175360/20047782. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((a b)(^x.b))) REDUCED to normal form. ------ 175361/20047809. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a) a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(a a)))) 7. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(a a)))) 8. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(a a)))) 9. ==[ beta ]==> (((a a) a)(^y.(a a))) 10. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 175362/20047890. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175363/20047917. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 175364/20047944. ------ 1. ==[ start ]==> ((a (b a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))((a a)(^x.(a a)))) REDUCED to normal form. ------ 175365/20048034. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.a))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175366/20048115. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175367/20048250. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175368/20048286. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(b ((^z.z) b))) 3. ==[ beta ]==> ((a (^y.(a a)))(b ((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b ((^y.y) b))) 5. ==[ beta ]==> ((a (^x.(a a)))(b b)) REDUCED to normal form. ------ 175369/20048304. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a b)(a b))(^y.(a a))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(a a))) REDUCED to normal form. ------ 175370/20048313. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(a ((a a)(a a)))) REDUCED to normal form. ------ 175371/20048367. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 175372/20048394. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((b a) a)) REDUCED to normal form. ------ 175373/20048421. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 175374/20048448. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 175375/20048673. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x) b)(^y.y))) 3. ==[ beta ]==> (((a b)(a (a a)))(b (^y.y))) 4. ==[ alpha ]==> (((a b)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 175376/20048700. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175377/20048727. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 175378/20048781. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 175379/20048790. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(a a))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175380/20048871. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175381/20048952. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175382/20049114. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175383/20049258. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(c (b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (b a))) REDUCED to normal form. ------ 175384/20049285. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 175385/20049312. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(a ((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a b)) REDUCED to normal form. ------ 175386/20049366. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((b a)(a (^x1.x1)))) REDUCED to normal form. ------ 175387/20049672. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 175388/20049699. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 175389/20049708. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175390/20049735. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))(a (a a))) 6. ==[ alpha ]==> ((^x.(a a))(a (a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175391/20049870. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175392/20050032. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.(a a))(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(y y)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175393/20050059. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 175394/20050113. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 175395/20050176. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 175396/20050203. ------ 1. ==[ start ]==> (((a b)(^c.a))(b (b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (b a))) REDUCED to normal form. ------ 175397/20050230. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(a (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 175398/20050257. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((b a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((b a)(a a))) REDUCED to normal form. ------ 175399/20050311. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a) a)) REDUCED to normal form. ------ 175400/20050338. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a b)(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))((a b)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(a (a a)))) REDUCED to normal form. ------ 175401/20050536. ------ 1. ==[ start ]==> (((a b)((a a) a))((b a)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((b a)(^x.x))) REDUCED to normal form. ------ 175402/20050563. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175403/20050590. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(^y.a))) REDUCED to normal form. ------ 175404/20050644. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175405/20050671. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((b (a a))((^y.y)(^z.a))) 6. ==[ alpha ]==> ((b (a a))((^x.x)(^y.a))) 7. ==[ beta ]==> ((b (a a))(^y.a)) 8. ==[ alpha ]==> ((b (a a))(^x.a)) REDUCED to normal form. ------ 175406/20050698. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a (a a))(^x.b))) REDUCED to normal form. ------ 175407/20050734. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175408/20050869. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175409/20050977. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175410/20051013. ------ 1. ==[ start ]==> ((((^a.a) b) b)(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((b b)(c ((^y.y)(a a)))) 4. ==[ alpha ]==> ((b b)(c ((^x.x)(a a)))) 5. ==[ beta ]==> ((b b)(c (a a))) REDUCED to normal form. ------ 175411/20051040. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(b ((a a)(^x.x)))) REDUCED to normal form. ------ 175412/20051094. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 175413/20051121. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 175414/20051202. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 8. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 175415/20051229. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (a a))((a a) a))) REDUCED to normal form. ------ 175416/20051283. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 175417/20051427. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 175418/20051454. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 175419/20051508. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x) a)(^y.b))) 3. ==[ beta ]==> (((a (a a))(b a))(a (^y.b))) 4. ==[ alpha ]==> (((a (a a))(b a))(a (^x.b))) REDUCED to normal form. ------ 175420/20051535. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 175421/20051589. ------ 1. ==[ start ]==> (((a b)(a b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 175422/20051616. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(a a)) b)) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(a a)) b)) 5. ==[ beta ]==> (((a a)((a a) a))((a a) b)) REDUCED to normal form. ------ 175423/20051643. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a b) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b) c)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b) c)) REDUCED to normal form. ------ 175424/20052165. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 175425/20052192. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 11. ==[ beta ]==> ((^y.y)(^z.z)) 12. ==[ alpha ]==> ((^x.x)(^y.y)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175426/20052246. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 175427/20052327. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175428/20052435. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175429/20052471. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b (a b))) 3. ==[ beta ]==> ((b (^y.a))(b (a b))) 4. ==[ alpha ]==> ((b (^x.a))(b (a b))) REDUCED to normal form. ------ 175430/20052498. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 175431/20052561. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a) c)) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 175432/20052723. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b)(^y.y))) 3. ==[ beta ]==> (((a b)(a a))((a b)(^y.y))) 4. ==[ alpha ]==> (((a b)(a a))((a b)(^x.x))) REDUCED to normal form. ------ 175433/20052750. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 175434/20052777. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.a)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.a)) REDUCED to normal form. ------ 175435/20052831. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 175436/20052858. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (^y.y))(^z.a))) 5. ==[ beta ]==> ((b a)((a (^y.y))(^z.a))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 175437/20052885. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a a)(^y.b))) REDUCED to normal form. ------ 175438/20052939. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((a a) a) b)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((a a) a) b)) 3. ==[ beta ]==> ((a (^y.y))(((a a) a) b)) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a) b)) REDUCED to normal form. ------ 175439/20053029. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 175440/20053218. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c (^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175441/20053353. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) a))) 7. ==[ beta ]==> ((^y.(y y))((^z.z) a)) 8. ==[ alpha ]==> ((^x.(x x))((^y.y) a)) 9. ==[ beta ]==> (((^y.y) a)((^y.y) a)) 10. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 11. ==[ beta ]==> (a ((^y.y) a)) 12. ==[ alpha ]==> (a ((^x.x) a)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175442/20053380. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (a a)))) 5. ==[ beta ]==> ((^y.a)(a (a a))) 6. ==[ alpha ]==> ((^x.a)(a (a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175443/20053434. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.z)((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.z)((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.y)((a a) a))) 7. ==[ beta ]==> ((b b)((^y.y)((a a) a))) 8. ==[ alpha ]==> ((b b)((^x.x)((a a) a))) 9. ==[ beta ]==> ((b b)((a a) a)) REDUCED to normal form. ------ 175444/20053515. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.a))) 5. ==[ beta ]==> (b ((^y.a)(^y.a))) 6. ==[ alpha ]==> (b ((^x.a)(^y.a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175445/20053524. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d ((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(d a)) REDUCED to normal form. ------ 175446/20053551. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c (a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c (a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (a (a a)))) REDUCED to normal form. ------ 175447/20053578. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(b (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (^z.z))) REDUCED to normal form. ------ 175448/20053632. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 175449/20053659. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 175450/20053686. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(a a)) REDUCED to normal form. ------ 175451/20053740. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175452/20053776. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175453/20053803. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175454/20053830. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a (^y.a))) 6. ==[ alpha ]==> ((a ((a a)(a a)))(a (^x.a))) REDUCED to normal form. ------ 175455/20053857. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 175456/20053884. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 175457/20053911. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x)(^y.y)) a)) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y) a)) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x) a)) 5. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 175458/20053938. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 175459/20054046. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 175460/20054073. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y)) b)) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y)) b)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x)) b)) 5. ==[ beta ]==> ((b (a (a a)))(b b)) REDUCED to normal form. ------ 175461/20054100. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a) c)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a) c)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a) c)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a) c)) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 175462/20054181. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (a a))(^y.y))) REDUCED to normal form. ------ 175463/20054190. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z))(a a))) 5. ==[ beta ]==> (((^z.(z z))(a a))(^y.y)) 6. ==[ alpha ]==> (((^x.(x x))(a a))(^y.y)) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 175464/20054595. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 7. ==[ beta ]==> ((^y.a)(^z.z)) 8. ==[ alpha ]==> ((^x.a)(^y.y)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 175465/20054622. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175466/20054631. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b (a (^z.z)))) REDUCED to normal form. ------ 175467/20054649. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 175468/20054703. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 175469/20054739. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c a)) 3. ==[ beta ]==> (((^y.y)(^z.z))(c a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c a)) 5. ==[ beta ]==> ((^y.y)(c a)) 6. ==[ alpha ]==> ((^x.x)(c a)) 7. ==[ beta ]==> (c a) REDUCED to normal form. ------ 175470/20054766. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 175471/20054784. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 175472/20054847. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (a (^z.z)))) REDUCED to normal form. ------ 175473/20054892. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175474/20054928. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 175475/20054955. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (a a))) REDUCED to normal form. ------ 175476/20065974. ------ 1. ==[ start ]==> ((^a.(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175477/20066217. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (^x.(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (^x.((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175478/20066337. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 175479/20066769. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 175480/20066784. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175481/20066910. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175482/20067606. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 175483/20067675. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(a a)) c)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 175484/20068794. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(z (^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(y (^z.z)))) 7. ==[ beta ]==> ((^y.(y (^z.z)))(^y.(y (^z.z)))) 8. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(z (^x1.x1)))) 9. ==[ beta ]==> ((^z.(z (^x1.x1)))(^y.y)) 10. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 11. ==[ beta ]==> ((^z.z)(^y.y)) 12. ==[ alpha ]==> ((^x.x)(^y.y)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175485/20070252. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 175486/20071251. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 175487/20072169. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 175488/20072448. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^c.(b a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(b a))) REDUCED to normal form. ------ 175489/20073714. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(c (a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(c (a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175490/20074437. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 175491/20075373. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.a))) 7. ==[ beta ]==> ((b b)(^y.(^z.a))) 8. ==[ alpha ]==> ((b b)(^x.(^y.a))) REDUCED to normal form. ------ 175492/20075382. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^b.((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.((a a) a))) REDUCED to normal form. ------ 175493/20075985. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 175494/20076111. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 175495/20076516. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) a))) 5. ==[ beta ]==> (b (^y.((^z.z) a))) 6. ==[ alpha ]==> (b (^x.((^y.y) a))) 7. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 175496/20076678. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.z))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 7. ==[ beta ]==> (^y.(^z.y)) 8. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 175497/20076723. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175498/20076786. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175499/20076831. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.x1)) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175500/20076867. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 175501/20076894. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 175502/20076951. ------ 1. ==[ start ]==> ((a (^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 175503/20076978. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 175504/20077005. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 175505/20077014. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 175506/20077041. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175507/20077086. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175508/20077095. ------ 1. ==[ start ]==> (((a a) b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 175509/20077122. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 175510/20077149. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 175511/20077167. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175512/20077194. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 175513/20077230. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 175514/20077302. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 175515/20077311. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a (^x.x)) b)(a (a (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a (a (^y.y)))) REDUCED to normal form. ------ 175516/20077338. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a a)((^z.z)(^y.y))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175517/20077356. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((^y.y) a)(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (a (((^y.(^z.z)) a) b)) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 175518/20077383. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 5. ==[ beta ]==> ((b (^y.y)) c) 6. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 175519/20077608. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 175520/20077635. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a)) a)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 175521/20077743. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 175522/20077761. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 175523/20077779. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(a a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(a a))) 5. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 175524/20077806. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 175525/20077833. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 175526/20077860. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a a))(b (a (a a)))) REDUCED to normal form. ------ 175527/20077887. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.(^z.z)))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 175528/20078355. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 175529/20078409. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 175530/20078445. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a)(b a))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(b a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(b a))) 5. ==[ beta ]==> (b ((^y.a)(b a))) 6. ==[ alpha ]==> (b ((^x.a)(b a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175531/20078472. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 175532/20078490. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a (a a))(^y.y))) 3. ==[ beta ]==> (((a a) a)((a (a a))(^y.y))) 4. ==[ alpha ]==> (((a a) a)((a (a a))(^x.x))) REDUCED to normal form. ------ 175533/20078526. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 175534/20078553. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 175535/20078580. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 175536/20078652. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(a a)) c)) REDUCED to normal form. ------ 175537/20078823. ------ 1. ==[ start ]==> (((^a.b) a)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175538/20079237. ------ 1. ==[ start ]==> (((a a)(a b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 175539/20079264. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z)(b a))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(b a))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(b a)) REDUCED to normal form. ------ 175540/20079291. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a a))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 175541/20079318. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(a ((^x.x) b))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a b)) REDUCED to normal form. ------ 175542/20079345. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z))((a a)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((a (^y.y))((a a)(a a)))) 7. ==[ beta ]==> (a ((a (^y.y))((a a)(a a)))) 8. ==[ alpha ]==> (a ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 175543/20079372. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 175544/20079435. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175545/20079462. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (((^y.y) b)(^z.a)) 6. ==[ alpha ]==> (((^x.x) b)(^y.a)) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 175546/20079516. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((b a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a)(^y.(^z.z))) 8. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 175547/20079597. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (b ((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a b)(^x.(a a)))) REDUCED to normal form. ------ 175548/20079606. ------ 1. ==[ start ]==> (((a b) b)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b) b) b) REDUCED to normal form. ------ 175549/20079660. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 175550/20079678. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175551/20079687. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 175552/20079741. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175553/20079768. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(b (^z.z)))) 7. ==[ beta ]==> (((^y.y)(b (^z.z)))((^y.y)(b (^z.z)))) 8. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.z)(b (^x1.x1)))) 9. ==[ beta ]==> ((b (^y.y))((^z.z)(b (^x1.x1)))) 10. ==[ alpha ]==> ((b (^x.x))((^y.y)(b (^z.z)))) 11. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 12. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 175554/20079813. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a)(a a)) b)) 3. ==[ beta ]==> (b (((a a)(a a)) b)) REDUCED to normal form. ------ 175555/20079822. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175556/20079849. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 175557/20080038. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(^a.a))(^d.a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175558/20080470. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(c (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(c (^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(c (^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c (^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(c (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(c (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175559/20080497. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b (^y.(a a)))) REDUCED to normal form. ------ 175560/20080578. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 175561/20080947. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.(^x1.x1))) c)) 5. ==[ beta ]==> (b ((a (^z.(^x1.x1))) c)) 6. ==[ alpha ]==> (b ((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 175562/20081091. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 175563/20081199. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 175564/20081226. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(a a))) REDUCED to normal form. ------ 175565/20081298. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175566/20081424. ------ 1. ==[ start ]==> (((a a)(b a))(((a a) a)(a b))) REDUCED to normal form. ------ 175567/20081451. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 175568/20081478. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a))((a (a a))((a a)(^y.y)))) 6. ==[ alpha ]==> ((a (a a))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 175569/20081505. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x) a)(b a))) 3. ==[ beta ]==> (((a (a a))(a b))(a (b a))) REDUCED to normal form. ------ 175570/20081532. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 175571/20081559. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a a)((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((a a) b)) REDUCED to normal form. ------ 175572/20081703. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175573/20081784. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a a)(((^z.z)(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(a a)))) 9. ==[ beta ]==> ((a a)(^y.(a a))) 10. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 175574/20081865. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175575/20081973. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((b a) c)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175576/20082090. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 175577/20082117. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 175578/20082198. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 175579/20082225. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 175580/20082270. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175581/20082315. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 175582/20082342. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((a a)(a (a a)))) REDUCED to normal form. ------ 175583/20082369. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a b)(^z.z))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 175584/20082396. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 175585/20082423. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(a b))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(a b))) 7. ==[ beta ]==> ((a b)((^y.y)(a b))) 8. ==[ alpha ]==> ((a b)((^x.x)(a b))) 9. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 175586/20082450. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (a a))((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (a a))(a a))) REDUCED to normal form. ------ 175587/20082477. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(^x.x))(a ((a a)(^z.z)))) 6. ==[ alpha ]==> (((a b)(^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 175588/20082504. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (^y.y))(b a))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (^y.y))(b a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.x))(b a))) REDUCED to normal form. ------ 175589/20082531. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 175590/20082576. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175591/20082621. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 175592/20082648. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(a a))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(a a))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(z z))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(y y))) 7. ==[ beta ]==> ((a a)(^y.(y y))) 8. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 175593/20082783. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 175594/20082891. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((b a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175595/20082927. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 175596/20082954. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 175597/20082981. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 175598/20083062. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(z z))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(^z.(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175599/20083089. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 175600/20083116. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.a))(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 175601/20083143. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 175602/20083287. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) b)(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a) b)(((a a) a)(^y.y))) 6. ==[ alpha ]==> (((a a) b)(((a a) a)(^x.x))) REDUCED to normal form. ------ 175603/20083314. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.y1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 175604/20083341. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (a a))(a b))) 3. ==[ beta ]==> ((a (b a))((a (a a))(a b))) REDUCED to normal form. ------ 175605/20083368. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a ((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 175606/20083395. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> ((a a)((a (^y.y))((a a)(^z.z)))) 8. ==[ alpha ]==> ((a a)((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 175607/20083422. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a a)(b a))) REDUCED to normal form. ------ 175608/20083647. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(a a))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(a a))) 7. ==[ beta ]==> (a (^y.(a a))) 8. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 175609/20083782. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(a a)) c)) 3. ==[ beta ]==> (b (((^z.z)(a a)) c)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) c)) 5. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 175610/20083926. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 175611/20084052. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(a a)) c)) 3. ==[ beta ]==> (((b a)(b a))((^y.(a a)) c)) 4. ==[ alpha ]==> (((b a)(b a))((^x.(a a)) c)) 5. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 175612/20084196. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(c (^x1.(a a)))) REDUCED to normal form. ------ 175613/20084277. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175614/20084304. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 175615/20084691. ------ 1. ==[ start ]==> ((a (b (^a.a)))(c (a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(c (a b))) REDUCED to normal form. ------ 175616/20084781. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(a a)) b)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(a a)) b)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(a a)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(a a)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175617/20085006. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(a a))(a a))) 3. ==[ beta ]==> ((b c)((^y.(a a))(a a))) 4. ==[ alpha ]==> ((b c)((^x.(a a))(a a))) 5. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 175618/20085033. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b)(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 175619/20085078. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.x))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((b (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((b (^x.x))(^y.(y y))) REDUCED to normal form. ------ 175620/20085105. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 175621/20085141. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a) a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 175622/20085159. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.b))) REDUCED to normal form. ------ 175623/20085168. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 175624/20085240. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a b) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a b) b)) 3. ==[ beta ]==> (b ((a b) b)) REDUCED to normal form. ------ 175625/20085249. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 175626/20085276. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 175627/20085357. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 175628/20085384. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 175629/20085411. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 175630/20085474. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 175631/20085501. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z) a)) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y) a)) 7. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 175632/20085528. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((a b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 175633/20085555. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a (^z.z))) REDUCED to normal form. ------ 175634/20085582. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.y)(b a))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))((a a) a))) 5. ==[ beta ]==> ((b a)((a (^y.y))((a a) a))) 6. ==[ alpha ]==> ((b a)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 175635/20085609. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a a)(a b))) REDUCED to normal form. ------ 175636/20086023. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b) a)) 3. ==[ beta ]==> (b ((^x1.b) a)) 4. ==[ alpha ]==> (b ((^x.b) a)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175637/20086248. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (a ((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 175638/20086266. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a (a a))(^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a (a a))(^z.a))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.a))) 7. ==[ beta ]==> ((a (a a))(^y.a)) 8. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 175639/20086293. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(y y))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 175640/20086347. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)(^z.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)(^z.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)(^z.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)(^z.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)(^y.a))) 7. ==[ beta ]==> ((b b)((a a)(^y.a))) 8. ==[ alpha ]==> ((b b)((a a)(^x.a))) REDUCED to normal form. ------ 175641/20086356. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a a) a)) REDUCED to normal form. ------ 175642/20086428. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (a a)) c)) 3. ==[ beta ]==> (b ((a (a a)) c)) REDUCED to normal form. ------ 175643/20086437. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 175644/20086464. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 175645/20086491. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 175646/20086653. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175647/20086770. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c d)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c d)) 3. ==[ beta ]==> (((a (a a)) b)(c d)) REDUCED to normal form. ------ 175648/20086905. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(c a)) REDUCED to normal form. ------ 175649/20086959. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.x1))) REDUCED to normal form. ------ 175650/20086986. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (a a))(a a))) 3. ==[ beta ]==> ((b (a (a a)))((a (a a))(a a))) REDUCED to normal form. ------ 175651/20087013. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y) a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)(a (^y.y)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(a (a (^x.x)))) REDUCED to normal form. ------ 175652/20087067. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)(a (a a)))) 5. ==[ beta ]==> ((a a)((a a)(a (a a)))) REDUCED to normal form. ------ 175653/20087085. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 175654/20087103. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))(^z.z))) 5. ==[ beta ]==> (((a (a a))(^z.z))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 175655/20087490. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)((^z.z) a))) 5. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175656/20087508. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a) a)) 5. ==[ beta ]==> ((^y.y)(((^z.z) a) a)) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a) a)) 7. ==[ beta ]==> (((^y.y) a) a) 8. ==[ alpha ]==> (((^x.x) a) a) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175657/20087517. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a)(^z.z))) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 175658/20087535. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z)) b)) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z)) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 175659/20087544. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 175660/20087616. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z)) b)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y)) b)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 175661/20087652. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.a))) 5. ==[ beta ]==> ((^y.y)(a (^z.a))) 6. ==[ alpha ]==> ((^x.x)(a (^y.a))) 7. ==[ beta ]==> (a (^y.a)) 8. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 175662/20087679. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 175663/20087697. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a a)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 175664/20087760. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175665/20087805. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175666/20087841. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 175667/20087868. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 175668/20088735. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175669/20098068. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^z.(^x1.(^y1.y1)))((^z.(^x1.(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175670/20098950. ------ 1. ==[ start ]==> ((^a.b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(a a))(a (a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 175671/20099220. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.a)(b (^x1.x1)))) 3. ==[ eta ]==> ((^y.y)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175672/20099268. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 175673/20099715. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175674/20099718. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 175675/20100141. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 175676/20100273. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.(^y2.y2)))((^z2.z2)(^x3.x3))))((^y3.(^z3.(^x4.x4)))((^y4.y4)(^z4.z4)))) 5. ==[ beta ]==> (((^y.(^z.z))((^z1.(^x2.(^y2.y2)))((^z2.z2)(^x3.x3))))((^y3.(^z3.(^x4.x4)))((^y4.y4)(^z4.z4)))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2))))((^y2.(^z2.(^x3.x3)))((^y3.y3)(^z3.z3)))) 7. ==[ beta ]==> ((^y.y)((^y2.(^z2.(^x3.x3)))((^y3.y3)(^z3.z3)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175677/20100786. ------ 1. ==[ start ]==> ((^a.(a b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^z.(^x1.x1))) b) 4. ==[ alpha ]==> (((^x.b)(^y.(^z.z))) b) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175678/20100960. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.b)(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (b (^z.(^x1.x1))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175679/20101173. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (^y.(((a b)((^z.z)(a a)))((a b)((^z.z)(a a))))) 4. ==[ alpha ]==> (^x.(((a b)((^y.y)(a a)))((a b)((^z.z)(a a))))) 5. ==[ beta ]==> (^x.(((a b)(a a))((a b)((^z.z)(a a))))) 6. ==[ alpha ]==> (^x.(((a b)(a a))((a b)((^y.y)(a a))))) 7. ==[ beta ]==> (^x.(((a b)(a a))((a b)(a a)))) REDUCED to normal form. ------ 175680/20102055. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((^z.a)(^x1.x1))((^z.a)(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.a)(^y.y))((^z.a)(^x1.x1)))(^y1.y1)) 5. ==[ beta ]==> ((a ((^z.a)(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> ((a ((^x.a)(^y.y)))(^z.z)) 7. ==[ beta ]==> ((a a)(^z.z)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175681/20102472. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.((a a)(a a)))) 3. ==[ beta ]==> (b (^z.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 175682/20102811. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))((^x1.x1) b))) 3. ==[ eta ]==> (b ((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175683/20103360. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a b)((a a) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 175684/20103543. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.(x x)))) REDUCED to normal form. ------ 175685/20104251. ------ 1. ==[ start ]==> ((^a.(^b.b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)(a (^z.z)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175686/20105406. ------ 1. ==[ start ]==> (((a b)((a a) a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175687/20105565. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((^y.(^z.z))((a a) a))((^y.(^z.z))((a a) a)))(((^y.(^z.z))((a a) a))((^y.(^z.z))((a a) a)))) 4. ==[ alpha ]==> ((((^x.(^y.y))((a a) a))((^z.(^x1.x1))((a a) a)))(((^y1.(^z1.z1))((a a) a))((^x2.(^y2.y2))((a a) a)))) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1))((a a) a)))(((^y1.(^z1.z1))((a a) a))((^x2.(^y2.y2))((a a) a)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((a a) a)))(((^x1.(^y1.y1))((a a) a))((^z1.(^x2.x2))((a a) a)))) 7. ==[ beta ]==> (((^y.(^z.z))((a a) a))(((^x1.(^y1.y1))((a a) a))((^z1.(^x2.x2))((a a) a)))) 8. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.(^x1.x1))((a a) a))((^y1.(^z1.z1))((a a) a)))) 9. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))((a a) a))((^y1.(^z1.z1))((a a) a)))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((a a) a))((^x1.(^y1.y1))((a a) a)))) 11. ==[ beta ]==> (((^y.(^z.z))((a a) a))((^x1.(^y1.y1))((a a) a))) 12. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.x1))((a a) a))) 13. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a) a))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 15. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 16. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175688/20105955. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(b x1))) 3. ==[ eta ]==> (((^x.(^y.y))((^z.z) b)) b) 4. ==[ beta ]==> ((^y.y) b) 5. ==[ alpha ]==> ((^x.x) b) 6. ==[ beta ]==> b REDUCED to normal form. ------ 175689/20106459. ------ 1. ==[ start ]==> (((a b)(a b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 175690/20106645. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175691/20107593. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.(y y)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.(y y)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(x x)))) REDUCED to normal form. ------ 175692/20107806. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.b)(^y1.y1))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.b)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175693/20107980. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(x1 b))) 3. ==[ beta ]==> (b (^x1.(x1 b))) 4. ==[ alpha ]==> (b (^x.(x b))) REDUCED to normal form. ------ 175694/20108313. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 175695/20108493. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.((z1 z1) z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((z1 z1) z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z) z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175696/20108625. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 175697/20108781. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 175698/20108916. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 175699/20109048. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^z.(^x1.x1)))((a (^z.(^x1.x1)))(^y.y))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 175700/20109051. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 175701/20109447. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.a))) 5. ==[ beta ]==> (b (^y.(^z.a))) 6. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 175702/20109609. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.c)) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.c)) 5. ==[ beta ]==> ((^y.y)(^z.c)) 6. ==[ alpha ]==> ((^x.x)(^y.c)) 7. ==[ beta ]==> (^y.c) 8. ==[ alpha ]==> (^x.c) REDUCED to normal form. ------ 175703/20109717. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.b)) REDUCED to normal form. ------ 175704/20109798. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175705/20109900. ------ 1. ==[ start ]==> (((^a.a) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x) a)((b (^y.y))(^z.a))) 3. ==[ beta ]==> (a ((b (^y.y))(^z.a))) 4. ==[ alpha ]==> (a ((b (^x.x))(^y.a))) REDUCED to normal form. ------ 175706/20109927. ------ 1. ==[ start ]==> (((a a) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a) a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 175707/20109936. ------ 1. ==[ start ]==> ((a b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a b)((^x.(a a))(a (a a)))) 3. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 175708/20109954. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 175709/20109981. ------ 1. ==[ start ]==> (((^a.a) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 175710/20109990. ------ 1. ==[ start ]==> (((a a)(a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 175711/20110008. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((b a)(^z.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 175712/20110035. ------ 1. ==[ start ]==> (((a a) b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 175713/20110116. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 175714/20110152. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175715/20110170. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.(a a))) 6. ==[ alpha ]==> ((a (a a))(^x.(a a))) REDUCED to normal form. ------ 175716/20110179. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 175717/20110206. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 175718/20110251. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 175719/20110278. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a) a)((a (a (^y.y))) a)) 3. ==[ beta ]==> ((a a)((a (a (^y.y))) a)) 4. ==[ alpha ]==> ((a a)((a (a (^x.x))) a)) REDUCED to normal form. ------ 175720/20110305. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 175721/20110332. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1)) c)) REDUCED to normal form. ------ 175722/20110395. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 175723/20110674. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(a a))(b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a a)(a a))(b ((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 175724/20110701. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a (a (^z.z))))) REDUCED to normal form. ------ 175725/20110791. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(a a)) d)) 3. ==[ beta ]==> ((b b)((^y.(a a)) d)) 4. ==[ alpha ]==> ((b b)((^x.(a a)) d)) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 175726/20110836. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175727/20110863. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 5. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 175728/20110917. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(a a)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))((^z1.z1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 175729/20110971. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(b a))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(b a))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(b a))) 7. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 175730/20110998. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 175731/20111052. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 175732/20111124. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 175733/20111232. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((a a)((^y.y)(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (a a)))) 7. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 175734/20111259. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 175735/20111412. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175736/20111466. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(a a)))) REDUCED to normal form. ------ 175737/20111547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175738/20111574. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((b (^y.y)) b)) REDUCED to normal form. ------ 175739/20111637. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 175740/20111664. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 175741/20111745. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 175742/20111772. ------ 1. ==[ start ]==> ((a (a b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 175743/20111943. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b (a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b (a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 175744/20111970. ------ 1. ==[ start ]==> (((^a.a)(a b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a b))((b (^y.y))(a a))) 3. ==[ beta ]==> ((a b)((b (^y.y))(a a))) 4. ==[ alpha ]==> ((a b)((b (^x.x))(a a))) REDUCED to normal form. ------ 175745/20111997. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 175746/20112051. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 175747/20112132. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (b (((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a b))) 5. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 175748/20112159. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))((a b)(a a))) REDUCED to normal form. ------ 175749/20112546. ------ 1. ==[ start ]==> (((a b) b)((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) b)((a b)(^x.(a a)))) REDUCED to normal form. ------ 175750/20112627. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 175751/20112681. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 175752/20112735. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((b (^y.y)) a)) REDUCED to normal form. ------ 175753/20112762. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(a a)) b)) REDUCED to normal form. ------ 175754/20112789. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z) b) c)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b) c)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b) c)) 5. ==[ beta ]==> (((a a)(^x.x))(b c)) REDUCED to normal form. ------ 175755/20112825. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 175756/20112906. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a))(^z.b))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 175757/20112933. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.b)(^z.(a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.b)(^y.(a a)))) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 175758/20113014. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 175759/20113041. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 175760/20113077. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(b ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(b ((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 175761/20113212. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 175762/20113221. ------ 1. ==[ start ]==> (((a b) c)((^d.a) e)) 2. ==[ alpha ]==> (((a b) c)((^x.a) e)) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 175763/20113293. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(a b))) REDUCED to normal form. ------ 175764/20113320. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((a a) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 175765/20113374. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a (a a))(b a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (a a))(b a))) REDUCED to normal form. ------ 175766/20113455. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a a)((a a)(a a)))) 3. ==[ beta ]==> (b ((a a)((a a)(a a)))) REDUCED to normal form. ------ 175767/20113491. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a)(a a))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(a a))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a))(^z.z))) REDUCED to normal form. ------ 175768/20113518. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 175769/20113554. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 175770/20113608. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 175771/20113635. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(a a))((a a) a))) 3. ==[ beta ]==> (((a (a a))((a a) a))(a a)) REDUCED to normal form. ------ 175772/20113662. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(a b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(a b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(a b))) 7. ==[ beta ]==> ((^y.y)((^z.b)(a b))) 8. ==[ alpha ]==> ((^x.x)((^y.b)(a b))) 9. ==[ beta ]==> ((^y.b)(a b)) 10. ==[ alpha ]==> ((^x.b)(a b)) 11. ==[ beta ]==> b REDUCED to normal form. ------ 175773/20113716. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 175774/20113743. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y y))(b a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((b a)(b a))) REDUCED to normal form. ------ 175775/20113770. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 175776/20113797. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 175777/20114157. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(b ((^y.y) b))) 3. ==[ beta ]==> (((a b)(a b))(b ((^y.y) b))) 4. ==[ alpha ]==> (((a b)(a b))(b ((^x.x) b))) 5. ==[ beta ]==> (((a b)(a b))(b b)) REDUCED to normal form. ------ 175778/20114220. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 175779/20114238. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (^y.(^z.z)))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 175780/20114247. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 175781/20114346. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)((a a) a))) REDUCED to normal form. ------ 175782/20114499. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(b (^z.z))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 175783/20114526. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(a (^x.(a a)))) REDUCED to normal form. ------ 175784/20114553. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z)(a a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(a a))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 175785/20114580. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175786/20114625. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175787/20114922. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((b a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((b a) c)) REDUCED to normal form. ------ 175788/20115210. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175789/20115219. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 175790/20115237. ------ 1. ==[ start ]==> ((a (^b.b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((b a)(a (^y.y)))) REDUCED to normal form. ------ 175791/20115471. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175792/20115516. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175793/20115525. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 175794/20115840. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((b a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((b a) b)) REDUCED to normal form. ------ 175795/20115867. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) a)(((a a)(^y.y)) c)) 3. ==[ beta ]==> ((b a)(((a a)(^y.y)) c)) 4. ==[ alpha ]==> ((b a)(((a a)(^x.x)) c)) REDUCED to normal form. ------ 175796/20116047. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(c ((a a)(^y.y)))) 3. ==[ beta ]==> (b (c ((a a)(^y.y)))) 4. ==[ alpha ]==> (b (c ((a a)(^x.x)))) REDUCED to normal form. ------ 175797/20116110. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175798/20116155. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((a a)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175799/20116389. ------ 1. ==[ start ]==> (((a b)((a a) a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 175800/20116497. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 175801/20116524. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 175802/20116551. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 175803/20116911. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(b ((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(b ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 175804/20116938. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(a (b a))) 3. ==[ beta ]==> ((^y.y)(a (b a))) 4. ==[ alpha ]==> ((^x.x)(a (b a))) 5. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 175805/20116992. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> (((b a)(b a))((a a)(a (^y.y)))) 6. ==[ alpha ]==> (((b a)(b a))((a a)(a (^x.x)))) REDUCED to normal form. ------ 175806/20117073. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175807/20117181. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175808/20117217. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 175809/20117244. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 175810/20117280. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.b)((^y.y) a))) 3. ==[ beta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 175811/20117307. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 175812/20117334. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 175813/20117361. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(x x))((a a) a))) 3. ==[ beta ]==> (((a (a a))(b a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 175814/20117388. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.a)(a b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)(a b))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)(a b))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(a b))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 175815/20117415. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 175816/20117442. ------ 1. ==[ start ]==> (((a b)(a b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.x)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)(a b))((a a)(^y.y))) 4. ==[ alpha ]==> (((a b)(a b))((a a)(^x.x))) REDUCED to normal form. ------ 175817/20117496. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 175818/20117577. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175819/20117631. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.b))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 175820/20117721. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(a a))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(a a))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175821/20117802. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (a a)))) 5. ==[ beta ]==> (b ((^y.y)(a (a a)))) 6. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 175822/20117910. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175823/20117946. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> ((b c)(((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> ((b c)(((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> ((b c)((a a)(^y.y))) 6. ==[ alpha ]==> ((b c)((a a)(^x.x))) REDUCED to normal form. ------ 175824/20117973. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 175825/20118081. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.a))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.a))) REDUCED to normal form. ------ 175826/20118108. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.b))) REDUCED to normal form. ------ 175827/20118189. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b) b)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b) b)) REDUCED to normal form. ------ 175828/20118216. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a) a) c)) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a) c)) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a) c)) REDUCED to normal form. ------ 175829/20118522. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(c (^z.a))) 3. ==[ beta ]==> (((^y.y)(b a))(c (^z.a))) 4. ==[ alpha ]==> (((^x.x)(b a))(c (^y.a))) 5. ==[ beta ]==> ((b a)(c (^y.a))) 6. ==[ alpha ]==> ((b a)(c (^x.a))) REDUCED to normal form. ------ 175830/20118549. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b (^y.b))) REDUCED to normal form. ------ 175831/20118576. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a (^y.(a a)))) 3. ==[ beta ]==> (((a b)(a a))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(a (^x.(a a)))) REDUCED to normal form. ------ 175832/20118603. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.b)(a a))) 3. ==[ beta ]==> (((a a)(a b))((^y.b)(a a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.b)(a a))) 5. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 175833/20118684. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 175834/20118711. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 175835/20118738. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175836/20118792. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.z))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 175837/20118963. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (a b))) 3. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 175838/20119071. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175839/20119188. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 175840/20119296. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 175841/20119323. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((a a) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175842/20119377. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a)) c)) REDUCED to normal form. ------ 175843/20119476. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(a ((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175844/20119485. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 175845/20119512. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 175846/20119539. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y)) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(c c)) REDUCED to normal form. ------ 175847/20119611. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 175848/20119656. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 175849/20119683. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 175850/20119710. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)((^y.y) a))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 175851/20119737. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a (a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a (a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175852/20119764. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 175853/20119791. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 175854/20119818. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 175855/20119845. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 175856/20119899. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 175857/20120007. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b (^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(y y)))) 5. ==[ beta ]==> ((a a)(b (^y.(y y)))) 6. ==[ alpha ]==> ((a a)(b (^x.(x x)))) REDUCED to normal form. ------ 175858/20120034. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.(^z.z)))) REDUCED to normal form. ------ 175859/20120430. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a)(^z.a))) 3. ==[ beta ]==> (((^y.y) b)((a a)(^z.a))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(^y.a))) 5. ==[ beta ]==> (b ((a a)(^y.a))) 6. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 175860/20120457. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a) a) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y) a) a)) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a a)) REDUCED to normal form. ------ 175861/20120484. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z)) b)) REDUCED to normal form. ------ 175862/20120502. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b (a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(b (a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(b (a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 175863/20120556. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y))(a a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))(a a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))(a a))) REDUCED to normal form. ------ 175864/20120592. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) c)) 5. ==[ beta ]==> ((^y.y)((^z.z) c)) 6. ==[ alpha ]==> ((^x.x)((^y.y) c)) 7. ==[ beta ]==> ((^y.y) c) 8. ==[ alpha ]==> ((^x.x) c) 9. ==[ beta ]==> c REDUCED to normal form. ------ 175865/20120619. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 175866/20120637. ------ 1. ==[ start ]==> (((^a.b)(b a))(b b)) 2. ==[ alpha ]==> (((^x.b)(b a))(b b)) 3. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 175867/20120700. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a) b)) REDUCED to normal form. ------ 175868/20120745. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175869/20120781. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 175870/20120808. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a) a)) REDUCED to normal form. ------ 175871/20120861. ------ 1. ==[ start ]==> (^a.(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (^x.(((^y.(^z.z)) x)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^x.((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 175872/20120862. ------ 1. ==[ start ]==> (a (((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (a (((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 175873/20121684. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175874/20131848. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a))) a) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1))) a) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1))) a) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) a) 5. ==[ beta ]==> ((^y.(^z.z)) a) 6. ==[ alpha ]==> ((^x.(^y.y)) a) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175875/20131854. ------ 1. ==[ start ]==> ((^a.a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175876/20131881. ------ 1. ==[ start ]==> ((^a.(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x x))((b (^y.y))(^z.a))) 3. ==[ beta ]==> (((b (^y.y))(^z.a))((b (^y.y))(^z.a))) 4. ==[ alpha ]==> (((b (^x.x))(^y.a))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 175877/20131908. ------ 1. ==[ start ]==> ((^a.b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.b)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 175878/20131944. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175879/20131989. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((b a)(^z.b))) 3. ==[ beta ]==> (((b a)(^z.b))(^y.y)) 4. ==[ alpha ]==> (((b a)(^x.b))(^y.y)) REDUCED to normal form. ------ 175880/20132106. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 175881/20132673. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175882/20132676. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 175883/20133231. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a (^y.(^z.z)))(^x1.(^y1.y1)))((a (^y.(^z.z)))(^x1.(^y1.y1))))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2))))((a (^z2.(^x3.x3)))(^y3.(^z3.z3)))) REDUCED to normal form. ------ 175884/20133927. ------ 1. ==[ start ]==> (((a b) a)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) a)(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> (((a b) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 175885/20134305. ------ 1. ==[ start ]==> (((^a.b) b)(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(^y.(b (^z.z)))) 3. ==[ beta ]==> (b (^y.(b (^z.z)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 175886/20134338. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((b (^z.z))(^x1.x1))((b (^z.z))(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((b (^y.y))(^z.z))((b (^x1.x1))(^y1.y1)))) 5. ==[ beta ]==> (((b (^y.y))(^z.z))((b (^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> (((b (^x.x))(^y.y))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 175887/20135439. ------ 1. ==[ start ]==> (((a b)(^b.a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 175888/20135769. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.y))(^z.z))) 3. ==[ eta ]==> (b ((a (^y.y))(^z.z))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 175889/20136606. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x1.x1))(^y1.(y1 y1)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 175890/20137524. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175891/20138085. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 175892/20138922. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(b z))) 3. ==[ eta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 175893/20139165. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 175894/20139417. ------ 1. ==[ start ]==> (((a b)(a b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175895/20140764. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a b) a)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a b) a)) 3. ==[ eta ]==> ((^y.(^z.z))((a b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175896/20140938. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> (b (^x1.(^y1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 175897/20141451. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175898/20141460. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((y1 y1) y1))) REDUCED to normal form. ------ 175899/20141583. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 175900/20141739. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 175901/20142018. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^z.(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175902/20142423. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a))) 7. ==[ beta ]==> (^y.((^z.z) a)) 8. ==[ alpha ]==> (^x.((^y.y) a)) 9. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 175903/20142567. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z)))) 7. ==[ beta ]==> (^y.(a (^z.z))) 8. ==[ alpha ]==> (^x.(a (^y.y))) REDUCED to normal form. ------ 175904/20142783. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.b)) REDUCED to normal form. ------ 175905/20142837. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.y1)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.y1)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175906/20142849. ------ 1. ==[ start ]==> ((a a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 175907/20142876. ------ 1. ==[ start ]==> ((a (a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (a a))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 175908/20142903. ------ 1. ==[ start ]==> ((a b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a b)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 175909/20142939. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 175910/20142984. ------ 1. ==[ start ]==> ((a (a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((b a)(^y.b))) REDUCED to normal form. ------ 175911/20143047. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 175912/20143074. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^z.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 175913/20143101. ------ 1. ==[ start ]==> ((a (^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 175914/20143119. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 175915/20143182. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.a)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 175916/20143209. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175917/20143263. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> (a ((^y.(y (^z.z)))(^x1.x1))) 6. ==[ alpha ]==> (a ((^x.(x (^y.y)))(^z.z))) 7. ==[ beta ]==> (a ((^z.z)(^y.y))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 175918/20143479. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175919/20143560. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 175920/20143650. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(b (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.y))) REDUCED to normal form. ------ 175921/20143668. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 175922/20143686. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x (^y.y))) a)) 3. ==[ beta ]==> (((a a)(a (a a)))(a (^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 175923/20143758. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> ((b b)(((a a)(a a))((^y.y) a))) 4. ==[ alpha ]==> ((b b)(((a a)(a a))((^x.x) a))) 5. ==[ beta ]==> ((b b)(((a a)(a a)) a)) REDUCED to normal form. ------ 175924/20143893. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a)) b)((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a (a a)) b)((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (((a (a a)) b)((a a)(a a))) REDUCED to normal form. ------ 175925/20143920. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y) a)((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x) a)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> (a ((a b)((a a)(^y.y)))) 6. ==[ alpha ]==> (a ((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 175926/20143947. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 175927/20143974. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 175928/20144001. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((a (^y.a))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.a))((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a (^x.a))((a (a a)) b)) REDUCED to normal form. ------ 175929/20144028. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 175930/20144055. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(b (^z.z)))) 7. ==[ beta ]==> ((a (^y.y))(b (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 175931/20144118. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 175932/20144145. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((b (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 175933/20144172. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 175934/20144199. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(z z)))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(b (^y.(y y)))) 8. ==[ alpha ]==> ((a a)(b (^x.(x x)))) REDUCED to normal form. ------ 175935/20144226. ------ 1. ==[ start ]==> ((a ((a a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 175936/20144316. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (a ((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (a ((^x.(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 175937/20144397. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 175938/20144424. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((^y.(y y))((^z.z) b)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) b)) 7. ==[ beta ]==> (((^y.y) b)((^y.y) b)) 8. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 9. ==[ beta ]==> (b ((^y.y) b)) 10. ==[ alpha ]==> (b ((^x.x) b)) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 175939/20144478. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(b (^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(b (^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(b (^z.z)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 175940/20144748. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 175941/20144829. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))(^x1.x1))) IRREDUCIBLE: cycle. ------ 175942/20144892. ------ 1. ==[ start ]==> ((((a a) a) b)(b (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(b (b (^x.x)))) REDUCED to normal form. ------ 175943/20144919. ------ 1. ==[ start ]==> (((a b) a)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) a)(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a b) a)(a (^y.y))) 4. ==[ alpha ]==> (((a b) a)(a (^x.x))) REDUCED to normal form. ------ 175944/20144946. ------ 1. ==[ start ]==> (((a a)(^a.b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.b))((b (^y.y))(a a))) REDUCED to normal form. ------ 175945/20145000. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b ((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.z) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 175946/20145027. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 175947/20145054. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((b a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((b a)((^y.y)(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 175948/20145081. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))((a a) a))) REDUCED to normal form. ------ 175949/20145108. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a b)(^x.x))((a a)(a b))) REDUCED to normal form. ------ 175950/20145297. ------ 1. ==[ start ]==> (((^a.b) b)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((a a)(b (^y.y)))) 3. ==[ beta ]==> (b ((a a)(b (^y.y)))) 4. ==[ alpha ]==> (b ((a a)(b (^x.x)))) REDUCED to normal form. ------ 175951/20145333. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((b (^y.y))(^z.z))) 3. ==[ beta ]==> ((a (a a))((b (^y.y))(^z.z))) 4. ==[ alpha ]==> ((a (a a))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 175952/20145369. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 175953/20145423. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 175954/20145504. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (b ((^x1.(a a))(a b))) 4. ==[ alpha ]==> (b ((^x.(a a))(a b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 175955/20145585. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175956/20145639. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)((^z1.z1) b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)((^z1.z1) b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)((^y1.y1) b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1) b))) 9. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1) b))) 10. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) b))) 11. ==[ beta ]==> ((^y.a)((^z.z) b)) 12. ==[ alpha ]==> ((^x.a)((^y.y) b)) 13. ==[ beta ]==> a REDUCED to normal form. ------ 175957/20146044. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175958/20146188. ------ 1. ==[ start ]==> (((a b) c)((b a)(a (a a)))) REDUCED to normal form. ------ 175959/20146215. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) b)(((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 175960/20146242. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)((a a) a))) REDUCED to normal form. ------ 175961/20146296. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 175962/20146323. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.b))((^y.y)((a a)(^z.z)))) 7. ==[ beta ]==> ((a (^x.b))((a a)(^z.z))) 8. ==[ alpha ]==> ((a (^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 175963/20146377. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175964/20146404. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a (^y.y)) b)) REDUCED to normal form. ------ 175965/20146422. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(b (^z.(a a)))) 3. ==[ beta ]==> (b (b (^z.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 175966/20146431. ------ 1. ==[ start ]==> (((a b)(^b.a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 175967/20146521. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 175968/20146548. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((b a)(^y.(y y)))) REDUCED to normal form. ------ 175969/20146575. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 175970/20146629. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(^x1.b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.b))) 7. ==[ beta ]==> ((^y.y)((a b)(^z.b))) 8. ==[ alpha ]==> ((^x.x)((a b)(^y.b))) 9. ==[ beta ]==> ((a b)(^y.b)) 10. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 175971/20146656. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 175972/20146683. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b) a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a b) a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 175973/20146737. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 175974/20146764. ------ 1. ==[ start ]==> ((a (b a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (b a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 175975/20146854. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b ((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 175976/20146935. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175977/20147043. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 175978/20147106. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(a a)))(c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 175979/20147124. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 175980/20147133. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(b ((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(^x.b))(b b)) REDUCED to normal form. ------ 175981/20147187. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 175982/20147214. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 175983/20147241. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.a))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.a))((b a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.a))((b a) a)) REDUCED to normal form. ------ 175984/20147268. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) REDUCED to normal form. ------ 175985/20147520. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> (((a a) a)(((^y.y) b)(^z.z))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b)(^y.y))) 7. ==[ beta ]==> (((a a) a)(b (^y.y))) 8. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 175986/20147547. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 175987/20147601. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 175988/20147691. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.a)(a b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.a)(a b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.a)(a b))) 5. ==[ beta ]==> ((a a)((^z.a)(a b))) 6. ==[ alpha ]==> ((a a)((^x.a)(a b))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 175989/20147772. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> (b ((^x1.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 175990/20147880. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175991/20147934. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 175992/20147988. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.b)(^x1.a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.b)(^x1.a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b)(^z.a))) 7. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.a))) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 175993/20148069. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 175994/20148132. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 175995/20148186. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(a a))) REDUCED to normal form. ------ 175996/20148249. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 175997/20148492. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 175998/20148519. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 175999/20148690. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> (b (((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (b ((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 176000/20148798. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.(^y2.y2)))(^z2.z2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2)))(^z2.z2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176001/20148852. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176002/20148879. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(z z))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(y y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176003/20149014. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176004/20149023. ------ 1. ==[ start ]==> (((a b)(^c.a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 176005/20149050. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b (b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b (b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (b a))) REDUCED to normal form. ------ 176006/20149077. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 176007/20149131. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a)(^y1.y1))(a (^z1.z1)))) REDUCED to normal form. ------ 176008/20149158. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x))((a a)((^z.z) a))) 6. ==[ alpha ]==> ((b (^x.x))((a a)((^y.y) a))) 7. ==[ beta ]==> ((b (^x.x))((a a) a)) REDUCED to normal form. ------ 176009/20149383. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((b a)(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b a)(^z.z))) 5. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 176010/20149410. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 176011/20149464. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b)(^x1.(x1 x1)))) REDUCED to normal form. ------ 176012/20149491. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> ((b (a a))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 176013/20149554. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a b))) 5. ==[ beta ]==> ((^y.(y y))(a b)) 6. ==[ alpha ]==> ((^x.(x x))(a b)) 7. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 176014/20149689. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176015/20149797. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176016/20149914. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(a (b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (b a))) REDUCED to normal form. ------ 176017/20149941. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))(a a))) REDUCED to normal form. ------ 176018/20150022. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 176019/20150049. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.b))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 8. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 176020/20150103. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (a b))) REDUCED to normal form. ------ 176021/20150148. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176022/20150157. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)((a a)(^x1.x1)))) REDUCED to normal form. ------ 176023/20150247. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a b)(^x.a))) REDUCED to normal form. ------ 176024/20150274. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 176025/20150301. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 176026/20150328. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (a a))(^x.a))) REDUCED to normal form. ------ 176027/20150355. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.b))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.b))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.b))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.b))) REDUCED to normal form. ------ 176028/20150382. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 176029/20150409. ------ 1. ==[ start ]==> (((a b)(a b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 176030/20150436. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((a a)(^y.y)) a)) 3. ==[ beta ]==> (((a a)((a a) a))(((a a)(^y.y)) a)) 4. ==[ alpha ]==> (((a a)((a a) a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 176031/20150463. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(a a)) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a)) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a) b)) REDUCED to normal form. ------ 176032/20150877. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(b (^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176033/20150985. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 176034/20151012. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176035/20151066. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 176036/20151147. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176037/20151255. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176038/20151291. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c ((a a) a))) 3. ==[ beta ]==> ((b (^y.a))(c ((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))(c ((a a) a))) REDUCED to normal form. ------ 176039/20151318. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b (a b))) REDUCED to normal form. ------ 176040/20151381. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b) b)) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 176041/20151570. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a b)(^y.y))) 3. ==[ beta ]==> (((a a)(a b))((a b)(^y.y))) 4. ==[ alpha ]==> (((a a)(a b))((a b)(^x.x))) REDUCED to normal form. ------ 176042/20151597. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 176043/20151651. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 176044/20151678. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(((^y.y) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((b a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 176045/20151759. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a b) a)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a b) a)) 3. ==[ beta ]==> ((a (^y.y))((a b) a)) 4. ==[ alpha ]==> ((a (^x.x))((a b) a)) REDUCED to normal form. ------ 176046/20151849. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(z z)))) 7. ==[ beta ]==> ((^y.(y y))(^z.(z z))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) 9. ==[ beta ]==> ((^y.(y y))(^y.(y y))) 10. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) IRREDUCIBLE: cycle. ------ 176047/20151930. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (b ((^x.x)(^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 176048/20152173. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176049/20152200. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((^y.(y y))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) a)) 7. ==[ beta ]==> (((^y.y) a)((^y.y) a)) 8. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176050/20152254. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 176051/20152335. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176052/20152398. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (a (a a)))) REDUCED to normal form. ------ 176053/20152452. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((a a) a))) REDUCED to normal form. ------ 176054/20152479. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(a a))) 7. ==[ beta ]==> ((b (^x.(x x)))(a a)) REDUCED to normal form. ------ 176055/20152506. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 176056/20152560. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (a a)))) 7. ==[ beta ]==> ((a (^y.y))(a (a a))) 8. ==[ alpha ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 176057/20152578. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 176058/20152623. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 176059/20152650. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 176060/20152677. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a)(^y.a))) 5. ==[ beta ]==> (((a (a a)) b)(a (^y.a))) 6. ==[ alpha ]==> (((a (a a)) b)(a (^x.a))) REDUCED to normal form. ------ 176061/20152704. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 176062/20152731. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 176063/20152758. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z) a)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y) a)) 5. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 176064/20152785. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a)) b)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (a a)) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a)) b)) 5. ==[ beta ]==> (((a a)(a a))((a (a a)) b)) REDUCED to normal form. ------ 176065/20152812. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a c)) REDUCED to normal form. ------ 176066/20152893. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y)) a)) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 176067/20152920. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(y y)) b)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y)) b)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x)) b)) 5. ==[ beta ]==> ((((a a)(a a)) a)(b b)) REDUCED to normal form. ------ 176068/20152992. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((a a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(a (a a)))) REDUCED to normal form. ------ 176069/20153010. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^z.(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176070/20153397. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b c)) 3. ==[ beta ]==> (((^y.y) b)(b c)) 4. ==[ alpha ]==> (((^x.x) b)(b c)) 5. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 176071/20153415. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((^y.y)((^z.z) a)) 8. ==[ alpha ]==> ((^x.x)((^y.y) a)) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 176072/20153442. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 176073/20153469. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176074/20153559. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)((a a)(a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 176075/20153604. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176076/20153667. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (a a))) REDUCED to normal form. ------ 176077/20153712. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b (^x1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176078/20153748. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 176079/20153775. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a b)) REDUCED to normal form. ------ 176080/20153829. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a a)) 5. ==[ beta ]==> ((^y.(^z.z))(a a)) 6. ==[ alpha ]==> ((^x.(^y.y))(a a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176081/20164824. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a))) b) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1))) b) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1))) b) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) b) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176082/20164848. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176083/20164929. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176084/20165091. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176085/20165238. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((a a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 176086/20165679. ------ 1. ==[ start ]==> (((a a)(a (a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 176087/20165784. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176088/20166507. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176089/20166549. ------ 1. ==[ start ]==> ((^a.(^a.b))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.b))((b (^z.z)) b)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 176090/20167299. ------ 1. ==[ start ]==> (((a b)(a a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 176091/20167695. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 176092/20169486. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.((^y.y) b))) 3. ==[ beta ]==> (((a b)(a (a a)))(^x.b)) REDUCED to normal form. ------ 176093/20170194. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176094/20170476. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176095/20171070. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 176096/20171349. ------ 1. ==[ start ]==> (((a b)((a a) a))(^c.(b a))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(b a))) REDUCED to normal form. ------ 176097/20172906. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176098/20173536. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(a b))) 3. ==[ beta ]==> (((a b)(a a))(^y.(a b))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(a b))) REDUCED to normal form. ------ 176099/20174283. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((a a) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176100/20174445. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.a))) REDUCED to normal form. ------ 176101/20174886. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))(^x.(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 176102/20174991. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a)(a (a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a)(a (a a)))(^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(a (a a)))(^x.x))) REDUCED to normal form. ------ 176103/20175417. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^y.a)) REDUCED to normal form. ------ 176104/20175579. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.x1))) REDUCED to normal form. ------ 176105/20175741. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 176106/20175768. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(a a))) REDUCED to normal form. ------ 176107/20175822. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176108/20175852. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176109/20175879. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 176110/20175906. ------ 1. ==[ start ]==> (((^a.a)(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 176111/20175933. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 176112/20175942. ------ 1. ==[ start ]==> (((^a.a) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176113/20175969. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176114/20175987. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176115/20176014. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 176116/20176050. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 176117/20176077. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 176118/20176095. ------ 1. ==[ start ]==> ((a (^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176119/20176131. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176120/20176212. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 176121/20176239. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a a)((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a a)((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 176122/20176257. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a (^z.z))) a)) 3. ==[ beta ]==> (((^y.y) a)((a (a (^z.z))) a)) 4. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y))) a)) 5. ==[ beta ]==> (a ((a (a (^y.y))) a)) 6. ==[ alpha ]==> (a ((a (a (^x.x))) a)) REDUCED to normal form. ------ 176123/20176266. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.a))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 176124/20176284. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((^y.(^z.z)) a) b) 6. ==[ alpha ]==> (((^x.(^y.y)) a) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 176125/20176563. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 176126/20176590. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 176127/20176680. ------ 1. ==[ start ]==> (((a a)(a (a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(a (a (a (^x.x))))) REDUCED to normal form. ------ 176128/20176707. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(a a))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a a))) 7. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 176129/20176734. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 176130/20176761. ------ 1. ==[ start ]==> (((a (a a))(a a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a a))(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a)(a a)) a)) REDUCED to normal form. ------ 176131/20176788. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))(b (a (a a)))) REDUCED to normal form. ------ 176132/20177085. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 176133/20177256. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 176134/20177310. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> (a (((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> (a (((^x.x)(a a))(^y.(a a)))) 7. ==[ beta ]==> (a ((a a)(^y.(a a)))) 8. ==[ alpha ]==> (a ((a a)(^x.(a a)))) REDUCED to normal form. ------ 176135/20177346. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> (b ((^y.b)((a a)(^z.z)))) 6. ==[ alpha ]==> (b ((^x.b)((a a)(^y.y)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176136/20177391. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176137/20177418. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a (a a))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 176138/20177427. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(((^y1.y1) b)((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) b)((^y1.y1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b ((^y1.y1) b))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b ((^x1.x1) b))) 7. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b b)) REDUCED to normal form. ------ 176139/20177454. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 176140/20177481. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 176141/20177508. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176142/20177553. ------ 1. ==[ start ]==> ((a (^a.b))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.b))((b (^y.y)) b)) REDUCED to normal form. ------ 176143/20177724. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176144/20178138. ------ 1. ==[ start ]==> (((a a)(a b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a a)(a b))((a b)(a a))) REDUCED to normal form. ------ 176145/20178165. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 176146/20178192. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(b a))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(b a))) 9. ==[ beta ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 176147/20178219. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 176148/20178246. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) a)((^x1.x1) b))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)((^z.z) b))) 7. ==[ beta ]==> (a (((^y.y) a)((^z.z) b))) 8. ==[ alpha ]==> (a (((^x.x) a)((^y.y) b))) 9. ==[ beta ]==> (a (a ((^y.y) b))) 10. ==[ alpha ]==> (a (a ((^x.x) b))) 11. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 176149/20178273. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 176150/20178300. ------ 1. ==[ start ]==> (((a b)(a a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 176151/20178336. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.(a a))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))((b (^y.y))(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176152/20178363. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 176153/20178417. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 176154/20178498. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (b ((a a)(^y.b))) 6. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 176155/20178507. ------ 1. ==[ start ]==> (((a b) b)((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))(a b))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 176156/20178534. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 176157/20178561. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 176158/20178588. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 176159/20178633. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.x1))) 9. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 11. ==[ beta ]==> (((^y.y) a)(^z.z)) 12. ==[ alpha ]==> (((^x.x) a)(^y.y)) 13. ==[ beta ]==> (a (^y.y)) 14. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 176160/20178642. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 176161/20178669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((a a)(a a)))) 7. ==[ beta ]==> (((^y.(^z.z))((a a)(a a)))((^y.(^z.z))((a a)(a a)))) 8. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 11. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 12. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176162/20178696. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 176163/20178714. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((b (^z.z)) a)) 3. ==[ beta ]==> (b ((b (^z.z)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 176164/20178939. ------ 1. ==[ start ]==> (((^a.b) c)((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176165/20179425. ------ 1. ==[ start ]==> (((a b)(^b.a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (^y.(a a)))) REDUCED to normal form. ------ 176166/20179848. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) b) b)) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) b) b)) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) b) b)) 5. ==[ beta ]==> (b (((^z.z) b) b)) 6. ==[ alpha ]==> (b (((^x.x) b) b)) 7. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 176167/20179992. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.b)(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) b) REDUCED to normal form. ------ 176168/20180100. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 176169/20180127. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 176170/20180199. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.y) b)) 3. ==[ beta ]==> (b ((^y.y) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176171/20180325. ------ 1. ==[ start ]==> (((a a)(b a))((a b)((a a) a))) REDUCED to normal form. ------ 176172/20180352. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a) a)(a b))) REDUCED to normal form. ------ 176173/20180379. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a (a a))((^y.y)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y)(a a)))) 9. ==[ beta ]==> ((a (a a))((^y.y)(a a))) 10. ==[ alpha ]==> ((a (a a))((^x.x)(a a))) 11. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 176174/20180406. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 176175/20180433. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) a)(b a))) 5. ==[ beta ]==> (((a a) a)(((^y.y) a)(b a))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) a)(b a))) 7. ==[ beta ]==> (((a a) a)(a (b a))) REDUCED to normal form. ------ 176176/20180460. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 176177/20180487. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a a)((^x.x) b))) 3. ==[ beta ]==> (((a b)(a (a a)))((a a) b)) REDUCED to normal form. ------ 176178/20180604. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176179/20180685. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a) a)(^z.b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a) a)(^z.b))) 5. ==[ beta ]==> ((a a)(((a a) a)(^z.b))) 6. ==[ alpha ]==> ((a a)(((a a) a)(^x.b))) REDUCED to normal form. ------ 176180/20180874. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176181/20180883. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 176182/20180901. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((b a) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a) c)) REDUCED to normal form. ------ 176183/20180991. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) b) REDUCED to normal form. ------ 176184/20181018. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.b))) 5. ==[ beta ]==> ((^y.b)((^z.a)(^x1.b))) 6. ==[ alpha ]==> ((^x.b)((^y.a)(^z.b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 176185/20181072. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176186/20181126. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 176187/20181171. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.x1) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176188/20181198. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176189/20181216. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((b a)(a (^z.z)))) REDUCED to normal form. ------ 176190/20181243. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(b a))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 176191/20181270. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(a (a a)))) REDUCED to normal form. ------ 176192/20181297. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a a))((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a))(a a))((a b)(^y.y))) 6. ==[ alpha ]==> (((a (a a))(a a))((a b)(^x.x))) REDUCED to normal form. ------ 176193/20181324. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a) a)((a a) a))) 5. ==[ beta ]==> ((a b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 176194/20181351. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))(a b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(a b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(a b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a b)) REDUCED to normal form. ------ 176195/20181378. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))((a (a a))(a a))) REDUCED to normal form. ------ 176196/20181405. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a)(a (a a)))(a ((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a)(a (a a)))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 176197/20181432. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (^z.z))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^z.z))(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))(b a))) REDUCED to normal form. ------ 176198/20181477. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(a (^x1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176199/20181522. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 176200/20181549. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((a a)(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 176201/20181684. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (b ((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 176202/20181792. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.(^x2.x2))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.(^x2.x2))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176203/20181801. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 176204/20181846. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((a a)(^z.z)) c)) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z)) c)) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y)) c)) 5. ==[ beta ]==> (b (((a a)(^y.y)) c)) 6. ==[ alpha ]==> (b (((a a)(^x.x)) c)) REDUCED to normal form. ------ 176205/20181855. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 176206/20181882. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 176207/20181963. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176208/20181990. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.b))(a a)) REDUCED to normal form. ------ 176209/20182017. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 176210/20182071. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 176211/20182188. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a b)(a (a a)))) 3. ==[ beta ]==> (((a a) b)((a b)(a (a a)))) REDUCED to normal form. ------ 176212/20182215. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 176213/20182242. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> ((a (b a))((^y.y)((a a) a))) 6. ==[ alpha ]==> ((a (b a))((^x.x)((a a) a))) 7. ==[ beta ]==> ((a (b a))((a a) a)) REDUCED to normal form. ------ 176214/20182269. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (a a))(a b))) REDUCED to normal form. ------ 176215/20182296. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y)(a a)))) 9. ==[ beta ]==> ((a a)(a ((^y.y)(a a)))) 10. ==[ alpha ]==> ((a a)(a ((^x.x)(a a)))) 11. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 176216/20182323. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 176217/20182350. ------ 1. ==[ start ]==> (((a b)((a a) a))((a a)(b a))) REDUCED to normal form. ------ 176218/20182548. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.b))) 5. ==[ beta ]==> ((a (a a))(^y.b)) 6. ==[ alpha ]==> ((a (a a))(^x.b)) REDUCED to normal form. ------ 176219/20182683. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z)) b)) 3. ==[ beta ]==> (b (((a a)(^z.z)) b)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) b)) REDUCED to normal form. ------ 176220/20182827. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((b b)((^y.(y y))(^z.b))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(^y.b))) 5. ==[ beta ]==> ((b b)((^y.b)(^y.b))) 6. ==[ alpha ]==> ((b b)((^x.b)(^y.b))) 7. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 176221/20182854. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(^y.(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 176222/20182953. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z)) b)) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y)) b)) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 176223/20183151. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 176224/20183763. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.a) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a) d)) 3. ==[ beta ]==> (b ((^z.a) d)) 4. ==[ alpha ]==> (b ((^x.a) d)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176225/20183907. ------ 1. ==[ start ]==> ((((^a.a) b) c)(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(a (^y.(^z.z)))) 3. ==[ beta ]==> ((b c)(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)(a (^x.(^y.y)))) REDUCED to normal form. ------ 176226/20183934. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a a)) REDUCED to normal form. ------ 176227/20183979. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((b (^y.y))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 176228/20184006. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z z))) 7. ==[ beta ]==> ((^y.y)(^z.(z z))) 8. ==[ alpha ]==> ((^x.x)(^y.(y y))) 9. ==[ beta ]==> (^y.(y y)) 10. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 176229/20184042. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 11. ==[ beta ]==> ((a (^x.x))(^z.z)) 12. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 176230/20184069. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 176231/20184141. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (b (((^z.z)(a a)) a)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) a)) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 176232/20184150. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 176233/20184177. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 176234/20184258. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.(^z1.z1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 176235/20184285. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 176236/20184312. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176237/20184375. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a b)(a a))) REDUCED to normal form. ------ 176238/20184402. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 176239/20184429. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((a b)((^y.y)((^z.z) a))) 8. ==[ alpha ]==> ((a b)((^x.x)((^y.y) a))) 9. ==[ beta ]==> ((a b)((^y.y) a)) 10. ==[ alpha ]==> ((a b)((^x.x) a)) 11. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 176240/20184456. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (a a))(a (a a)))) REDUCED to normal form. ------ 176241/20184483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)(((^y.y) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a)(a ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b a)(a ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((b a)(a (^y.y))) 10. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 176242/20184510. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 176243/20184537. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a)(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a a)(a b))) 3. ==[ beta ]==> (((a b)(a a))((a a)(a b))) REDUCED to normal form. ------ 176244/20185167. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176245/20185194. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (a a))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.a))) 5. ==[ beta ]==> ((a (a a))(^y.a)) 6. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 176246/20185248. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)((a (^y.y))(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 176247/20185257. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 176248/20185284. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((a a) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176249/20185329. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) b)) 5. ==[ beta ]==> (b ((^y.y) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176250/20185338. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176251/20185365. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.a)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 176252/20185392. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 176253/20185446. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.a)) REDUCED to normal form. ------ 176254/20185590. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 176255/20185860. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b (a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b (a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (a (a a)))) REDUCED to normal form. ------ 176256/20185887. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))(a ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))(a ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b (a (a a)))(a (^y.y))) 6. ==[ alpha ]==> ((b (a (a a)))(a (^x.x))) REDUCED to normal form. ------ 176257/20185914. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (a a))(a a))) REDUCED to normal form. ------ 176258/20185968. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a a)((a (^y.y))((^z.z) a))) 6. ==[ alpha ]==> ((a a)((a (^x.x))((^y.y) a))) 7. ==[ beta ]==> ((a a)((a (^x.x)) a)) REDUCED to normal form. ------ 176259/20185986. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b (^z.(z z)))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 176260/20185995. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)(a (a a)))) REDUCED to normal form. ------ 176261/20186391. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176262/20186409. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a)(^x1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.a))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.a))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.a))) 7. ==[ beta ]==> ((a a)(^y.a)) 8. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 176263/20186418. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((^z.z) a)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y) a)) 5. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 176264/20186436. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a) a)) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a) a)) 5. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 176265/20186445. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 176266/20186463. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b)) 5. ==[ beta ]==> ((a (^y.y)) b) 6. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 176267/20186517. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a) a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a) a)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a) a)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 176268/20186553. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 176269/20186580. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.a))) REDUCED to normal form. ------ 176270/20186598. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y))(^z.z))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.z))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 176271/20186661. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 176272/20186706. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176273/20186742. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 176274/20186769. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 176275/20186823. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176276/20186840. ------ 1. ==[ start ]==> (^a.((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (^x.((^y.(y (^z.z)))(x x))) 3. ==[ beta ]==> (^x.((x x)(^z.z))) 4. ==[ alpha ]==> (^x.((x x)(^y.y))) REDUCED to normal form. ------ 176277/20186841. ------ 1. ==[ start ]==> (a ((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (a ((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> (a ((a a)(^y.y))) 4. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 176278/20195754. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^b.(a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(a x1))) 3. ==[ eta ]==> ((^y.(^z.z))(^x1.(a x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a z))) 5. ==[ eta ]==> ((^x.(^y.y)) a) 6. ==[ beta ]==> (^y.y) 7. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176279/20197845. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a)) a) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a)) a) 3. ==[ beta ]==> (((a a)(^y.y)) a) 4. ==[ alpha ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 176280/20197851. ------ 1. ==[ start ]==> ((^a.a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 176281/20197986. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((^z.(^x1.(^y1.y1)))((a a) a))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176282/20198175. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(z z))((a a)(a a)))) 3. ==[ eta ]==> ((^y.y)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 176283/20198670. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176284/20198691. ------ 1. ==[ start ]==> (((a a)(a (a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 176285/20199123. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 176286/20199228. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(a (a a)))((^y.y)(a (a a))))((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(a (a a)))((^y.y)(a (a a))))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((a (a a))((^y.y)(a (a a))))((^z.z)(a (a a)))) 6. ==[ alpha ]==> (((a (a a))((^x.x)(a (a a))))((^y.y)(a (a a)))) 7. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(a (a a)))) 8. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(a (a a)))) 9. ==[ beta ]==> (((a (a a))(a (a a)))(a (a a))) REDUCED to normal form. ------ 176287/20199741. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^z.(a a))) b) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a))) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 176288/20199942. ------ 1. ==[ start ]==> (((^a.a)(a b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((^x.x)(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.z))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 176289/20200128. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (^y.((((^z.z)(a a))(a b))(((^z.z)(a a))(a b)))) 4. ==[ alpha ]==> (^x.((((^y.y)(a a))(a b))(((^z.z)(a a))(a b)))) 5. ==[ beta ]==> (^x.(((a a)(a b))(((^z.z)(a a))(a b)))) 6. ==[ alpha ]==> (^x.(((a a)(a b))(((^y.y)(a a))(a b)))) 7. ==[ beta ]==> (^x.(((a a)(a b))((a a)(a b)))) REDUCED to normal form. ------ 176290/20200707. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 176291/20201010. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^z.(z z))(^x1.(^y1.(^z1.z1))))((^z.(z z))(^x1.(^y1.(^z1.z1)))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2)))))(^z2.z2)) 5. ==[ beta ]==> ((((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2)))))(^z2.z2)) 6. ==[ alpha ]==> ((((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2))(^y2.(^z2.(^x3.x3)))))(^y3.y3)) 7. ==[ beta ]==> (((^y.(^z.z))((^x2.(x2 x2))(^y2.(^z2.(^x3.x3)))))(^y3.y3)) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1)))))(^x2.x2)) 9. ==[ beta ]==> ((^y.y)(^x2.x2)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176292/20201766. ------ 1. ==[ start ]==> ((^a.(b a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ eta ]==> (b ((^y.a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176293/20202315. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176294/20203182. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176295/20203206. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176296/20203497. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 176297/20203521. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176298/20204388. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 176299/20205441. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(^y.((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 176300/20205600. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176301/20205693. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.((y1 y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.((y1 y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.((x2 x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.((x2 x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176302/20206575. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(^z.(y y)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.(y y)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(x x)))) REDUCED to normal form. ------ 176303/20206761. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.a)(a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.x1)(a b))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.x1)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176304/20206764. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^b.(a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(^z.(a z))) 3. ==[ eta ]==> ((a ((^x.(^y.y)) a)) a) 4. ==[ beta ]==> ((a (^y.y)) a) 5. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 176305/20206935. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((a a) a))) 3. ==[ beta ]==> (b (^x1.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 176306/20207580. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 176307/20207628. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 176308/20207763. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 176309/20207898. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176310/20208003. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b (^z.(z z)))) 3. ==[ beta ]==> ((b (^z.(z z)))((b (^z.(z z)))(^y.y))) 4. ==[ alpha ]==> ((b (^x.(x x)))((b (^y.(y y)))(^z.z))) REDUCED to normal form. ------ 176311/20208528. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.((^z.z) y))) 3. ==[ eta ]==> (((^x.(x x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.y)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 176312/20208591. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.c)) REDUCED to normal form. ------ 176313/20208717. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176314/20208753. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.x1)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176315/20208834. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.a)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176316/20208852. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.z)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 176317/20208864. ------ 1. ==[ start ]==> ((a a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> ((a a)((a a)(^y.y))) 4. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 176318/20208882. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (a (((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (a (((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 176319/20208909. ------ 1. ==[ start ]==> (((a a) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a) a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 176320/20208936. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 176321/20208963. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (b (b (^y.(^z.z)))) 6. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 176322/20208972. ------ 1. ==[ start ]==> (((a a)(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 176323/20208999. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 176324/20209017. ------ 1. ==[ start ]==> (((a a) b)((b a)(^a.b))) 2. ==[ alpha ]==> (((a a) b)((b a)(^x.b))) REDUCED to normal form. ------ 176325/20209044. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 176326/20209152. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176327/20209161. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 176328/20209188. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 176329/20209260. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((a a)((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a a)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 176330/20209287. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a (^y.y))) a)) REDUCED to normal form. ------ 176331/20209314. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 176332/20209341. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b (^z.z)) c)) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z)) c)) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) c)) REDUCED to normal form. ------ 176333/20209404. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 176334/20209683. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 176335/20209701. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 176336/20209818. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176337/20209845. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176338/20209899. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(a b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(a b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 7. ==[ beta ]==> (((a a)(^y.y))(a b)) 8. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 176339/20209953. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.y)((a b)((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 7. ==[ beta ]==> ((a b)((a a)(^y.y))) 8. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 176340/20209980. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(b a))) 5. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 176341/20210034. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 176342/20210133. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 176343/20210241. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.x)(a (a a)))) 3. ==[ beta ]==> ((a ((a a) a))(a (a a))) REDUCED to normal form. ------ 176344/20210367. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 176345/20210448. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a))(^x1.x1))) REDUCED to normal form. ------ 176346/20210556. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y) a)) 5. ==[ beta ]==> ((((a a) a)(^x.x)) a) REDUCED to normal form. ------ 176347/20210646. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(y y))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(x x))) REDUCED to normal form. ------ 176348/20210673. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 176349/20210754. ------ 1. ==[ start ]==> ((a (a b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 176350/20210925. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(b (b (^z.z)))) 3. ==[ beta ]==> (b (b (b (^z.z)))) 4. ==[ alpha ]==> (b (b (b (^x.x)))) REDUCED to normal form. ------ 176351/20210952. ------ 1. ==[ start ]==> (((^a.a)(a b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a b)(a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((a b)(a ((^x.(^y.y)) a))) 5. ==[ beta ]==> ((a b)(a (^y.y))) 6. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 176352/20210979. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((b (^z.z))(a a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(a a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(a a))) 5. ==[ beta ]==> ((b (^y.y))(a a)) 6. ==[ alpha ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 176353/20211015. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a)) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a)) c)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 176354/20211033. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(b ((^y.y) a))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(b ((^x.x) a))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(b a)) REDUCED to normal form. ------ 176355/20211114. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> (b (((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 176356/20211141. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((a (^x.(a a)))((a a)(a b))) REDUCED to normal form. ------ 176357/20211528. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(a a))(^y.b))) 3. ==[ beta ]==> (((a b) b)((a a)(^y.b))) 4. ==[ alpha ]==> (((a b) b)((a a)(^x.b))) REDUCED to normal form. ------ 176358/20211555. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a b)(^y.(a a)))) 3. ==[ beta ]==> (((a a) a)((a b)(^y.(a a)))) 4. ==[ alpha ]==> (((a a) a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 176359/20211582. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 176360/20211663. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 176361/20211744. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 176362/20211771. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a)) b)) REDUCED to normal form. ------ 176363/20211807. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.a)) 6. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 176364/20211834. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 176365/20211915. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(a a))(^z.b))) 5. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.b))) 6. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.b))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 176366/20211942. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.b)(^y.(a a)))) 5. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 176367/20211969. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 176368/20212023. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 176369/20212059. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(c ((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(c ((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)(c ((^y.y) b))) 5. ==[ beta ]==> (c ((^y.y) b)) 6. ==[ alpha ]==> (c ((^x.x) b)) 7. ==[ beta ]==> (c b) REDUCED to normal form. ------ 176370/20212194. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 176371/20212203. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.(^a.a))) d)) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z))) d)) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 176372/20212275. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)((a a) a))) REDUCED to normal form. ------ 176373/20212302. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a b)(a b))) 3. ==[ beta ]==> ((^y.y)((a b)(a b))) 4. ==[ alpha ]==> ((^x.x)((a b)(a b))) 5. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 176374/20212356. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> ((((a a) a)((a a) a))((a a)(^y.y))) 8. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)(^x.x))) REDUCED to normal form. ------ 176375/20212437. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (b ((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 176376/20212500. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(a a))(^z.z))) REDUCED to normal form. ------ 176377/20212536. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 176378/20212563. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 176379/20212644. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))((a a) a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((a a) a))) 7. ==[ beta ]==> ((^y.y)((^z.(a a))((a a) a))) 8. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a) a))) 9. ==[ beta ]==> ((^y.(a a))((a a) a)) 10. ==[ alpha ]==> ((^x.(a a))((a a) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176380/20212671. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.b)(a b))) 3. ==[ beta ]==> ((((a a) a)(a (a a))) b) REDUCED to normal form. ------ 176381/20212698. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 176382/20212725. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 176383/20212752. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((b a)(b a))) REDUCED to normal form. ------ 176384/20212779. ------ 1. ==[ start ]==> ((a (b a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 176385/20213139. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b)(a b))(c (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b)(a b))(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 176386/20213202. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 176387/20213220. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y) b)(a a))) 3. ==[ beta ]==> (b (((^y.y) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 176388/20213229. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y) b)) 3. ==[ beta ]==> (((a b)(^x.(x x))) b) REDUCED to normal form. ------ 176389/20213256. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1))) c)) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 176390/20213328. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 176391/20213508. ------ 1. ==[ start ]==> (((a b)(a (a a)))(b (^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 176392/20213562. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 176393/20213607. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176394/20213904. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 176395/20213931. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((b a) c)) REDUCED to normal form. ------ 176396/20214192. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(a ((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176397/20214201. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 176398/20214219. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 176399/20214507. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(a (^z.z))) REDUCED to normal form. ------ 176400/20214534. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 176401/20214822. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 176402/20214849. ------ 1. ==[ start ]==> ((((^a.a) b) a)((b a) b)) 2. ==[ alpha ]==> ((((^x.x) b) a)((b a) b)) 3. ==[ beta ]==> ((b a)((b a) b)) REDUCED to normal form. ------ 176403/20214876. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 176404/20215137. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((b a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176405/20215173. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 176406/20215344. ------ 1. ==[ start ]==> ((((a a) a)(a b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(c (^x.(^y.y)))) REDUCED to normal form. ------ 176407/20215398. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^y.y))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176408/20215479. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a a)) REDUCED to normal form. ------ 176409/20215506. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((b (a a))((^y.b)(a (a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.b)(a (a a)))) 5. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 176410/20215920. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(b ((a a)(^y.y)))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 176411/20215974. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a)(^y.y))(a a))) 3. ==[ beta ]==> (((b a)(b a))(((a a)(^y.y))(a a))) 4. ==[ alpha ]==> (((b a)(b a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 176412/20216055. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (b (((a a) a)(a (a a)))) REDUCED to normal form. ------ 176413/20216163. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a (^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176414/20216226. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 176415/20216262. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 176416/20216289. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 176417/20216343. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 176418/20216370. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((a a) a))) 7. ==[ beta ]==> (((a a)(^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 176419/20216397. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.a)(a b))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.a)(a b))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)(a b))) 5. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 176420/20216424. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 176421/20216451. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a)((a a) a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a a)((a a) a))((a a)(^x.x))) REDUCED to normal form. ------ 176422/20216532. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 176423/20216559. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 176424/20216586. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 176425/20216613. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((a (b (^x.x)))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 176426/20216703. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(a ((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(a ((a a)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((a a)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((a a)(^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176427/20216784. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (b (((a a) a)((^z.z) a))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x) a))) 5. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 176428/20216892. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176429/20216955. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(a a))(^y.y))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((a a)(^x.x))) REDUCED to normal form. ------ 176430/20217063. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 176431/20217171. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a a) a)) REDUCED to normal form. ------ 176432/20217198. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b) b)) 3. ==[ beta ]==> (((a a)(^y.b))((a b) b)) 4. ==[ alpha ]==> (((a a)(^x.b))((a b) b)) REDUCED to normal form. ------ 176433/20217558. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b (^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(b (^y.b))) 3. ==[ beta ]==> (((a b)(a a))(b (^y.b))) 4. ==[ alpha ]==> (((a b)(a a))(b (^x.b))) REDUCED to normal form. ------ 176434/20217585. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(a (^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(a (^x.(a a)))) REDUCED to normal form. ------ 176435/20217612. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 176436/20217666. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 176437/20217693. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> ((b a)((^y.(y y))(a (a a)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))(a (a a)))) 7. ==[ beta ]==> ((b a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 176438/20217720. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 176439/20217774. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.a)(a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.z)(a b))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a b))) 5. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 176440/20217945. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b ((a a) a))) 3. ==[ beta ]==> (b (b ((a a) a))) REDUCED to normal form. ------ 176441/20218053. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176442/20218170. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((a a) a)(^z.z))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(^y.y))) 5. ==[ beta ]==> (a (((a a) a)(^y.y))) 6. ==[ alpha ]==> (a (((a a) a)(^x.x))) REDUCED to normal form. ------ 176443/20218278. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 176444/20218359. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 176445/20218386. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (a a)) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (a a)) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a)) c)) REDUCED to normal form. ------ 176446/20218458. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(b ((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176447/20218494. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a) a)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a) a)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a) a)) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 176448/20218521. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 176449/20218593. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 176450/20218611. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 176451/20218638. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.a))) REDUCED to normal form. ------ 176452/20218665. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 176453/20218692. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> (((a (a a)) b)((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 176454/20218719. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.a)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 176455/20218746. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 176456/20218773. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 176457/20218800. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 176458/20218827. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 176459/20218881. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 176460/20218908. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 176461/20219016. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (^y.(y y)))) REDUCED to normal form. ------ 176462/20219025. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a a)(a (a a)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(a (a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 176463/20219412. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((a (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 176464/20219430. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b c)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b c)) 3. ==[ beta ]==> (((^z.z)(^y.y))(b c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b c)) 5. ==[ beta ]==> ((^y.y)(b c)) 6. ==[ alpha ]==> ((^x.x)(b c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 176465/20219439. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a)(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a)(^y.a))) REDUCED to normal form. ------ 176466/20219466. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a) a)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 176467/20219538. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a ((^y.y) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a ((^x.x) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 176468/20219574. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) b)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b)) 7. ==[ beta ]==> ((^y.(^z.z)) b) 8. ==[ alpha ]==> ((^x.(^y.y)) b) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176469/20219619. ------ 1. ==[ start ]==> (((^a.b)(b a))(c a)) 2. ==[ alpha ]==> (((^x.b)(b a))(c a)) 3. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 176470/20219682. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z)) a)) REDUCED to normal form. ------ 176471/20219727. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(a (a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176472/20219763. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 176473/20219790. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 176474/20219844. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176475/20219862. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a a)) 3. ==[ beta ]==> (((a a)(^y.y))(a a)) 4. ==[ alpha ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 176476/20219870. ------ 1. ==[ start ]==> (^a.((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (^x.((x (x (^y.y)))(^z.z))) REDUCED to normal form. ------ 176477/20219871. ------ 1. ==[ start ]==> (a ((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (a ((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 176478/20230875. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a)) b) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a)) b) 3. ==[ beta ]==> (((a a)(^y.y)) b) 4. ==[ alpha ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 176479/20230884. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a)) a) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 176480/20230890. ------ 1. ==[ start ]==> ((^a.a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 176481/20230899. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176482/20230917. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.(^z.z)) a)(^x1.(^y1.y1)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 7. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 8. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176483/20230944. ------ 1. ==[ start ]==> ((^a.b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.b)((b (^y.y))(^z.a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 176484/20231142. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.b)(b a))) 3. ==[ beta ]==> (^y.((^z.b)(b a))) 4. ==[ alpha ]==> (^x.((^y.b)(b a))) 5. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 176485/20231307. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (a (^y.(a (a (^z.z))))) 6. ==[ alpha ]==> (a (^x.(a (a (^y.y))))) REDUCED to normal form. ------ 176486/20232267. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((((^y.y) b)(^z.(z z)))(((^y.y) b)(^z.(z z))))(((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> (((((^x.x) b)(^y.(y y)))(((^z.z) b)(^x1.(x1 x1))))(((^y1.y1) b)(^z1.(z1 z1)))) 5. ==[ beta ]==> (((b (^y.(y y)))(((^z.z) b)(^x1.(x1 x1))))(((^y1.y1) b)(^z1.(z1 z1)))) 6. ==[ alpha ]==> (((b (^x.(x x)))(((^y.y) b)(^z.(z z))))(((^x1.x1) b)(^y1.(y1 y1)))) 7. ==[ beta ]==> (((b (^x.(x x)))(b (^z.(z z))))(((^x1.x1) b)(^y1.(y1 y1)))) 8. ==[ alpha ]==> (((b (^x.(x x)))(b (^y.(y y))))(((^z.z) b)(^x1.(x1 x1)))) 9. ==[ beta ]==> (((b (^x.(x x)))(b (^y.(y y))))(b (^x1.(x1 x1)))) 10. ==[ alpha ]==> (((b (^x.(x x)))(b (^y.(y y))))(b (^z.(z z)))) REDUCED to normal form. ------ 176487/20232990. ------ 1. ==[ start ]==> (((a a)(^a.b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 176488/20233764. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 176489/20234805. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> (b (((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 176490/20235231. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.((z z)(z z)))) REDUCED to normal form. ------ 176491/20235642. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((b a)(^x1.a))) 3. ==[ beta ]==> (((b a)(^x1.a))(^y.(^z.z))) 4. ==[ alpha ]==> (((b a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 176492/20236221. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176493/20236230. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^x1.b)) REDUCED to normal form. ------ 176494/20236527. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176495/20236560. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176496/20236842. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176497/20237559. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((((a a) a)(^y.(^z.z)))(((a a) a)(^y.(^z.z))))((((a a) a)(^y.(^z.z)))(((a a) a)(^y.(^z.z))))) 4. ==[ alpha ]==> (((((a a) a)(^x.(^y.y)))(((a a) a)(^z.(^x1.x1))))((((a a) a)(^y1.(^z1.z1)))(((a a) a)(^x2.(^y2.y2))))) REDUCED to normal form. ------ 176498/20237985. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(b y1))) 3. ==[ eta ]==> ((((^x.x) a)(^y.(^z.(^x1.x1)))) b) 4. ==[ beta ]==> ((a (^y.(^z.(^x1.x1)))) b) 5. ==[ alpha ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 176499/20238228. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 176500/20238732. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176501/20238957. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((b c)(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> ((b c)(^x.((^y.y)(a a)))) 5. ==[ beta ]==> ((b c)(^x.(a a))) REDUCED to normal form. ------ 176502/20239191. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 5. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 176503/20239800. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a a)(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a a)(^x1.b))) 3. ==[ eta ]==> ((^y.(^z.z))((a a)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176504/20240523. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((z z) z))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((z z) z))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((y y) y))) REDUCED to normal form. ------ 176505/20240802. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 176506/20241486. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^y.a)) REDUCED to normal form. ------ 176507/20241567. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.a))) REDUCED to normal form. ------ 176508/20241648. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.y))) 3. ==[ beta ]==> (b (^y.(^z.y))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 176509/20241711. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.c)) REDUCED to normal form. ------ 176510/20241756. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176511/20241792. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 176512/20241873. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(y1 y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(y1 y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176513/20241891. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176514/20241900. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 176515/20241912. ------ 1. ==[ start ]==> ((a a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 176516/20241921. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 176517/20241939. ------ 1. ==[ start ]==> ((a (a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 176518/20241966. ------ 1. ==[ start ]==> ((a b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a b)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 176519/20242020. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 176520/20242056. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176521/20242137. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176522/20242164. ------ 1. ==[ start ]==> ((a (^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.b)(b a))) 3. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 176523/20242182. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176524/20242209. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 176525/20242245. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.a)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 176526/20242272. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(b (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(b (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176527/20242326. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> (a ((^y.y)(a (a (^z.z))))) 6. ==[ alpha ]==> (a ((^x.x)(a (a (^y.y))))) 7. ==[ beta ]==> (a (a (a (^y.y)))) 8. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 176528/20242353. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 7. ==[ beta ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176529/20242542. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176530/20242650. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176531/20242776. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> (((a (^x.x)) a)(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.y))) REDUCED to normal form. ------ 176532/20242821. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((b b)((b (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((b b)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 176533/20242956. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a)) b)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 176534/20242983. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (a (((^y.y)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (a (((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (a ((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (a ((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 176535/20243010. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 176536/20243037. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a) a)(b a))) REDUCED to normal form. ------ 176537/20243064. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (^x.a))(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a (^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 176538/20243091. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 176539/20243118. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a)(a a)))) 7. ==[ beta ]==> (((^y.y) a)((a a)(a a))) 8. ==[ alpha ]==> (((^x.x) a)((a a)(a a))) 9. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 176540/20243208. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.x1))) 6. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.z))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 176541/20243235. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 176542/20243262. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))(^y.a))) 5. ==[ beta ]==> ((a a)(((a a)(a a))(^y.a))) 6. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 176543/20243289. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> ((a ((a a) a))(b (^y.(y y)))) 4. ==[ alpha ]==> ((a ((a a) a))(b (^x.(x x)))) REDUCED to normal form. ------ 176544/20243325. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176545/20243379. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(a b))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 176546/20243487. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176547/20243541. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)((a a)(a a)))) 7. ==[ beta ]==> ((a a)((^y.a)((a a)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.a)((a a)(a a)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 176548/20243640. ------ 1. ==[ start ]==> (((a a)((a a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a a)((a a) a))((b (^x.x)) b)) REDUCED to normal form. ------ 176549/20243811. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176550/20243892. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) IRREDUCIBLE: cycle. ------ 176551/20243955. ------ 1. ==[ start ]==> ((((a a) a) b)(c ((a a)(a a)))) REDUCED to normal form. ------ 176552/20243982. ------ 1. ==[ start ]==> (((a b) a)(b (b (^a.a)))) 2. ==[ alpha ]==> (((a b) a)(b (b (^x.x)))) REDUCED to normal form. ------ 176553/20244009. ------ 1. ==[ start ]==> (((a a)(^a.b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(^x.b))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.y))) REDUCED to normal form. ------ 176554/20244063. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 176555/20244090. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(b ((^y.y) a))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(b a)) REDUCED to normal form. ------ 176556/20244117. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176557/20244144. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((b a)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 176558/20244171. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 176559/20244360. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> (b ((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 176560/20244486. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((^y.y)((^z.z) a)) 8. ==[ alpha ]==> ((^x.x)((^y.y) a)) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 176561/20244567. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176562/20244621. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a a)((^y.b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.b)((^y.y)(a a)))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 176563/20244648. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.a)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.a)((a a)(^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176564/20244702. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.y)((^z.(z z))(a (^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.(^x1.x1))))) 11. ==[ beta ]==> ((^y.(y y))(a (^z.(^x1.x1)))) 12. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z)))) 13. ==[ beta ]==> ((a (^y.(^z.z)))(a (^y.(^z.z)))) 14. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 176565/20244783. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 176566/20244855. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) b) c)) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) b) c)) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b) c)) 5. ==[ beta ]==> (((a a)(a a))(b c)) REDUCED to normal form. ------ 176567/20245107. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176568/20245251. ------ 1. ==[ start ]==> (((a b) c)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y)))((^z.z) a))) 3. ==[ beta ]==> (((a b) c)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 176569/20245278. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((b a)(a (a a)))) 3. ==[ beta ]==> (((a a) b)((b a)(a (a a)))) REDUCED to normal form. ------ 176570/20245305. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 176571/20245359. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a b)(a b))) REDUCED to normal form. ------ 176572/20245386. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.b))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.b))(((a a) a)(a a))) REDUCED to normal form. ------ 176573/20245440. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (a a))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(b a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176574/20245467. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 176575/20245485. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(c (^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(c (^z.z))) 3. ==[ beta ]==> (b (c (^z.z))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 176576/20245494. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.a))((a (^y.y)) b)) REDUCED to normal form. ------ 176577/20245521. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 176578/20245584. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 176579/20245611. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 176580/20245638. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((b a)(^y.(y y)))) 3. ==[ beta ]==> ((a (a b))((b a)(^y.(y y)))) 4. ==[ alpha ]==> ((a (a b))((b a)(^x.(x x)))) REDUCED to normal form. ------ 176581/20245665. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 176582/20245719. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((a b)(^x.b))) REDUCED to normal form. ------ 176583/20245746. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a) a)(^y.(a a)))) 3. ==[ beta ]==> (((a b) a)(((a a) a)(^y.(a a)))) 4. ==[ alpha ]==> (((a b) a)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 176584/20245827. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 176585/20245917. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> (b ((^z.(a a))(^x1.x1))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176586/20246106. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((b a)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((b a)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 176587/20246133. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176588/20246187. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 176589/20246196. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 176590/20246250. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 176591/20246277. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(b (a a))) REDUCED to normal form. ------ 176592/20246304. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 176593/20246331. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a) a)) REDUCED to normal form. ------ 176594/20246610. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 176595/20246664. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((b a)(^z.a))) REDUCED to normal form. ------ 176596/20246754. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.b)((a a) a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.b)((a a) a))) 5. ==[ beta ]==> ((a a)((^z.b)((a a) a))) 6. ==[ alpha ]==> ((a a)((^x.b)((a a) a))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 176597/20246835. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (b (((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 176598/20246943. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176599/20246970. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 176600/20247051. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 176601/20247132. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176602/20247195. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(c (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(c (b a))) REDUCED to normal form. ------ 176603/20247240. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176604/20247249. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a b)) REDUCED to normal form. ------ 176605/20247285. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 176606/20247546. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176607/20247582. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 176608/20247591. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176609/20247753. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176610/20247861. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176611/20247996. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 176612/20248077. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (b ((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176613/20248086. ------ 1. ==[ start ]==> (((a b)(^c.a))(d ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(d ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(d (a a))) REDUCED to normal form. ------ 176614/20248113. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(c ((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(c ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c ((a a)(^z.z)))) REDUCED to normal form. ------ 176615/20248140. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(b (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(b (b a))) REDUCED to normal form. ------ 176616/20248194. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((b a)(a a))) REDUCED to normal form. ------ 176617/20248221. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 176618/20248473. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((b a)(^y.y))) REDUCED to normal form. ------ 176619/20248527. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^x1.a))) REDUCED to normal form. ------ 176620/20248554. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a b)(^y.(y y)))) 3. ==[ beta ]==> ((b (a a))((a b)(^y.(y y)))) 4. ==[ alpha ]==> ((b (a a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 176621/20248581. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 176622/20248617. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176623/20248860. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176624/20248941. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 176625/20248968. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176626/20248977. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b ((a a)(^z.z)))) REDUCED to normal form. ------ 176627/20249004. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(a (b a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a (b a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (b a))) REDUCED to normal form. ------ 176628/20249085. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a b) a)) REDUCED to normal form. ------ 176629/20249112. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 176630/20249166. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (a a))((a a) a))) REDUCED to normal form. ------ 176631/20249220. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 176632/20249247. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 176633/20249310. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 176634/20249337. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a b)(^z.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a b)(^y.a))) REDUCED to normal form. ------ 176635/20249364. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 176636/20249391. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(b a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(b a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.y))) REDUCED to normal form. ------ 176637/20249445. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) a)(^y.b))) 5. ==[ beta ]==> ((((a a) a)(a a))(a (^y.b))) 6. ==[ alpha ]==> ((((a a) a)(a a))(a (^x.b))) REDUCED to normal form. ------ 176638/20249472. ------ 1. ==[ start ]==> (((a b)(a b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 176639/20249526. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 176640/20249580. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a b) c)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b) c)) REDUCED to normal form. ------ 176641/20249976. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((b c)((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((b c)((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((b c)((a a)(a a))) REDUCED to normal form. ------ 176642/20250048. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 176643/20250129. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^z1.z1)(^x2.x2))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)((^x2.x2)(^y2.y2)))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)((^z1.z1)(^x2.x2)))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(^x2.x2))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 11. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 12. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 176644/20250210. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (b ((^y.y)(a a))) 6. ==[ alpha ]==> (b ((^x.x)(a a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176645/20250318. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176646/20250444. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 176647/20250471. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b) b)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 176648/20250498. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a) c)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a) c)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a) c)) 5. ==[ beta ]==> ((a b)((^y.a) c)) 6. ==[ alpha ]==> ((a b)((^x.a) c)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 176649/20250660. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a b)(^y.y))) REDUCED to normal form. ------ 176650/20250714. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.a)) REDUCED to normal form. ------ 176651/20250741. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (a a))(^y.(y y)))) 5. ==[ beta ]==> ((b a)((a (a a))(^y.(y y)))) 6. ==[ alpha ]==> ((b a)((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 176652/20250768. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 176653/20250822. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a a)(^a.b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a a)(^z.b))) 3. ==[ beta ]==> ((a (^y.y))((a a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 176654/20250912. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176655/20250993. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176656/20251263. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176657/20251317. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(a (a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(a (a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(a (a a)))) 7. ==[ beta ]==> ((b b)((^y.a)(a (a a)))) 8. ==[ alpha ]==> ((b b)((^x.a)(a (a a)))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 176658/20251398. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176659/20251506. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176660/20251515. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.y1))) REDUCED to normal form. ------ 176661/20251542. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a ((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(a ((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a ((a a) a))) REDUCED to normal form. ------ 176662/20251569. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(a a)) REDUCED to normal form. ------ 176663/20251623. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> (((^y.y) a)((^z.z) a)) 8. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176664/20251713. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 8. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 176665/20251740. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 176666/20251767. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(^y1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 176667/20251794. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 176668/20251821. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 176669/20251848. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z)) a)) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y)) a)) 7. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 8. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 176670/20251875. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (a a)) b)) REDUCED to normal form. ------ 176671/20251983. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y)) a)) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 176672/20252037. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a) c)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a) c)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a) c)) 5. ==[ beta ]==> ((a a)((^y.a) c)) 6. ==[ alpha ]==> ((a a)((^x.a) c)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 176673/20252055. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 176674/20252073. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.(z z)))) 5. ==[ beta ]==> ((b (^z.(z z)))(^y.y)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 176675/20252460. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c b)) 3. ==[ beta ]==> (((^y.y) b)(c b)) 4. ==[ alpha ]==> (((^x.x) b)(c b)) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 176676/20252478. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176677/20252487. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b c)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b c)) REDUCED to normal form. ------ 176678/20252505. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z) a)) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) a)) 7. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 176679/20252532. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176680/20252586. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(^y.a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.a)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.a)) REDUCED to normal form. ------ 176681/20252622. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(a a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a))) 7. ==[ beta ]==> ((a (^y.y))(a a)) 8. ==[ alpha ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 176682/20252649. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 176683/20252667. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(a (^y.a))) 3. ==[ beta ]==> (b (a (^y.a))) 4. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 176684/20252730. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a c)) REDUCED to normal form. ------ 176685/20252775. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176686/20252811. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 176687/20252838. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b a)) REDUCED to normal form. ------ 176688/20252892. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a a))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176689/20252910. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (^z.z))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 176690/20252919. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a a)) REDUCED to normal form. ------ 176691/20263941. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a)) b) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y)) b) REDUCED to normal form. ------ 176692/20263965. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176693/20264046. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176694/20264382. ------ 1. ==[ start ]==> (((a a)(^b.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 176695/20264451. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b (^z.z)) c)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 176696/20264823. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 176697/20264901. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176698/20265651. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176699/20265666. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 176700/20266440. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(b (^z.z)))((a a)(b (^z.z))))) 4. ==[ alpha ]==> ((^x.x)(((a a)(b (^y.y)))((a a)(b (^z.z))))) 5. ==[ beta ]==> (((a a)(b (^y.y)))((a a)(b (^z.z)))) 6. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 176701/20266830. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176702/20266839. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 176703/20268297. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 176704/20269296. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 176705/20269311. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.b) a)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176706/20269917. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 176707/20272023. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(a a)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(a a)))) REDUCED to normal form. ------ 176708/20272050. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176709/20272257. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 176710/20272266. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 176711/20272491. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 176712/20272680. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(a b))) 3. ==[ beta ]==> (((a a)(a b))(^y.(a b))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(a b))) REDUCED to normal form. ------ 176713/20273265. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(^x1.b))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.b))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.b))) 5. ==[ beta ]==> (a (^y.(^z.b))) 6. ==[ alpha ]==> (a (^x.(^y.b))) REDUCED to normal form. ------ 176714/20273589. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.a))) REDUCED to normal form. ------ 176715/20273733. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 176716/20274030. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^x.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 176717/20274108. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^z.z))((^x1.x1) a))(((a (^z.z))((^x1.x1) a))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a (^z.z))((^x1.x1) a))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x)) a)(((a (^z.z))((^x1.x1) a))(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x)) a)(((a (^y.y))((^z.z) a))(^x1.x1))) 7. ==[ beta ]==> (((a (^x.x)) a)(((a (^y.y)) a)(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) a)(((a (^y.y)) a)(^z.z))) REDUCED to normal form. ------ 176718/20274561. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^z.a)) REDUCED to normal form. ------ 176719/20274714. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.c)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.c)) 3. ==[ beta ]==> (b (^y.c)) 4. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 176720/20274777. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 176721/20274885. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 176722/20274939. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176723/20274957. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.a)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 176724/20274966. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 176725/20274980. ------ 1. ==[ start ]==> (^a.(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 176726/20274981. ------ 1. ==[ start ]==> (a (^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176727/20274996. ------ 1. ==[ start ]==> ((a (^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 176728/20275005. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (a ((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> (a ((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> (a ((a a)(^y.y))) 6. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 176729/20275023. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176730/20275050. ------ 1. ==[ start ]==> (((^a.a)(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((a a)((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((a a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 176731/20275077. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(^z.(z z)))) REDUCED to normal form. ------ 176732/20275086. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (b ((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176733/20275113. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176734/20275140. ------ 1. ==[ start ]==> (((a a) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 176735/20275158. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 176736/20275185. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 176737/20275221. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 176738/20275275. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.a)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(a (^y.(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 176739/20275320. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((^y.a)((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((^x.a)((a (a a))(^y.(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 176740/20275356. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 176741/20275383. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 176742/20275401. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> (a ((a a)(^y.(y (^z.z))))) 6. ==[ alpha ]==> (a ((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 176743/20275410. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a a)(^x.a))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.a))(a (a (^y.y)))) REDUCED to normal form. ------ 176744/20275428. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 5. ==[ beta ]==> ((a (a (^y.y))) a) 6. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 176745/20275437. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^z1.z1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 176746/20275482. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y)) c)) REDUCED to normal form. ------ 176747/20275653. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 176748/20275734. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 176749/20275824. ------ 1. ==[ start ]==> (((a a)(a (a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a (a a)))(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(b (^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 176750/20275851. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(a (a (a (^z.z))))) 3. ==[ beta ]==> (((a (^x.x)) a)(a (a (a (^z.z))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a (a (a (^y.y))))) REDUCED to normal form. ------ 176751/20275878. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a a))) 7. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 176752/20275905. ------ 1. ==[ start ]==> (((a (a a))(a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 176753/20275932. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))(((a a)(a a)) a)) REDUCED to normal form. ------ 176754/20275941. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a)) d)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a)) d)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) d)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176755/20276229. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 176756/20276256. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)(^y.y))) REDUCED to normal form. ------ 176757/20276400. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 176758/20276454. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> (a (((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 176759/20276490. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176760/20276517. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 176761/20276562. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 9. ==[ beta ]==> (^y.(^z.(^x1.x1))) 10. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176762/20276571. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 176763/20276598. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(x x)))(((^z.z) b)((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.(x x)))(b ((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.(x x)))(b ((^y.y) b))) 9. ==[ beta ]==> ((a (^x.(x x)))(b b)) REDUCED to normal form. ------ 176764/20276625. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 176765/20276652. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(b (^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176766/20276679. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 176767/20276697. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a (^x.b))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((a (^x.b))((^z.z) a)) 4. ==[ alpha ]==> ((a (^x.b))((^y.y) a)) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 176768/20276868. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176769/20277030. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 176770/20277282. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a))(a b))) 3. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 176771/20277309. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a b)(a a))) REDUCED to normal form. ------ 176772/20277336. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(((a a) a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 176773/20277363. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(b a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(b a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(b a)) REDUCED to normal form. ------ 176774/20277390. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a a))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((^y.y) a)((a (a a))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((^x.x) a)((a (a a))(a (^y.(^z.z))))) 7. ==[ beta ]==> (a ((a (a a))(a (^y.(^z.z))))) 8. ==[ alpha ]==> (a ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 176775/20277417. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a ((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a b)) REDUCED to normal form. ------ 176776/20277435. ------ 1. ==[ start ]==> (((^a.b) b)(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(c (^y.(a a)))) 3. ==[ beta ]==> (b (c (^y.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 176777/20277444. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 176778/20277471. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a a)(b (^y.y)))) 3. ==[ beta ]==> ((a (a a))((a a)(b (^y.y)))) 4. ==[ alpha ]==> ((a (a a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 176779/20277507. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 176780/20277561. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.a))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.a))) 7. ==[ beta ]==> (((^y.y) b)(^z.a)) 8. ==[ alpha ]==> (((^x.x) b)(^y.a)) 9. ==[ beta ]==> (b (^y.a)) 10. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 176781/20277642. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 176782/20277651. ------ 1. ==[ start ]==> (((a b) b)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 176783/20277678. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))(a b))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))(a b))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 176784/20277696. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a b)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a a)((a b)(^y.(a a)))) 6. ==[ alpha ]==> ((a a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 176785/20277705. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 176786/20277723. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 176787/20277732. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 176788/20277777. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (a a))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (a a))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.(^x1.x1))))) 11. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 12. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176789/20277786. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 176790/20277813. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(y y))((^z.a)((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.(x x))((^y.a)((^z.z) b))) 7. ==[ beta ]==> (((^y.a)((^z.z) b))((^y.a)((^z.z) b))) 8. ==[ alpha ]==> (((^x.a)((^y.y) b))((^z.a)((^x1.x1) b))) 9. ==[ beta ]==> (a ((^z.a)((^x1.x1) b))) 10. ==[ alpha ]==> (a ((^x.a)((^y.y) b))) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176791/20277840. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 176792/20277867. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 176793/20278083. ------ 1. ==[ start ]==> (((^a.b) c)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176794/20278317. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z) c)) 3. ==[ beta ]==> (b ((^z.z) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 176795/20278569. ------ 1. ==[ start ]==> (((a b)(^b.a))(c (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(c (^y.y))) REDUCED to normal form. ------ 176796/20278596. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b (^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(a a)))) REDUCED to normal form. ------ 176797/20278992. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(a a)) a)) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(a a)) a)) 5. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 176798/20279136. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 176799/20279271. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 176800/20279325. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 176801/20279343. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(a a)) a)) 3. ==[ beta ]==> (b ((^y.(a a)) a)) 4. ==[ alpha ]==> (b ((^x.(a a)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 176802/20279469. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(b a))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(b a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a a)(b a))((a a)(^x.x))) REDUCED to normal form. ------ 176803/20279496. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a b)((a a) a))) REDUCED to normal form. ------ 176804/20279523. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((a a) a)(a b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a) a)(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a) a)(a b))) 5. ==[ beta ]==> ((a (a a))(((a a) a)(a b))) REDUCED to normal form. ------ 176805/20279550. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a b))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a b))((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))(a b))((^y.y)(a a))) 6. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(a a))) 7. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 176806/20279577. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (a a))((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)((a (a a))((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a) a)((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 176807/20279604. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z) a)(b a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) a)(b a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a (b a))) REDUCED to normal form. ------ 176808/20279631. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 176809/20279658. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a a)((^z.z) b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a a)((^z.z) b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a a)((^y.y) b))) 5. ==[ beta ]==> (((a a) a)((a a)((^y.y) b))) 6. ==[ alpha ]==> (((a a) a)((a a)((^x.x) b))) 7. ==[ beta ]==> (((a a) a)((a a) b)) REDUCED to normal form. ------ 176810/20279730. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176811/20279748. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((b a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((b a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)(^x1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176812/20279829. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a b)(^z.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a b)(^z.a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a b)(^z.a))) 5. ==[ beta ]==> ((a a)((a b)(^z.a))) 6. ==[ alpha ]==> ((a a)((a b)(^x.a))) REDUCED to normal form. ------ 176813/20279910. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 176814/20280018. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1) b) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176815/20280027. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 176816/20280045. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 176817/20280054. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 176818/20280072. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((b a) c)) 3. ==[ beta ]==> ((^y.y)((b a) c)) 4. ==[ alpha ]==> ((^x.x)((b a) c)) 5. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 176819/20280135. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 176820/20280162. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((^y.b)((^z.b)(^x1.a))) 6. ==[ alpha ]==> ((^x.b)((^y.b)(^z.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 176821/20280216. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176822/20280324. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 176823/20280342. ------ 1. ==[ start ]==> ((a (^b.b))((^b.b) a)) 2. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 176824/20280360. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 176825/20280387. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((b a)(a (^y.y)))) REDUCED to normal form. ------ 176826/20280414. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 176827/20280441. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> (((a (a a))(a a))((a a)(a (a a)))) REDUCED to normal form. ------ 176828/20280468. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((a b)((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a b)((a b)((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a b)((a b)(^y.y))) 8. ==[ alpha ]==> ((a b)((a b)(^x.x))) REDUCED to normal form. ------ 176829/20280495. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 176830/20280522. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.z)(a b))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(a b))) 7. ==[ beta ]==> (((a b)(^x.x))(a b)) REDUCED to normal form. ------ 176831/20280549. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (a a))((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))((a (a a))(a a))) REDUCED to normal form. ------ 176832/20280576. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a ((a a)(^z.z)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(a ((a a)(^y.y)))) REDUCED to normal form. ------ 176833/20280621. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176834/20280630. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 176835/20280666. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 176836/20280693. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((b a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((b a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 176837/20280828. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> (b ((^y.y)(^z.b))) 6. ==[ alpha ]==> (b ((^x.x)(^y.b))) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 176838/20280936. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176839/20280945. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 176840/20280972. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 176841/20280990. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((b a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((b a) b)) 3. ==[ beta ]==> (((^y.y) b)((b a) b)) 4. ==[ alpha ]==> (((^x.x) b)((b a) b)) 5. ==[ beta ]==> (b ((b a) b)) REDUCED to normal form. ------ 176842/20281107. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176843/20281134. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 176844/20281161. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 176845/20281188. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 176846/20281260. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.(^x2.x2))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176847/20281332. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a) b)((a a)((^y.y) a))) 6. ==[ alpha ]==> (((a a) b)((a a)((^x.x) a))) 7. ==[ beta ]==> (((a a) b)((a a) a)) REDUCED to normal form. ------ 176848/20281359. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a b)(a (a a)))) REDUCED to normal form. ------ 176849/20281386. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (b a))(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a (b a))(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a (b a))(((a a) a)(^y.y))) 6. ==[ alpha ]==> ((a (b a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 176850/20281413. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.y)((a a) a))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 176851/20281440. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (a a))(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (a a))(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (a a))(a b))) 5. ==[ beta ]==> (((^y.y)(a a))((a (a a))(a b))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(a b))) 7. ==[ beta ]==> ((a a)((a (a a))(a b))) REDUCED to normal form. ------ 176852/20281467. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a b))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a b))(a ((^x.x)(a a)))) 5. ==[ beta ]==> ((((a a) a)(a b))(a (a a))) REDUCED to normal form. ------ 176853/20281494. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 176854/20281521. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a a)(b a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a a)(b a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a a)(b a))) 5. ==[ beta ]==> (((a a)(^y.y))((a a)(b a))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(b a))) REDUCED to normal form. ------ 176855/20281692. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 7. ==[ beta ]==> ((^y.y)(^z.a)) 8. ==[ alpha ]==> ((^x.x)(^y.a)) 9. ==[ beta ]==> (^y.a) 10. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 176856/20281827. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((b a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((b a) a)) 3. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 176857/20281971. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 176858/20281998. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(^y.b))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.b)(^y.b))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b)(^y.b))) 5. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 176859/20282052. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 176860/20282295. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(c (^x1.(a a)))) REDUCED to normal form. ------ 176861/20282322. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 176862/20282907. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.b) c)) 3. ==[ beta ]==> (b ((^z.b) c)) 4. ==[ alpha ]==> (b ((^x.b) c)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 176863/20283051. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(b (^y.(a a)))) 3. ==[ beta ]==> ((b c)(b (^y.(a a)))) 4. ==[ alpha ]==> ((b c)(b (^x.(a a)))) REDUCED to normal form. ------ 176864/20283078. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 176865/20283123. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 176866/20283150. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.a))) 5. ==[ beta ]==> (((a a) a)(^y.a)) 6. ==[ alpha ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 176867/20283186. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 176868/20283204. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (a a))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 176869/20283213. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(((^y1.y1)(^z1.z1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 10. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 176870/20283285. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a a)(^z.(a a)))) 3. ==[ beta ]==> (b ((a a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 176871/20283294. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(a a))) 5. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 176872/20283321. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(^z.z))) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 176873/20283402. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 176874/20283429. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.a))(^z.z)) 8. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 176875/20283456. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 176876/20283519. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a (a a))) REDUCED to normal form. ------ 176877/20283546. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a b)(a a))) REDUCED to normal form. ------ 176878/20283573. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)(a (^y.y)))) 5. ==[ beta ]==> ((a b)(((a a) a)(a (^y.y)))) 6. ==[ alpha ]==> ((a b)(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 176879/20283600. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1) a)) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z) a)) 7. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 176880/20283627. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((b a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 176881/20283654. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 176882/20283681. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a (^y.y))((a a) a))) 3. ==[ beta ]==> (((a b)(a a))((a (^y.y))((a a) a))) 4. ==[ alpha ]==> (((a b)(a a))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 176883/20283708. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a a)(a b))) 3. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 176884/20283987. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) c)) 7. ==[ beta ]==> (((^y.y)(^z.z)) c) 8. ==[ alpha ]==> (((^x.x)(^y.y)) c) 9. ==[ beta ]==> ((^y.y) c) 10. ==[ alpha ]==> ((^x.x) c) 11. ==[ beta ]==> c REDUCED to normal form. ------ 176885/20284176. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176886/20284293. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(a (^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(a (^z.b))) 3. ==[ beta ]==> (((^y.y) a)(a (^z.b))) 4. ==[ alpha ]==> (((^x.x) a)(a (^y.b))) 5. ==[ beta ]==> (a (a (^y.b))) 6. ==[ alpha ]==> (a (a (^x.b))) REDUCED to normal form. ------ 176887/20284311. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((a a) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a) a)(^z.z))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.z))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 176888/20284338. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176889/20284392. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)(^z.(z z)))) 7. ==[ beta ]==> ((b b)(((^y.y) a)(^z.(z z)))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)(^y.(y y)))) 9. ==[ beta ]==> ((b b)(a (^y.(y y)))) 10. ==[ alpha ]==> ((b b)(a (^x.(x x)))) REDUCED to normal form. ------ 176890/20284401. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 176891/20284428. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176892/20284473. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((a a) a) a)) 3. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 176893/20284482. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 176894/20284509. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 176895/20284536. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 176896/20284590. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 176897/20284617. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.a)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.a)) REDUCED to normal form. ------ 176898/20284734. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 176899/20284761. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 176900/20284869. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c d)) REDUCED to normal form. ------ 176901/20285031. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b (a (a a)))) 3. ==[ beta ]==> ((b (a (a a)))(b (a (a a)))) REDUCED to normal form. ------ 176902/20285058. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(a ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a (^y.y))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.x))) REDUCED to normal form. ------ 176903/20285112. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(a (^z.z)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(a (^y.y)))) 7. ==[ beta ]==> ((a a)(a (a (^y.y)))) 8. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 176904/20285139. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a (^y.y)) a)) REDUCED to normal form. ------ 176905/20285535. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a)(a a))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(a a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(a a))) 5. ==[ beta ]==> (b ((^y.a)(a a))) 6. ==[ alpha ]==> (b ((^x.a)(a a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 176906/20285553. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 176907/20285562. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 176908/20285580. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a a)(^z.a))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)(^z.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 176909/20285589. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((^x1.x1) a)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z) a)) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 176910/20285607. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1) a) a)) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a)) 5. ==[ beta ]==> (((^y.y) a) a) 6. ==[ alpha ]==> (((^x.x) a) a) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176911/20285697. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c (^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(c (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.z))) 5. ==[ beta ]==> ((^y.y)(c (^z.z))) 6. ==[ alpha ]==> ((^x.x)(c (^y.y))) 7. ==[ beta ]==> (c (^y.y)) 8. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 176912/20285724. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 176913/20285742. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a) c)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y) c)) 3. ==[ beta ]==> (b ((^y.y) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 176914/20285805. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.z))) REDUCED to normal form. ------ 176915/20285850. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176916/20285886. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 176917/20285913. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 176918/20285967. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176919/20285985. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 176920/20285994. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 176921/20286009. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a)))) a) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1)))) a) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176922/20286011. ------ 1. ==[ start ]==> (^a.(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(x (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176923/20286012. ------ 1. ==[ start ]==> (a (a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (a (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 176924/20286015. ------ 1. ==[ start ]==> ((^a.a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 176925/20291370. ------ 1. ==[ start ]==> ((^a.(^b.b))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176926/20291685. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^a.(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176927/20297040. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176928/20297043. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a)))) a) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 176929/20297049. ------ 1. ==[ start ]==> ((^a.a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176930/20297052. ------ 1. ==[ start ]==> ((a a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 176931/20297076. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((^y.(y (^z.z)))(a a))((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(z (^x1.x1)))(a a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z (^x1.x1)))(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z)))(a a))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 176932/20297184. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)((^x1.x1)(^y1.y1)))(^y.y)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176933/20297373. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176934/20297475. ------ 1. ==[ start ]==> (((a a)(^b.a))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 176935/20297868. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(c (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(c (b (^x1.x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176936/20297916. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 176937/20298348. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 176938/20298939. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.b)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.b)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 176939/20299167. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.(^y.y))((a a) a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 176940/20299326. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (^y.((((a a)(^z.z))((a a) a))(((a a)(^z.z))((a a) a)))) 4. ==[ alpha ]==> (^x.((((a a)(^y.y))((a a) a))(((a a)(^z.z))((a a) a)))) REDUCED to normal form. ------ 176941/20299545. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))(^y.(b (^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 176942/20299932. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 176943/20300964. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(y y))(b a))) 3. ==[ eta ]==> (b ((^y.(y y))(b a))) 4. ==[ alpha ]==> (b ((^x.(x x))(b a))) 5. ==[ beta ]==> (b ((b a)(b a))) REDUCED to normal form. ------ 176944/20301408. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.((y y)(y y)))) 3. ==[ beta ]==> (b (^y.((y y)(y y)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 176945/20301513. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176946/20301801. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176947/20302404. ------ 1. ==[ start ]==> ((^a.(^b.b))(a ((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176948/20302407. ------ 1. ==[ start ]==> ((a (^b.b))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) b))) 3. ==[ beta ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 176949/20302719. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(a (^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(a (^z.z))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 176950/20302722. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^a.(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.z))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 176951/20303010. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 176952/20303325. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(y1 (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(y1 (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176953/20303613. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 176954/20303718. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((((^y.b)(a (a a)))((^y.b)(a (a a))))(((^y.b)(a (a a)))((^y.b)(a (a a))))) 4. ==[ alpha ]==> ((((^x.b)(a (a a)))((^y.b)(a (a a))))(((^z.b)(a (a a)))((^x1.b)(a (a a))))) 5. ==[ beta ]==> ((b ((^y.b)(a (a a))))(((^z.b)(a (a a)))((^x1.b)(a (a a))))) 6. ==[ alpha ]==> ((b ((^x.b)(a (a a))))(((^y.b)(a (a a)))((^z.b)(a (a a))))) 7. ==[ beta ]==> ((b b)(((^y.b)(a (a a)))((^z.b)(a (a a))))) 8. ==[ alpha ]==> ((b b)(((^x.b)(a (a a)))((^y.b)(a (a a))))) 9. ==[ beta ]==> ((b b)(b ((^y.b)(a (a a))))) 10. ==[ alpha ]==> ((b b)(b ((^x.b)(a (a a))))) 11. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 176955/20304162. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(b y))) 3. ==[ eta ]==> (((^x.(x x))(b a)) b) 4. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 176956/20304666. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 176957/20304798. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 176958/20305359. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 176959/20305584. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 176960/20305800. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.(y y)))) REDUCED to normal form. ------ 176961/20305959. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))((a a) a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176962/20306778. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 176963/20306988. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))(^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(^x.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 176964/20307123. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176965/20307807. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(a (^z.z)))) 3. ==[ beta ]==> (b (^y.(a (^z.z)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 176966/20307870. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 176967/20307978. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 176968/20308050. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(z z))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 176969/20308059. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.a)) REDUCED to normal form. ------ 176970/20308074. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 176971/20308077. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 176972/20308089. ------ 1. ==[ start ]==> ((a a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 176973/20308107. ------ 1. ==[ start ]==> (((^a.a) a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> (a ((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> (a ((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 176974/20308116. ------ 1. ==[ start ]==> ((a (a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> ((a (a a))((a a)(^y.y))) 4. ==[ alpha ]==> ((a (a a))((a a)(^x.x))) REDUCED to normal form. ------ 176975/20308134. ------ 1. ==[ start ]==> (((a a) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 176976/20308161. ------ 1. ==[ start ]==> (((a a)(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 176977/20308188. ------ 1. ==[ start ]==> (((^a.a) b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x) b)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> (b (((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 176978/20308215. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 176979/20308224. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 176980/20308242. ------ 1. ==[ start ]==> (((a a) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 176981/20308269. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b a)(^y.b))) REDUCED to normal form. ------ 176982/20308296. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 176983/20308359. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(b a))) 3. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 176984/20308377. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 176985/20308413. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 176986/20308512. ------ 1. ==[ start ]==> (((a a)(^b.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 176987/20308539. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a (^x1.x1))) a)) REDUCED to normal form. ------ 176988/20308566. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> ((a (^x.x))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 176989/20308656. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 176990/20308908. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(c (b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(c (b (^z.z)))) REDUCED to normal form. ------ 176991/20308953. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(y (^z.z)))) REDUCED to normal form. ------ 176992/20309043. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 176993/20309070. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (((^y.y) b)(a (a a))) 6. ==[ alpha ]==> (((^x.x) b)(a (a a))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 176994/20309124. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)((a a) a))) 5. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 7. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 176995/20309178. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 176996/20309205. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)((a a)(^y.y))) 6. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 176997/20309259. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 176998/20309385. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(y (^z.z))))) 6. ==[ alpha ]==> ((a a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 176999/20309592. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> (b (((^y.y)(a a))(^z.(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(a a)))) 7. ==[ beta ]==> (b ((a a)(^y.(a a)))) 8. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 177000/20309619. ------ 1. ==[ start ]==> ((((a a) a) a)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 177001/20309673. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 177002/20309700. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (a a))(^z.z))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 177003/20309727. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(a (^y.(a a)))) REDUCED to normal form. ------ 177004/20309898. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.(y y))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(x x))) REDUCED to normal form. ------ 177005/20309925. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177006/20309979. ------ 1. ==[ start ]==> ((a (a b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 177007/20310150. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(c ((a a)(a a)))) 3. ==[ beta ]==> (b (c ((a a)(a a)))) REDUCED to normal form. ------ 177008/20310177. ------ 1. ==[ start ]==> (((^a.a)(a b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(b (b (^y.y)))) 3. ==[ beta ]==> ((a b)(b (b (^y.y)))) 4. ==[ alpha ]==> ((a b)(b (b (^x.x)))) REDUCED to normal form. ------ 177009/20310204. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.y)(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> (a ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (a ((^x.(^y.y)) a)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177010/20310258. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 177011/20310339. ------ 1. ==[ start ]==> (((^a.b)(a a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (b ((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (b ((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((b a)(^y.y))) 6. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 177012/20310366. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 177013/20310546. ------ 1. ==[ start ]==> (((a b)(a a))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(c (^x.(a a)))) REDUCED to normal form. ------ 177014/20310582. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((^y.(a a))((a a)(b (^z.z)))) 4. ==[ alpha ]==> ((^x.(a a))((a a)(b (^y.y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177015/20310753. ------ 1. ==[ start ]==> (((a b) b)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b) b)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 177016/20310780. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.b))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.b))) REDUCED to normal form. ------ 177017/20310807. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 177018/20310834. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 177019/20310888. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 177020/20310915. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(^z.z))) 7. ==[ beta ]==> ((((^y.y) a)(^z.z))(((^y.y) a)(^z.z))) 8. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.x1))) 9. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.x1))) 10. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z))) 11. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 12. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 177021/20310942. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 177022/20310996. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((b (^z.z)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 177023/20311059. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.a)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 177024/20311086. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 177025/20311167. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(a a))(^z.b))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))(^y.b))) 5. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 177026/20311194. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) b) REDUCED to normal form. ------ 177027/20311419. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (b (((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (b (b (a (^y.y)))) 6. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 177028/20311428. ------ 1. ==[ start ]==> (((a b) c)((^b.b) c)) 2. ==[ alpha ]==> (((a b) c)((^x.x) c)) 3. ==[ beta ]==> (((a b) c) c) REDUCED to normal form. ------ 177029/20311500. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(((a a)(^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 177030/20311527. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y)(a a))((a a) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((a a) a)) 7. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 177031/20311581. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)(a a))) REDUCED to normal form. ------ 177032/20311662. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (a (^y.(^z.z))))) 6. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 177033/20311788. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 177034/20311815. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 177035/20311896. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(a a)) REDUCED to normal form. ------ 177036/20311923. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.b)(a b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.b)(a b))) 3. ==[ beta ]==> (((a b) a)((^y.b)(a b))) 4. ==[ alpha ]==> (((a b) a)((^x.b)(a b))) 5. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 177037/20311977. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 177038/20312004. ------ 1. ==[ start ]==> ((a (b a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((a (b a))((^x.(x x))(b a))) 3. ==[ beta ]==> ((a (b a))((b a)(b a))) REDUCED to normal form. ------ 177039/20312445. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(a ((a a)(a a)))) 3. ==[ beta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 177040/20312454. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 177041/20312481. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z) b)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 177042/20312553. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))(a (a a)))) REDUCED to normal form. ------ 177043/20312733. ------ 1. ==[ start ]==> (((a b)(a (a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177044/20312760. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(b (^z.z))) 3. ==[ beta ]==> (((a a)((^y.y) a))(b (^z.z))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(b (^y.y))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 177045/20312832. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177046/20312841. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 177047/20313129. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b a)) REDUCED to normal form. ------ 177048/20313156. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.(^y1.y1))) b)) REDUCED to normal form. ------ 177049/20313417. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(b (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177050/20313444. ------ 1. ==[ start ]==> ((a (^b.b))(a ((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) b))) 3. ==[ beta ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 177051/20313732. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 177052/20313759. ------ 1. ==[ start ]==> ((a ((^a.a) b))(a (^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(a (^y.y))) 3. ==[ beta ]==> ((a b)(a (^y.y))) 4. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 177053/20314047. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 177054/20314074. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (^y.(^z.z))) a)) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z))) a)) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 177055/20314101. ------ 1. ==[ start ]==> (((a a)(^b.b))((b a) b)) 2. ==[ alpha ]==> (((a a)(^x.x))((b a) b)) REDUCED to normal form. ------ 177056/20314362. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(a (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177057/20314371. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2))) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 177058/20314596. ------ 1. ==[ start ]==> (((a b)((a a) a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 177059/20314650. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177060/20314731. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((b (a a))((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((b (a a))((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((b (a a))(a a)) REDUCED to normal form. ------ 177061/20314758. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.b)(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 177062/20315145. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(c ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(c ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(c ((^y.y)(a a)))) 5. ==[ beta ]==> (c ((^y.y)(a a))) 6. ==[ alpha ]==> (c ((^x.x)(a a))) 7. ==[ beta ]==> (c (a a)) REDUCED to normal form. ------ 177063/20315199. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(a (b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(a (b a))) 3. ==[ beta ]==> (((b a)(b a))(a (b a))) REDUCED to normal form. ------ 177064/20315262. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(a a)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 177065/20315280. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((a b)((^y.y) a))) 3. ==[ beta ]==> (b ((a b)((^y.y) a))) 4. ==[ alpha ]==> (b ((a b)((^x.x) a))) 5. ==[ beta ]==> (b ((a b) a)) REDUCED to normal form. ------ 177066/20315388. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177067/20315514. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 177068/20315541. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 177069/20315568. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 177070/20315595. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 177071/20315622. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(y y))((a a) a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))((a a) a))) 5. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 177072/20315649. ------ 1. ==[ start ]==> (((a b)(a b))((^b.a)(a b))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(a b))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 177073/20315676. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 177074/20315703. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 177075/20315757. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 177076/20315784. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b)(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 177077/20315838. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 177078/20315928. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(b ((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(b ((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(b ((^x2.x2)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(b ((^x2.x2)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177079/20316009. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a b)(a (^z.z)))) 3. ==[ beta ]==> (b ((a b)(a (^z.z)))) 4. ==[ alpha ]==> (b ((a b)(a (^x.x)))) REDUCED to normal form. ------ 177080/20316117. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1) a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177081/20316288. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 177082/20316315. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 177083/20316396. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 177084/20316423. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a)) a)) 5. ==[ beta ]==> (((a a)(^x.b))((a a) a)) REDUCED to normal form. ------ 177085/20316621. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.(a a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 177086/20316783. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c (^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c (^y.a))) 3. ==[ beta ]==> (((a b)(a a))(c (^y.a))) 4. ==[ alpha ]==> (((a b)(a a))(c (^x.a))) REDUCED to normal form. ------ 177087/20316810. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(b (^y.b))) 3. ==[ beta ]==> (((a a)(a b))(b (^y.b))) 4. ==[ alpha ]==> (((a a)(a b))(b (^x.b))) REDUCED to normal form. ------ 177088/20316837. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a (^y.(a a)))) REDUCED to normal form. ------ 177089/20316918. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 177090/20316945. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 177091/20316999. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 177092/20317170. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (c ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (c ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (c (^y.y))) 6. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 177093/20317278. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(a (^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(a (^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177094/20317503. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 177095/20317530. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177096/20317584. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a) a)) REDUCED to normal form. ------ 177097/20317611. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 177098/20317638. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (a a)) c)) REDUCED to normal form. ------ 177099/20317746. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^c.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 177100/20317818. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a ((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a ((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 177101/20317863. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 177102/20317917. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(a a))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 177103/20317944. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(a (^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a (^x1.x1))(a (^x1.x1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 177104/20317971. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 177105/20317998. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 177106/20318025. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 177107/20318052. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 177108/20318106. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a)(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 177109/20318133. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 177110/20318160. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 177111/20318232. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a) c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a) c)) 3. ==[ beta ]==> ((a (^y.y))((^z.a) c)) 4. ==[ alpha ]==> ((a (^x.x))((^y.a) c)) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 177112/20318250. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a (^z.z))((^x1.x1) a))(^y.y)) 6. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.z)) 7. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 8. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 177113/20318637. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (b (((^y.y) a)(^z.z))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 177114/20318664. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 177115/20318682. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b c)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b c)) 3. ==[ beta ]==> ((a (a (^y.y)))(b c)) 4. ==[ alpha ]==> ((a (a (^x.x)))(b c)) REDUCED to normal form. ------ 177116/20318691. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)(^z.a))) REDUCED to normal form. ------ 177117/20318763. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b (a (^x.x)))) REDUCED to normal form. ------ 177118/20318799. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) a)) 5. ==[ beta ]==> ((^y.y)((^z.a) a)) 6. ==[ alpha ]==> ((^x.x)((^y.a) a)) 7. ==[ beta ]==> ((^y.a) a) 8. ==[ alpha ]==> ((^x.a) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 177119/20318826. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 177120/20318844. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a a)(a (^y.y)))) 3. ==[ beta ]==> (b ((a a)(a (^y.y)))) 4. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 177121/20318907. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 177122/20318952. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b (a a))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177123/20318988. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177124/20319015. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) b) REDUCED to normal form. ------ 177125/20319069. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a) a)) 5. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177126/20319087. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (a a))) 3. ==[ beta ]==> (((a a)(^y.y))(a (a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 177127/20319096. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 177128/20319111. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a)))) b) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1)))) b) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177129/20319114. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 177130/20319135. ------ 1. ==[ start ]==> ((^a.(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177131/20320836. ------ 1. ==[ start ]==> ((^a.(^a.b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 177132/20324481. ------ 1. ==[ start ]==> ((^a.(^b.b))(^b.(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177133/20330151. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177134/20330154. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a)))) b) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 177135/20330178. ------ 1. ==[ start ]==> ((^a.(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177136/20330181. ------ 1. ==[ start ]==> ((a (^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 177137/20330196. ------ 1. ==[ start ]==> ((^a.(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(x x))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a (a (^y.y)))(^z.z))((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 177138/20330223. ------ 1. ==[ start ]==> ((^a.b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 177139/20330304. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^z.z) b)(^x1.(^y1.y1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177140/20330421. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (^x.((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 177141/20330493. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ eta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177142/20330613. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 177143/20331546. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> (((((a a)(a a))(^y.a))(((a a)(a a))(^y.a)))(((a a)(a a))(^y.a))) 4. ==[ alpha ]==> (((((a a)(a a))(^x.a))(((a a)(a a))(^y.a)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 177144/20331879. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 177145/20331882. ------ 1. ==[ start ]==> ((a (^a.b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.b))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 177146/20334177. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.((a a)(a a)))) 5. ==[ beta ]==> (b (^z.((a a)(a a)))) 6. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 177147/20334528. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.(^z.(a a)))) 3. ==[ beta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 177148/20334537. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.((y y)(y y)))) REDUCED to normal form. ------ 177149/20334921. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 177150/20335203. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(^x1.x1))(^z1.z1)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(^y1.y1)) 5. ==[ beta ]==> ((^y.(^z.z))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177151/20335524. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177152/20335527. ------ 1. ==[ start ]==> ((a (^b.b))(^b.(^b.b))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177153/20335851. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177154/20336445. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177155/20336454. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(y1 (^z1.(^x2.x2))))) REDUCED to normal form. ------ 177156/20336838. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a b)(^y.(y y)))) 3. ==[ beta ]==> ((((a b)(^y.(y y)))((a b)(^y.(y y))))(((a b)(^y.(y y)))((a b)(^y.(y y))))) 4. ==[ alpha ]==> ((((a b)(^x.(x x)))((a b)(^y.(y y))))(((a b)(^z.(z z)))((a b)(^x1.(x1 x1))))) REDUCED to normal form. ------ 177157/20337012. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^b.(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(z a))) 3. ==[ beta ]==> (b (^z.(z a))) 4. ==[ alpha ]==> (b (^x.(x a))) REDUCED to normal form. ------ 177158/20338263. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^x.(a a))) REDUCED to normal form. ------ 177159/20339496. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.b))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.b))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 7. ==[ beta ]==> (^y.(^z.b)) 8. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 177160/20339658. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((a a) a))) 3. ==[ beta ]==> (b (^z.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 177161/20339829. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((y y) y))) REDUCED to normal form. ------ 177162/20340321. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a) c)) 3. ==[ beta ]==> (((^z.a) c)(((^z.a) c)(^y.y))) 4. ==[ alpha ]==> (((^x.a) c)(((^y.a) c)(^z.z))) 5. ==[ beta ]==> (a (((^y.a) c)(^z.z))) 6. ==[ alpha ]==> (a (((^x.a) c)(^y.y))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 177163/20340792. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a))) 5. ==[ beta ]==> (^y.((^z.z) a)) 6. ==[ alpha ]==> (^x.((^y.y) a)) 7. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 177164/20340882. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.x1)) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177165/20341071. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 177166/20341152. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.b)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177167/20341170. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177168/20341179. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 177169/20341194. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177170/20341197. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 177171/20341227. ------ 1. ==[ start ]==> ((a (^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177172/20341245. ------ 1. ==[ start ]==> ((a (a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (a a))((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 177173/20341254. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177174/20341272. ------ 1. ==[ start ]==> ((a b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 177175/20341326. ------ 1. ==[ start ]==> (((a a)(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 177176/20341353. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 177177/20341362. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177178/20341389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177179/20341470. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 177180/20341515. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177181/20341542. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177182/20341551. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 177183/20341578. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 177184/20341632. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (a ((^y.(^z.z))((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177185/20341659. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 177186/20341731. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x) a))((b (^y.y)) c)) 3. ==[ beta ]==> (((a a) a)((b (^y.y)) c)) 4. ==[ alpha ]==> (((a a) a)((b (^x.x)) c)) REDUCED to normal form. ------ 177187/20341902. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177188/20342109. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((a (a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 177189/20342127. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((b b)(((^y.(^z.z)) a)(a a))) 4. ==[ alpha ]==> ((b b)(((^x.(^y.y)) a)(a a))) 5. ==[ beta ]==> ((b b)((^y.y)(a a))) 6. ==[ alpha ]==> ((b b)((^x.x)(a a))) 7. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 177190/20342262. ------ 1. ==[ start ]==> (((a (a a)) b)((b a)((a a) a))) REDUCED to normal form. ------ 177191/20342289. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> (a (((a a)(^y.y))(a b))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(a b))) REDUCED to normal form. ------ 177192/20342316. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 177193/20342343. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 177194/20342370. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a) a)(b a))) 3. ==[ beta ]==> ((a (^y.a))(((a a) a)(b a))) 4. ==[ alpha ]==> ((a (^x.a))(((a a) a)(b a))) REDUCED to normal form. ------ 177195/20342397. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 177196/20342424. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((^z.z) b))) 5. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) b))) 6. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) b))) 7. ==[ beta ]==> ((a (a a))((^y.y) b)) 8. ==[ alpha ]==> ((a (a a))((^x.x) b)) 9. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 177197/20342541. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177198/20342568. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((b (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 177199/20342595. ------ 1. ==[ start ]==> ((a ((a a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((a a) a))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 177200/20342631. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(a (a a))) 6. ==[ alpha ]==> ((^x.x)(a (a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 177201/20342766. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) a)((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 177202/20342847. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> ((a a)((^y.(y y))((^z.z) b))) 8. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y) b))) 9. ==[ beta ]==> ((a a)(((^y.y) b)((^y.y) b))) 10. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y) b))) 11. ==[ beta ]==> ((a a)(b ((^y.y) b))) 12. ==[ alpha ]==> ((a a)(b ((^x.x) b))) 13. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 177203/20342928. ------ 1. ==[ start ]==> ((a (^a.b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.b))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 177204/20342946. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y) a)) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x) a)) 5. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 177205/20342973. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((b (^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b (^x1.x1)) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z)) b)) REDUCED to normal form. ------ 177206/20343117. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 177207/20343279. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177208/20343288. ------ 1. ==[ start ]==> (((a b) a)(c ((a a)(a a)))) REDUCED to normal form. ------ 177209/20343315. ------ 1. ==[ start ]==> (((a a)(^a.b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(b (b (^y.y)))) REDUCED to normal form. ------ 177210/20343369. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b (^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(a a))) REDUCED to normal form. ------ 177211/20343396. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 177212/20343423. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.a)(((^z.z) b)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) b)((^z.z) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177213/20343450. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 177214/20343477. ------ 1. ==[ start ]==> (((a b)(^a.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.x))((b a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 177215/20343666. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (b (((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (b (a ((^y.y) b))) 6. ==[ alpha ]==> (b (a ((^x.x) b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 177216/20343792. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 8. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177217/20343927. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(a b))) 5. ==[ beta ]==> ((a a)((^y.(a a))(a b))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(a b))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 177218/20343954. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177219/20344008. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(b a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(b a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(b a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(b a))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 11. ==[ beta ]==> ((^y.(^z.z))(b a)) 12. ==[ alpha ]==> ((^x.(^y.y))(b a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177220/20344089. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177221/20344161. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a)(a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 177222/20344188. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) b) c)) 3. ==[ beta ]==> (((a (^x.x))(a b))(b c)) REDUCED to normal form. ------ 177223/20344413. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177224/20344557. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) b)(a (^y.y)))) 3. ==[ beta ]==> (((a b) c)(b (a (^y.y)))) 4. ==[ alpha ]==> (((a b) c)(b (a (^x.x)))) REDUCED to normal form. ------ 177225/20344584. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a a) b)((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (((a a) b)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 177226/20344611. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((b a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((b a)(a (a a)))) REDUCED to normal form. ------ 177227/20344665. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)((a a) a))) REDUCED to normal form. ------ 177228/20344692. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a b)(a b))) 3. ==[ beta ]==> ((a (^y.b))((a b)(a b))) 4. ==[ alpha ]==> ((a (^x.b))((a b)(a b))) REDUCED to normal form. ------ 177229/20344746. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177230/20344773. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (a a))(b a))) REDUCED to normal form. ------ 177231/20344800. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^x.a))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 177232/20344827. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 177233/20344854. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)((a a)(a a)))) REDUCED to normal form. ------ 177234/20344890. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 177235/20344917. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 177236/20344944. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> ((a (a b))((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 177237/20344971. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 177238/20344998. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177239/20345052. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a b)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a b)(^y.b))) 3. ==[ beta ]==> (((a b) a)((a b)(^y.b))) 4. ==[ alpha ]==> (((a b) a)((a b)(^x.b))) REDUCED to normal form. ------ 177240/20345079. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 177241/20345223. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)((a a)(a a)))) 5. ==[ beta ]==> (b ((^z.z)((a a)(a a)))) 6. ==[ alpha ]==> (b ((^x.x)((a a)(a a)))) 7. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 177242/20345304. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177243/20345412. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.b)(^z.b))) 3. ==[ beta ]==> ((b a)((^y.b)(^z.b))) 4. ==[ alpha ]==> ((b a)((^x.b)(^y.b))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 177244/20345556. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b ((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 177245/20345574. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 177246/20345583. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(a ((a a)(a a)))) REDUCED to normal form. ------ 177247/20345610. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b)(a a))) 5. ==[ beta ]==> (((a a)(^x.a))(b (a a))) REDUCED to normal form. ------ 177248/20345637. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) REDUCED to normal form. ------ 177249/20345970. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 177250/20345979. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177251/20346060. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^z.(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 177252/20346141. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177253/20346249. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.y1)((^z1.z1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177254/20346276. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177255/20346303. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177256/20346438. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.b))) 4. ==[ alpha ]==> (b ((^x.a)(^y.b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177257/20346546. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177258/20346555. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 177259/20346573. ------ 1. ==[ start ]==> ((a (^b.b))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 177260/20346591. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z) a)) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 177261/20346618. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 177262/20346852. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177263/20346897. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(a (^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z))) 3. ==[ beta ]==> ((^y.y)(a (^z.z))) 4. ==[ alpha ]==> ((^x.x)(a (^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177264/20346924. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.(^y2.y2)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.(^y2.y2)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177265/20347059. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)((a a) a))) 3. ==[ beta ]==> (b ((^z.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177266/20347167. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177267/20347221. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177268/20347302. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 177269/20347383. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177270/20347491. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177271/20347500. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 177272/20347527. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((b a)(a a))) 3. ==[ beta ]==> ((b (^y.y))((b a)(a a))) 4. ==[ alpha ]==> ((b (^x.x))((b a)(a a))) REDUCED to normal form. ------ 177273/20347563. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z)) c)) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y)) c)) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 177274/20347833. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 177275/20347860. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> ((b (a a))((a a)(^y.a))) 6. ==[ alpha ]==> ((b (a a))((a a)(^x.a))) REDUCED to normal form. ------ 177276/20347887. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a b)(^x.(x x)))) REDUCED to normal form. ------ 177277/20347923. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177278/20348058. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(b a))) 3. ==[ beta ]==> (b ((^z.z)(b a))) 4. ==[ alpha ]==> (b ((^x.x)(b a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 177279/20348166. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177280/20348247. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> (((a a)(a a))((^y.b)(^y.b))) 6. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.b))) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 177281/20348274. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(a a))) 6. ==[ alpha ]==> ((^x.a)(^y.(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177282/20348283. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(c ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(c (a a))) REDUCED to normal form. ------ 177283/20348310. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(b ((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(b ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b ((a a)(^x1.x1)))) REDUCED to normal form. ------ 177284/20348391. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 177285/20348418. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((a b)((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.b))((a b) a)) REDUCED to normal form. ------ 177286/20348472. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 177287/20348526. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a (a b))) REDUCED to normal form. ------ 177288/20348553. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 177289/20348580. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 177290/20348616. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 177291/20348643. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 177292/20348670. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a b)(^x1.a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a b)(^x1.a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(^z.a))) REDUCED to normal form. ------ 177293/20348697. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 177294/20348724. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 9. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177295/20348778. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(^y.b))) 3. ==[ beta ]==> (((a b)(a b))(a (^y.b))) 4. ==[ alpha ]==> (((a b)(a b))(a (^x.b))) REDUCED to normal form. ------ 177296/20348805. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 177297/20348886. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(a a)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a)) b)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a) b)) REDUCED to normal form. ------ 177298/20348913. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b) c)) 3. ==[ beta ]==> ((b (a (^y.y)))((a b) c)) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b) c)) REDUCED to normal form. ------ 177299/20349057. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))(^z2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177300/20349282. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (^y.y))(a b))) 3. ==[ beta ]==> ((b c)((a (^y.y))(a b))) 4. ==[ alpha ]==> ((b c)((a (^x.x))(a b))) REDUCED to normal form. ------ 177301/20349309. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a a)((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a)(a a))) REDUCED to normal form. ------ 177302/20349354. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a))(a a))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 177303/20349381. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((^y.b)(a (^z.z))) 6. ==[ alpha ]==> ((^x.b)(a (^y.y))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177304/20349435. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 177305/20349516. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177306/20349777. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 177307/20349804. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b) b)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b) b)) 5. ==[ beta ]==> ((a b)((^y.b) b)) 6. ==[ alpha ]==> ((a b)((^x.b) b)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 177308/20350020. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 177309/20350047. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.a))) 7. ==[ beta ]==> ((b a)((^y.y)(^z.a))) 8. ==[ alpha ]==> ((b a)((^x.x)(^y.a))) 9. ==[ beta ]==> ((b a)(^y.a)) 10. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 177310/20350074. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 177311/20350218. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 177312/20350299. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177313/20350524. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a a)((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((a a)((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((a a)((a a) a))) 5. ==[ beta ]==> (a ((a a)((a a) a))) REDUCED to normal form. ------ 177314/20350542. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(a (^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(a (^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.b))) 5. ==[ beta ]==> ((^y.y)(a (^z.b))) 6. ==[ alpha ]==> ((^x.x)(a (^y.b))) 7. ==[ beta ]==> (a (^y.b)) 8. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 177315/20350569. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a a))) 5. ==[ beta ]==> ((^y.a)(a a)) 6. ==[ alpha ]==> ((^x.a)(a a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177316/20350623. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))((^x1.x1) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))((^z.z) a))) 7. ==[ beta ]==> ((b b)((^y.(y y))((^z.z) a))) 8. ==[ alpha ]==> ((b b)((^x.(x x))((^y.y) a))) 9. ==[ beta ]==> ((b b)(((^y.y) a)((^y.y) a))) 10. ==[ alpha ]==> ((b b)(((^x.x) a)((^y.y) a))) 11. ==[ beta ]==> ((b b)(a ((^y.y) a))) 12. ==[ alpha ]==> ((b b)(a ((^x.x) a))) 13. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 177317/20350704. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.z)((a a) a))) 3. ==[ beta ]==> (b ((^z.z)((a a) a))) 4. ==[ alpha ]==> (b ((^x.x)((a a) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 177318/20350812. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.a)(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177319/20350821. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (a (a a)))) REDUCED to normal form. ------ 177320/20350848. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x)))(b (^z.z))) 6. ==[ alpha ]==> ((b (^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 177321/20350875. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a ((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a ((a a) a))) REDUCED to normal form. ------ 177322/20350929. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.y)))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 177323/20351046. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a (a a)) b)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a (a a)) b)(^y.y)) 8. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 177324/20351073. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 177325/20351100. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) a)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(b a))(a (^y.a))) 4. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.a))) REDUCED to normal form. ------ 177326/20351127. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 177327/20351154. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 177328/20351181. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 177329/20351343. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(z z)) b)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y)) b)) 5. ==[ beta ]==> ((a a)((^y.(y y)) b)) 6. ==[ alpha ]==> ((a a)((^x.(x x)) b)) 7. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 177330/20351361. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 177331/20351370. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a) c)) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 177332/20351784. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a)(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a a))) 5. ==[ beta ]==> ((^y.y)((^z.a)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a a))) 7. ==[ beta ]==> ((^y.a)(a a)) 8. ==[ alpha ]==> ((^x.a)(a a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 177333/20351811. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177334/20351820. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b c)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b c)) REDUCED to normal form. ------ 177335/20351838. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.y1)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 177336/20351892. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 177337/20351928. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.z) a))) 5. ==[ beta ]==> ((^y.y)(a ((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)(a ((^y.y) a))) 7. ==[ beta ]==> (a ((^y.y) a)) 8. ==[ alpha ]==> (a ((^x.x) a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177338/20351955. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 177339/20351973. ------ 1. ==[ start ]==> (((^a.b)(b a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(b (^y.(^z.z)))) 3. ==[ beta ]==> (b (b (^y.(^z.z)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 177340/20352036. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b b)) REDUCED to normal form. ------ 177341/20352081. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177342/20352117. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 177343/20352144. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 177344/20352198. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a b)) 5. ==[ beta ]==> ((^y.(^z.z))(a b)) 6. ==[ alpha ]==> ((^x.(^y.y))(a b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177345/20352216. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 177346/20352225. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (a a))) REDUCED to normal form. ------ 177347/20352240. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a)))) c) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1)))) c) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177348/20352243. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 177349/20352260. ------ 1. ==[ start ]==> (^a.((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (^x.((x x)(x (x (^y.y))))) REDUCED to normal form. ------ 177350/20352261. ------ 1. ==[ start ]==> (a ((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (a ((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 177351/20357934. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 177352/20363289. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177353/20363292. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a)))) c) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z)))) c) REDUCED to normal form. ------ 177354/20363310. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a)))) a) 2. ==[ alpha ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 177355/20363316. ------ 1. ==[ start ]==> ((^a.a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((a a)(a (a (^y.y)))) 4. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 177356/20363337. ------ 1. ==[ start ]==> (((^a.a) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177357/20363406. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177358/20363568. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (^x.((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 177359/20363769. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(a (a (^y1.y1))))) REDUCED to normal form. ------ 177360/20363811. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 177361/20364210. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 177362/20364261. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177363/20365800. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a (^z.z))((a a)(a a)))((a (^z.z))((a a)(a a))))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.y))((a a)(a a)))((a (^z.z))((a a)(a a))))) 5. ==[ beta ]==> (((a (^y.y))((a a)(a a)))((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 177364/20366226. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 177365/20367324. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (b (^z.(^x1.(a a)))) 6. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 177366/20367684. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 177367/20368359. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 177368/20368692. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 177369/20368986. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 177370/20368989. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a b)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 177371/20369304. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 177372/20369601. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(^x2.(^y2.y2))))) REDUCED to normal form. ------ 177373/20370159. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^z.(^x1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 177374/20371653. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(^y.(a a))) REDUCED to normal form. ------ 177375/20371878. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^y.(y y))) REDUCED to normal form. ------ 177376/20372805. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^z.(^x1.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 177377/20372814. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((a a) a))) REDUCED to normal form. ------ 177378/20372976. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 177379/20373468. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((^z.z) a)(a (^x1.x1)))((((^z.z) a)(a (^x1.x1)))(^y.y))) 4. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((((^z.z) a)(a (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((a (a (^y.y)))((((^z.z) a)(a (^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((a (a (^x.x)))((((^y.y) a)(a (^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((a (a (^x.x)))((a (a (^z.z)))(^x1.x1))) 8. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 177380/20373867. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z)))) 5. ==[ beta ]==> (b (^y.(^z.(z z)))) 6. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 177381/20374029. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.a))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 7. ==[ beta ]==> (^y.(^z.a)) 8. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 177382/20374218. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 177383/20374299. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177384/20374326. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 177385/20374341. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177386/20374344. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 177387/20374362. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 177388/20374374. ------ 1. ==[ start ]==> ((a a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 177389/20374392. ------ 1. ==[ start ]==> (((^a.a) a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (a (a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (a (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177390/20374410. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177391/20374419. ------ 1. ==[ start ]==> (((a a) a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 4. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 177392/20374437. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 177393/20374464. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 177394/20374518. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177395/20374527. ------ 1. ==[ start ]==> (((a a) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) b)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 177396/20374554. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 177397/20374572. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b a)(^z.b))) 3. ==[ beta ]==> ((a (^y.y))((b a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(^y.b))) REDUCED to normal form. ------ 177398/20374599. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 177399/20374626. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 177400/20374662. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^z.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177401/20374707. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 177402/20374743. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 177403/20374770. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 177404/20374797. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 177405/20374815. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 177406/20374824. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (a (^x1.x1)))) REDUCED to normal form. ------ 177407/20374851. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))((^x1.x1)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 177408/20374869. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z) b)) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y) b)) 5. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 177409/20374959. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 177410/20375040. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 177411/20375067. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 177412/20375121. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 177413/20375148. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177414/20375238. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x)) a)(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a (^x.x)) a)(b (^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.y))) REDUCED to normal form. ------ 177415/20375265. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((a (a (^y.y)))(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (a (a (^y.y))))) REDUCED to normal form. ------ 177416/20375292. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(a a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(a a))) 5. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 177417/20375319. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 177418/20375616. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a ((a a)(a a)))) REDUCED to normal form. ------ 177419/20375643. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 177420/20375670. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a ((^y.y) a))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((a a)((^y.(^z.z)) a))) 6. ==[ alpha ]==> ((a a)((a a)((^x.(^y.y)) a))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 177421/20375787. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 177422/20375841. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b a)(^z.a))) 5. ==[ beta ]==> (a ((b a)(^z.a))) 6. ==[ alpha ]==> (a ((b a)(^x.a))) REDUCED to normal form. ------ 177423/20375877. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a b))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a b))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177424/20375904. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 177425/20375922. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) a)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 177426/20375958. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 177427/20375985. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177428/20376003. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (a a))(^z.z))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))(^z.z))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))(^y.y))) 7. ==[ beta ]==> ((a a)((a (a a))(^y.y))) 8. ==[ alpha ]==> ((a a)((a (a a))(^x.x))) REDUCED to normal form. ------ 177429/20376012. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.a))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> (((a (a a))(^x.a))(b ((^z.z) b))) 6. ==[ alpha ]==> (((a (a a))(^x.a))(b ((^y.y) b))) 7. ==[ beta ]==> (((a (a a))(^x.a))(b b)) REDUCED to normal form. ------ 177430/20376039. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177431/20376066. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 177432/20376417. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(x x))(^y.y))) 3. ==[ beta ]==> ((((a a) a) b)((^y.y)(^y.y))) 4. ==[ alpha ]==> ((((a a) a) b)((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a) a) b)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 177433/20376444. ------ 1. ==[ start ]==> (((a b) a)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 177434/20376669. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(a b))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 177435/20376696. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a a)(a b))) REDUCED to normal form. ------ 177436/20376723. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a b)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a b)(a a))) REDUCED to normal form. ------ 177437/20376750. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 177438/20376777. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> (a (((^y.y)(^z.z))(b a))) 8. ==[ alpha ]==> (a (((^x.x)(^y.y))(b a))) 9. ==[ beta ]==> (a ((^y.y)(b a))) 10. ==[ alpha ]==> (a ((^x.x)(b a))) 11. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 177439/20376804. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 177440/20376831. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a b)(a a))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a b)(a a))(a ((^x.x) b))) 5. ==[ beta ]==> (((a b)(a a))(a b)) REDUCED to normal form. ------ 177441/20376858. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 177442/20376948. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 177443/20377029. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 177444/20377083. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.b))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.b))) 7. ==[ beta ]==> ((a a)((a a)(^y.b))) 8. ==[ alpha ]==> ((a a)((a a)(^x.b))) REDUCED to normal form. ------ 177445/20377092. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 177446/20377110. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(a a))) 6. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 177447/20377119. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 177448/20377173. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177449/20377200. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))((^z.(z z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((^y.(y y))(a (^z.(^x1.x1))))((^y.(y y))(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 9. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 11. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^z1.(^x2.x2)))(a (^z1.(^x2.x2))))) 12. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a (^x2.(^y2.y2))))) REDUCED to normal form. ------ 177450/20377227. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 177451/20377245. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 177452/20377254. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177453/20377281. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 177454/20377470. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(a a))(^z.b))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.b))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 177455/20377704. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a)) b)) 3. ==[ beta ]==> (b ((^z.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 177456/20378010. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.(a a)))) REDUCED to normal form. ------ 177457/20378379. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a a)(^z.(a a)))) 5. ==[ beta ]==> (b ((a a)(^z.(a a)))) 6. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 177458/20378460. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 177459/20378523. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 177460/20378631. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 177461/20378712. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177462/20378739. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(a a))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(a a))) REDUCED to normal form. ------ 177463/20378856. ------ 1. ==[ start ]==> (((a a)(b a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(b a))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 177464/20378883. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 177465/20378910. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a b)((a a) a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a b)((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a b)((a a) a))) 5. ==[ beta ]==> ((a (a a))((a b)((a a) a))) REDUCED to normal form. ------ 177466/20378937. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a) a)(a b))) REDUCED to normal form. ------ 177467/20378964. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a) a)((^y.y)((^z.z)(a a)))) 8. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y)(a a)))) 9. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 10. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 11. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 177468/20378991. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 177469/20379018. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x) a)(b a))) 3. ==[ beta ]==> (((a b)(a (a a)))(a (b a))) REDUCED to normal form. ------ 177470/20379045. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 177471/20379072. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a) b)) REDUCED to normal form. ------ 177472/20379117. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.x1)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177473/20379135. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177474/20379216. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)((a a)(^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 177475/20379297. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (b (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 177476/20379405. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177477/20379414. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z) b)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 177478/20379432. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) b) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b) a)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 177479/20379441. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 177480/20379459. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z))) b)) 5. ==[ beta ]==> ((a (^y.(^z.z))) b) 6. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 177481/20379522. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 177482/20379549. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177483/20379603. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 177484/20379630. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177485/20379657. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 177486/20379711. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 177487/20379747. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(a ((^z.z) b))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 177488/20379774. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 177489/20379801. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((b a)(a (^z.z)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((b a)(a (^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)(a (^y.y)))) REDUCED to normal form. ------ 177490/20379828. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a (a a))(a a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 177491/20379855. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))(a (a a)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))(a (a a)))) 7. ==[ beta ]==> ((a b)((a a)(a (a a)))) REDUCED to normal form. ------ 177492/20379882. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a b)(^y.y))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)(^x.x))) REDUCED to normal form. ------ 177493/20379909. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 177494/20379936. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(^z.z))(a b))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(a b))) 6. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(a b))) 7. ==[ beta ]==> (((a a)(a (a a)))(a b)) REDUCED to normal form. ------ 177495/20379963. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((a (a a))(a a))) REDUCED to normal form. ------ 177496/20380008. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(c (^d.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(c (^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177497/20380017. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (^z.z))(b a))) REDUCED to normal form. ------ 177498/20380044. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a b)((a a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a b)((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 177499/20380080. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.(^x2.x2)))(^y2.y2))) 3. ==[ beta ]==> ((^y.y)((a (^z1.(^x2.x2)))(^y2.y2))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177500/20380215. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a) a)(^z.a))) 3. ==[ beta ]==> (b (((a a) a)(^z.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 177501/20380332. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 177502/20380359. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((b a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 177503/20380377. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y) b)((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z))) a)) 5. ==[ beta ]==> (b ((a (^y.(^z.z))) a)) 6. ==[ alpha ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 177504/20380386. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177505/20380404. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((b a) b)) 3. ==[ beta ]==> ((^y.y)((b a) b)) 4. ==[ alpha ]==> ((^x.x)((b a) b)) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 177506/20380494. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177507/20380521. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 177508/20380548. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 177509/20380575. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 177510/20380602. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 177511/20380656. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) REDUCED to normal form. ------ 177512/20380719. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 177513/20380746. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 177514/20380773. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a b)(a (a a)))) 3. ==[ beta ]==> ((a (b a))((a b)(a (a a)))) REDUCED to normal form. ------ 177515/20380800. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 177516/20380827. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))((a a) a))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))((a a) a))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((a a) a))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((a a) a))) 9. ==[ beta ]==> ((a a)((^y.y)((a a) a))) 10. ==[ alpha ]==> ((a a)((^x.x)((a a) a))) 11. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 177517/20380854. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (a a))(a b))) REDUCED to normal form. ------ 177518/20380881. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)((a a) a))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b)((a a) a))(a ((^x.x)(a a)))) 5. ==[ beta ]==> (((a b)((a a) a))(a (a a))) REDUCED to normal form. ------ 177519/20380908. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 177520/20380935. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(b a))) REDUCED to normal form. ------ 177521/20381079. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 177522/20381358. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 177523/20381385. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 177524/20381439. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 177525/20381565. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(a a)) c)) 3. ==[ beta ]==> (b ((^y.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 177526/20381709. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (^z.(a a)))) REDUCED to normal form. ------ 177527/20381736. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 177528/20382294. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(a a)) b)) 3. ==[ beta ]==> (b ((^z.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 177529/20382438. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c (^y.b))) 3. ==[ beta ]==> ((b c)(c (^y.b))) 4. ==[ alpha ]==> ((b c)(c (^x.b))) REDUCED to normal form. ------ 177530/20382465. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(b (^x.(a a)))) REDUCED to normal form. ------ 177531/20382510. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> ((b (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 177532/20382537. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 177533/20382573. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 177534/20382591. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(x2 x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(^x2.(x2 x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(^z1.(z1 z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.(z1 z1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(y1 y1))) REDUCED to normal form. ------ 177535/20382600. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 177536/20382672. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.b))) REDUCED to normal form. ------ 177537/20382681. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 177538/20382708. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 177539/20382816. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 177540/20382843. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177541/20382906. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b (a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b (a b))) REDUCED to normal form. ------ 177542/20382933. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 177543/20382960. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a b)(a a))) 3. ==[ beta ]==> ((a ((^y.y) b))((a b)(a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a b)(a a))) 5. ==[ beta ]==> ((a b)((a b)(a a))) REDUCED to normal form. ------ 177544/20382987. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((a a) a)(a (^z.z)))) REDUCED to normal form. ------ 177545/20383014. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((b a)((^y.y)((^z.z) a))) 8. ==[ alpha ]==> ((b a)((^x.x)((^y.y) a))) 9. ==[ beta ]==> ((b a)((^y.y) a)) 10. ==[ alpha ]==> ((b a)((^x.x) a)) 11. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 177546/20383041. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 177547/20383068. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(a a))(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a b)(a a))(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a b)(a a))(a (^y.y))) 8. ==[ alpha ]==> (((a b)(a a))(a (^x.x))) REDUCED to normal form. ------ 177548/20383095. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a (^y.y))((a a) a))) 3. ==[ beta ]==> (((a a)(a b))((a (^y.y))((a a) a))) 4. ==[ alpha ]==> (((a a)(a b))((a (^x.x))((a a) a))) REDUCED to normal form. ------ 177549/20383122. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a a)(a b))) REDUCED to normal form. ------ 177550/20383374. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a) b)) 5. ==[ beta ]==> ((^y.y)(((a a) a) b)) 6. ==[ alpha ]==> ((^x.x)(((a a) a) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 177551/20383563. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177552/20383680. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b (^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(b (^z.a))) 3. ==[ beta ]==> (((^y.y) a)(b (^z.a))) 4. ==[ alpha ]==> (((^x.x) a)(b (^y.a))) 5. ==[ beta ]==> (a (b (^y.a))) 6. ==[ alpha ]==> (a (b (^x.a))) REDUCED to normal form. ------ 177553/20383725. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((a a) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.y))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 177554/20383779. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (a a))(^z.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (a a))(^z.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (a a))(^z.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (a a))(^y.a))) 7. ==[ beta ]==> ((b b)((a (a a))(^y.a))) 8. ==[ alpha ]==> ((b b)((a (a a))(^x.a))) REDUCED to normal form. ------ 177555/20383788. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(a ((^y.y) a))) 7. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 177556/20383815. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(a (a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177557/20383860. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a)(^z.a))) 3. ==[ beta ]==> (b ((a a)(^z.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 177558/20383869. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 177559/20383896. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 177560/20383923. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 177561/20383977. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 177562/20384004. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177563/20384031. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.a)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.a)) REDUCED to normal form. ------ 177564/20384121. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 177565/20384148. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 177566/20384175. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a a)(^y.y))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((a a)(^x.x))) REDUCED to normal form. ------ 177567/20384283. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c d)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c d)) REDUCED to normal form. ------ 177568/20384418. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c ((^y.y) a))) 3. ==[ beta ]==> ((b (a (a a)))(c ((^y.y) a))) 4. ==[ alpha ]==> ((b (a (a a)))(c ((^x.x) a))) 5. ==[ beta ]==> ((b (a (a a)))(c a)) REDUCED to normal form. ------ 177569/20384445. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b (a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b (a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b (a (a a)))) REDUCED to normal form. ------ 177570/20384499. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (a a))(a a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(a a))) 5. ==[ beta ]==> ((a a)((a (a a))(a a))) REDUCED to normal form. ------ 177571/20384526. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(a (a (^y.y)))) REDUCED to normal form. ------ 177572/20384535. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.a) c)) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.a) c)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a) c)) 5. ==[ beta ]==> (((^z.a) c)(^y.y)) 6. ==[ alpha ]==> (((^x.a) c)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177573/20384922. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(a (^z.(z z)))) 3. ==[ beta ]==> (((^y.y) b)(a (^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) b)(a (^y.(y y)))) 5. ==[ beta ]==> (b (a (^y.(y y)))) 6. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 177574/20384940. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 7. ==[ beta ]==> (((^y.y) a)(^z.z)) 8. ==[ alpha ]==> (((^x.x) a)(^y.y)) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177575/20384949. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a)(a a))) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 177576/20384967. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 177577/20384976. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 177578/20384994. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.a))) 5. ==[ beta ]==> ((a a)(^y.a)) 6. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 177579/20385048. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y)) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y)) b)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x)) b)) REDUCED to normal form. ------ 177580/20385084. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 7. ==[ beta ]==> ((^y.y)(^z.a)) 8. ==[ alpha ]==> ((^x.x)(^y.a)) 9. ==[ beta ]==> (^y.a) 10. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 177581/20385129. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z)) b)) 3. ==[ beta ]==> (b ((^y.(^z.z)) b)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177582/20385192. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 177583/20385237. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (^x1.x1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177584/20385273. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 177585/20385300. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b (^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 177586/20385354. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177587/20385372. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a) a)) 3. ==[ beta ]==> (((a a)(^y.y))((a a) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 177588/20385381. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 177589/20385399. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 177590/20385417. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a a)) REDUCED to normal form. ------ 177591/20385425. ------ 1. ==[ start ]==> (^a.(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (^x.(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 177592/20385426. ------ 1. ==[ start ]==> (a (b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (a (b (^x.(x (^y.y))))) REDUCED to normal form. ------ 177593/20385456. ------ 1. ==[ start ]==> ((^a.(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177594/20396454. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(y1 y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177595/20396475. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a)))) b) 2. ==[ alpha ]==> (((a a)(a (a (^x.x)))) b) REDUCED to normal form. ------ 177596/20396490. ------ 1. ==[ start ]==> ((^a.a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 3. ==[ beta ]==> (b (^y.(y (^z.z)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 177597/20396499. ------ 1. ==[ start ]==> ((^a.(^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177598/20396517. ------ 1. ==[ start ]==> ((^a.(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 177599/20396520. ------ 1. ==[ start ]==> ((a (a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177600/20396544. ------ 1. ==[ start ]==> ((^a.b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.b)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 177601/20397084. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y.y)(^z.(^x1.x1)))((^y.y)(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.(^z1.z1)))((^x2.x2)(^y2.(^z2.z2))))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.(^z1.z1)))((^x2.x2)(^y2.(^z2.z2))))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.(^y1.y1)))((^z1.z1)(^x2.(^y2.y2))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177602/20397384. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 177603/20397816. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 177604/20398221. ------ 1. ==[ start ]==> (((a a)((a a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)((a a) a))(^x.(^z.z))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 177605/20398767. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^y.(((b a)((^z.z)(^x1.x1)))((b a)((^z.z)(^x1.x1))))) 4. ==[ alpha ]==> (^x.(((b a)((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1))))) 5. ==[ beta ]==> (^x.(((b a)(^z.z))((b a)((^x1.x1)(^y1.y1))))) 6. ==[ alpha ]==> (^x.(((b a)(^y.y))((b a)((^z.z)(^x1.x1))))) 7. ==[ beta ]==> (^x.(((b a)(^y.y))((b a)(^x1.x1)))) 8. ==[ alpha ]==> (^x.(((b a)(^y.y))((b a)(^z.z)))) REDUCED to normal form. ------ 177606/20399013. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 177607/20400405. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ eta ]==> (b ((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177608/20400954. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((b a)((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177609/20401242. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.b)(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1)(a a))) 3. ==[ beta ]==> (((^x1.x1)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 177610/20401845. ------ 1. ==[ start ]==> ((^a.(^b.b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177611/20401866. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 177612/20402160. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 177613/20402172. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(a (^y.(^z.z)))) REDUCED to normal form. ------ 177614/20402478. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 177615/20403159. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((((^y.(a a))((^z.z) a))((^y.(a a))((^z.z) a)))(((^y.(a a))((^z.z) a))((^y.(a a))((^z.z) a)))) 4. ==[ alpha ]==> ((((^x.(a a))((^y.y) a))((^z.(a a))((^x1.x1) a)))(((^y1.(a a))((^z1.z1) a))((^x2.(a a))((^y2.y2) a)))) 5. ==[ beta ]==> (((a a)((^z.(a a))((^x1.x1) a)))(((^y1.(a a))((^z1.z1) a))((^x2.(a a))((^y2.y2) a)))) 6. ==[ alpha ]==> (((a a)((^x.(a a))((^y.y) a)))(((^z.(a a))((^x1.x1) a))((^y1.(a a))((^z1.z1) a)))) 7. ==[ beta ]==> (((a a)(a a))(((^z.(a a))((^x1.x1) a))((^y1.(a a))((^z1.z1) a)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.(a a))((^y.y) a))((^z.(a a))((^x1.x1) a)))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^z.(a a))((^x1.x1) a)))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a))((^y.y) a)))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 177616/20404239. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177617/20404827. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 177618/20405052. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 177619/20405400. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177620/20405988. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 177621/20406219. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 177622/20406321. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.y))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.y))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.x))) REDUCED to normal form. ------ 177623/20406456. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 177624/20407203. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.x1)) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177625/20407392. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 177626/20407491. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.b)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 177627/20407515. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177628/20407518. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 177629/20407536. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 177630/20407557. ------ 1. ==[ start ]==> ((a a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 177631/20407566. ------ 1. ==[ start ]==> ((a (^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 177632/20407584. ------ 1. ==[ start ]==> ((a (a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177633/20407602. ------ 1. ==[ start ]==> (((a a) a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a) a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 177634/20407611. ------ 1. ==[ start ]==> ((a b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a b)((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> ((a b)((a a)(^y.y))) 4. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 177635/20407629. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177636/20407656. ------ 1. ==[ start ]==> (((^a.a) b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x) b)((b (^y.y))(^z.a))) 3. ==[ beta ]==> (b ((b (^y.y))(^z.a))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.a))) REDUCED to normal form. ------ 177637/20407683. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 177638/20407710. ------ 1. ==[ start ]==> (((a a) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 177639/20407764. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.b))) REDUCED to normal form. ------ 177640/20407791. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 177641/20407827. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 177642/20407854. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)(b a))) 3. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 177643/20407926. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 177644/20408007. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 177645/20408034. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a (^z.z))) a)) 3. ==[ beta ]==> ((a (^y.y))((a (a (^z.z))) a)) 4. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y))) a)) REDUCED to normal form. ------ 177646/20408151. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 177647/20408448. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 177648/20408466. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((b b)((^y.(y (^z.z))) a)) 4. ==[ alpha ]==> ((b b)((^x.(x (^y.y))) a)) 5. ==[ beta ]==> ((b b)(a (^y.y))) 6. ==[ alpha ]==> ((b b)(a (^x.x))) REDUCED to normal form. ------ 177649/20408511. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177650/20408538. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 177651/20408592. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177652/20408646. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(a b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(a b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 7. ==[ beta ]==> (((a a)(^y.y))(a b)) 8. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 177653/20408673. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 7. ==[ beta ]==> ((a a)((^y.y)(a a))) 8. ==[ alpha ]==> ((a a)((^x.x)(a a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 177654/20408727. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a) a)(b a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a) a)(b a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 177655/20408880. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 177656/20409060. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> (b (((a a)(^y.y))(^z.b))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 177657/20409087. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 177658/20409168. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 177659/20409195. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (a a))(^y.y))) REDUCED to normal form. ------ 177660/20409285. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 177661/20409393. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 177662/20409420. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 177663/20409645. ------ 1. ==[ start ]==> (((^a.a)(a b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(c ((a a)(a a)))) 3. ==[ beta ]==> ((a b)(c ((a a)(a a)))) REDUCED to normal form. ------ 177664/20409672. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(b (b (^z.z)))) 3. ==[ beta ]==> ((^y.y)(b (b (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(b (b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 177665/20409726. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((b (^y.y))(a a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b (^y.y))(a a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b (^x.x))(a a))) REDUCED to normal form. ------ 177666/20409762. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a)) c)) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a)) c)) 5. ==[ beta ]==> ((^y.a)((^z.(a a)) c)) 6. ==[ alpha ]==> ((^x.a)((^y.(a a)) c)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177667/20409807. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 177668/20409834. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (^x.(a a)))((b a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))((b a)(^y.y))) REDUCED to normal form. ------ 177669/20410050. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.y))((a a)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177670/20410077. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 177671/20410221. ------ 1. ==[ start ]==> (((a b) b)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 177672/20410275. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a a)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.b))) REDUCED to normal form. ------ 177673/20410302. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a b)(^z.(a a)))) REDUCED to normal form. ------ 177674/20410383. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))((a (a a))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(x x))((a (a a))(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a (a a))(^y.(^z.(^x1.x1))))((a (a a))(^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (a a))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 177675/20410410. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 177676/20410437. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 177677/20410527. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 177678/20410554. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(^y.a))) 5. ==[ beta ]==> ((a ((a a) a))(^y.a)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.a)) REDUCED to normal form. ------ 177679/20410581. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177680/20410662. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 177681/20410689. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 177682/20410887. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(a a))(a a))) 3. ==[ beta ]==> (b (((a a)(a a))(a a))) REDUCED to normal form. ------ 177683/20410896. ------ 1. ==[ start ]==> (((a b) c)((^c.(a a)) b)) 2. ==[ alpha ]==> (((a b) c)((^x.(a a)) b)) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 177684/20410923. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y) c)) 3. ==[ beta ]==> (((a a) b)((^y.y) c)) 4. ==[ alpha ]==> (((a a) b)((^x.x) c)) 5. ==[ beta ]==> (((a a) b) c) REDUCED to normal form. ------ 177685/20410968. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)(a (a a)))) REDUCED to normal form. ------ 177686/20410995. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 177687/20411049. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a b)(a b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a b)(a b))) REDUCED to normal form. ------ 177688/20411130. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 177689/20411283. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((a (a b))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(a (^y.y)))) 5. ==[ beta ]==> ((a (a b))(a (^y.y))) 6. ==[ alpha ]==> ((a (a b))(a (^x.x))) REDUCED to normal form. ------ 177690/20411310. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 177691/20411391. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))((a a) a))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))((a a) a))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 177692/20411418. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.b)(a b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(a b))) 5. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 177693/20411472. ------ 1. ==[ start ]==> ((a (b a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 177694/20411913. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(b ((^y.y) b))) 3. ==[ beta ]==> (b (b ((^y.y) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 177695/20411949. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(a a)) a)) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a)) a)) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 177696/20411976. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 177697/20412021. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((b a) a)) REDUCED to normal form. ------ 177698/20412255. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 177699/20412300. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177700/20412309. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.b)(a a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(a a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 177701/20412597. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)(^z.z))) REDUCED to normal form. ------ 177702/20412624. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1) b) a)) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 177703/20412912. ------ 1. ==[ start ]==> ((a (^b.b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 177704/20412930. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 177705/20413227. ------ 1. ==[ start ]==> ((a ((^a.a) b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a b)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177706/20413236. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 177707/20413542. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177708/20413569. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 177709/20413596. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((b a) b)) REDUCED to normal form. ------ 177710/20413830. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(b (b a))) 3. ==[ beta ]==> ((^y.(^z.z))(b (b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177711/20413866. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177712/20414199. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 177713/20414226. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 177714/20414667. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(b ((a a)(^y.y)))) 3. ==[ beta ]==> (((b a)(b a))(b ((a a)(^y.y)))) 4. ==[ alpha ]==> (((b a)(b a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 177715/20414730. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 177716/20414748. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> (b (((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> (b ((a a)(a (^y.y)))) 6. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 177717/20414757. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a)) c)) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 177718/20414856. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a (a a))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177719/20414982. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 177720/20415009. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 177721/20415036. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 177722/20415090. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 177723/20415117. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(x x))((a a) a))) 3. ==[ beta ]==> (((a b)(a b))(((a a) a)((a a) a))) REDUCED to normal form. ------ 177724/20415144. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.a)(a b))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.a)(a b))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.a)(a b))) 5. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 177725/20415171. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 177726/20415252. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(a a)) REDUCED to normal form. ------ 177727/20415279. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 177728/20415306. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 177729/20415477. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (b (((^z.z)(a a))(a a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 177730/20415585. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177731/20415756. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 177732/20415783. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.(y1 y1))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 177733/20415864. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 177734/20415891. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 177735/20416089. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 177736/20416116. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.(a a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(a a))) REDUCED to normal form. ------ 177737/20416278. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(c (^y.a))) 3. ==[ beta ]==> (((a a)(a b))(c (^y.a))) 4. ==[ alpha ]==> (((a a)(a b))(c (^x.a))) REDUCED to normal form. ------ 177738/20416305. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(b (^y.b))) REDUCED to normal form. ------ 177739/20416359. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.b)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 177740/20416386. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((b a)((^y.a)(a (^z.z)))) 6. ==[ alpha ]==> ((b a)((^x.a)(a (^y.y)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 177741/20416413. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177742/20416467. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 177743/20416638. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d (a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d (a (a a)))) 3. ==[ beta ]==> (b (d (a (a a)))) REDUCED to normal form. ------ 177744/20416746. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a) a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177745/20416881. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a a)((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a a)((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)((a a) a))) 5. ==[ beta ]==> ((^y.y)((a a)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((a a)((a a) a))) 7. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 177746/20416971. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.a))) REDUCED to normal form. ------ 177747/20416998. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177748/20417052. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 177749/20417079. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((a a) a) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((a a) a) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a) a)) REDUCED to normal form. ------ 177750/20417106. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) b) REDUCED to normal form. ------ 177751/20417268. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) b)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b)) 7. ==[ beta ]==> ((^y.(^z.z)) b) 8. ==[ alpha ]==> ((^x.(^y.y)) b) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177752/20417286. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (a a))(a (^z.z)))) REDUCED to normal form. ------ 177753/20417331. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (^z.(z z)))) REDUCED to normal form. ------ 177754/20417358. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 177755/20417385. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a (^y.a))) 3. ==[ beta ]==> (((a (a a)) b)(a (^y.a))) 4. ==[ alpha ]==> (((a (a a)) b)(a (^x.a))) REDUCED to normal form. ------ 177756/20417412. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177757/20417439. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(b a))((a (^y.y))(a (^y.y)))) 4. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 177758/20417466. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 177759/20417493. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(a (a a)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 177760/20417520. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 177761/20417574. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.(^z1.z1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 177762/20417601. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)(^z.a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)(^y.a))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 177763/20417628. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 177764/20417700. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z)) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z)) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y)) b)) 5. ==[ beta ]==> ((a (^x.x))(b b)) REDUCED to normal form. ------ 177765/20417718. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((((^z.z) a)(a (^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.z)) 7. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 177766/20418132. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a (^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.y))) REDUCED to normal form. ------ 177767/20418159. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 177768/20418177. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b c)) 3. ==[ beta ]==> ((^y.y)(b c)) 4. ==[ alpha ]==> ((^x.x)(b c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 177769/20418267. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a) c)) 5. ==[ beta ]==> ((^y.y)((a a) c)) 6. ==[ alpha ]==> ((^x.x)((a a) c)) 7. ==[ beta ]==> ((a a) c) REDUCED to normal form. ------ 177770/20418294. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 177771/20418312. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y))(a a))) 3. ==[ beta ]==> (b ((a (^y.y))(a a))) 4. ==[ alpha ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 177772/20418375. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 177773/20418456. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 177774/20418483. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177775/20418537. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177776/20418555. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a b)) 3. ==[ beta ]==> (((a a)(^y.y))(a b)) 4. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 177777/20418564. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a) a)) REDUCED to normal form. ------ 177778/20418582. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 177779/20418600. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (^y.y))) REDUCED to normal form. ------ 177780/20429646. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177781/20429700. ------ 1. ==[ start ]==> ((^a.(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177782/20429730. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 177783/20429745. ------ 1. ==[ start ]==> ((^a.b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.b)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 177784/20429826. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^z.(z z)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177785/20429943. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177786/20430015. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 177787/20430186. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 177788/20430510. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177789/20430603. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(y (y (^z.z))))) 3. ==[ beta ]==> ((b b)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> ((b b)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 177790/20431068. ------ 1. ==[ start ]==> ((^a.((a a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((b (^y.y))(^z.(^x1.x1)))((b (^y.y))(^z.(^x1.x1))))((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((b (^x.x))(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1))))((b (^x2.x2))(^y2.(^z2.z2)))) REDUCED to normal form. ------ 177791/20431401. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 177792/20431845. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> ((((^x.x) a)(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 177793/20433606. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ eta ]==> (b (((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177794/20434086. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.((y y)(y y)))) REDUCED to normal form. ------ 177795/20434443. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((((^x1.x1) b)(^y1.y1))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177796/20434752. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.x)(a (^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.x1)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177797/20435046. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177798/20435400. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(^z1.(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177799/20435697. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 177800/20436003. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (^y.y))(^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 177801/20436360. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((((^y.y)(a a))(^z.a))(((^y.y)(a a))(^z.a)))((((^y.y)(a a))(^z.a))(((^y.y)(a a))(^z.a)))) 4. ==[ alpha ]==> (((((^x.x)(a a))(^y.a))(((^z.z)(a a))(^x1.a)))((((^y1.y1)(a a))(^z1.a))(((^x2.x2)(a a))(^y2.a)))) 5. ==[ beta ]==> ((((a a)(^y.a))(((^z.z)(a a))(^x1.a)))((((^y1.y1)(a a))(^z1.a))(((^x2.x2)(a a))(^y2.a)))) 6. ==[ alpha ]==> ((((a a)(^x.a))(((^y.y)(a a))(^z.a)))((((^x1.x1)(a a))(^y1.a))(((^z1.z1)(a a))(^x2.a)))) 7. ==[ beta ]==> ((((a a)(^x.a))((a a)(^z.a)))((((^x1.x1)(a a))(^y1.a))(((^z1.z1)(a a))(^x2.a)))) 8. ==[ alpha ]==> ((((a a)(^x.a))((a a)(^y.a)))((((^z.z)(a a))(^x1.a))(((^y1.y1)(a a))(^z1.a)))) 9. ==[ beta ]==> ((((a a)(^x.a))((a a)(^y.a)))(((a a)(^x1.a))(((^y1.y1)(a a))(^z1.a)))) 10. ==[ alpha ]==> ((((a a)(^x.a))((a a)(^y.a)))(((a a)(^z.a))(((^x1.x1)(a a))(^y1.a)))) 11. ==[ beta ]==> ((((a a)(^x.a))((a a)(^y.a)))(((a a)(^z.a))((a a)(^y1.a)))) 12. ==[ alpha ]==> ((((a a)(^x.a))((a a)(^y.a)))(((a a)(^z.a))((a a)(^x1.a)))) REDUCED to normal form. ------ 177802/20437830. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 177803/20438601. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177804/20439045. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 5. ==[ beta ]==> (^y.(^z.b)) 6. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 177805/20439657. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 177806/20439843. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z)) b)) 3. ==[ beta ]==> (((^z.(z z)) b)(((^z.(z z)) b)(^y.y))) 4. ==[ alpha ]==> (((^x.(x x)) b)(((^y.(y y)) b)(^z.z))) 5. ==[ beta ]==> ((b b)(((^y.(y y)) b)(^z.z))) 6. ==[ alpha ]==> ((b b)(((^x.(x x)) b)(^y.y))) 7. ==[ beta ]==> ((b b)((b b)(^y.y))) 8. ==[ alpha ]==> ((b b)((b b)(^x.x))) REDUCED to normal form. ------ 177807/20440242. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) a))) 5. ==[ beta ]==> (b (^y.((^z.z) a))) 6. ==[ alpha ]==> (b (^x.((^y.y) a))) 7. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 177808/20440260. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 7. ==[ beta ]==> (^y.(^z.(z z))) 8. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 177809/20440431. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 177810/20440557. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177811/20440620. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 177812/20440692. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 177813/20440701. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.b)) REDUCED to normal form. ------ 177814/20440716. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 177815/20440719. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 177816/20440737. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.a)) REDUCED to normal form. ------ 177817/20440776. ------ 1. ==[ start ]==> ((a (^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 177818/20440785. ------ 1. ==[ start ]==> (((^a.a) a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)((a a)(a (a (^y.y))))) 3. ==[ beta ]==> (a ((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> (a ((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 177819/20440803. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 177820/20440821. ------ 1. ==[ start ]==> ((a b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a b)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 177821/20440830. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((a a)((a a)(^y.y))) 6. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 177822/20440875. ------ 1. ==[ start ]==> (((a a)(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a a))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 177823/20440902. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 177824/20440938. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177825/20440965. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 177826/20441019. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 177827/20441091. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 177828/20441100. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.a)((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 177829/20441127. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177830/20441181. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> (a ((^y.a)(b (^z.z)))) 6. ==[ alpha ]==> (a ((^x.a)(b (^y.y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177831/20441208. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177832/20441262. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(x x)))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 177833/20441280. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a a) a)(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> (((a a) a)((^y.y) b)) 6. ==[ alpha ]==> (((a a) a)((^x.x) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 177834/20441307. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 177835/20441370. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177836/20441397. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177837/20441478. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 177838/20441559. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 177839/20441586. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 177840/20441676. ------ 1. ==[ start ]==> (((^a.(a a)) b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(a (a (a (^y.y))))) 3. ==[ beta ]==> ((b b)(a (a (a (^y.y))))) 4. ==[ alpha ]==> ((b b)(a (a (a (^x.x))))) REDUCED to normal form. ------ 177841/20441685. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x (^y.y))) a)) 3. ==[ beta ]==> (((a (a a))(a a))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))(a (^x.x))) REDUCED to normal form. ------ 177842/20441811. ------ 1. ==[ start ]==> (((a (a a)) b)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)((a (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 177843/20441838. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b a)((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((b a)((a a) a))) 5. ==[ beta ]==> (a ((b a)((a a) a))) REDUCED to normal form. ------ 177844/20441865. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 177845/20441892. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a a)(a a))) REDUCED to normal form. ------ 177846/20441919. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.a))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.a))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 177847/20441946. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)(b a))) REDUCED to normal form. ------ 177848/20441973. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 11. ==[ beta ]==> (a (^y.(^z.z))) 12. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 177849/20442117. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.x1))) 6. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.z))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177850/20442144. ------ 1. ==[ start ]==> ((a ((a a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 177851/20442180. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(a a))((^y.y) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177852/20442234. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (a ((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 177853/20442315. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 177854/20442342. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.b)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.b)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.b)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.b)((a a)(^y.y))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177855/20442396. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.(^x1.x1))))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177856/20442477. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 177857/20442522. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1) a)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) a)) 7. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 177858/20442549. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((b (^y.y)) b)) 3. ==[ beta ]==> ((a (a (a a)))((b (^y.y)) b)) 4. ==[ alpha ]==> ((a (a (a a)))((b (^x.x)) b)) REDUCED to normal form. ------ 177859/20442747. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) IRREDUCIBLE: cycle. ------ 177860/20442828. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 5. ==[ beta ]==> (b ((^y.y)(^y.y))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177861/20442855. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 177862/20442864. ------ 1. ==[ start ]==> (((a a)(^a.b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(c ((a a)(a a)))) REDUCED to normal form. ------ 177863/20442918. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 177864/20442945. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b (^y.y))(a a))) REDUCED to normal form. ------ 177865/20442972. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.a)(((a a)(a a))(a (^z.z)))) 6. ==[ alpha ]==> ((^x.a)(((a a)(a a))(a (^y.y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 177866/20442999. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b ((^z.z) a))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 177867/20443026. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 177868/20443215. ------ 1. ==[ start ]==> (((^a.b) b)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) b)((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> (b ((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (b ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 177869/20443260. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (^z.(a a)))) 3. ==[ beta ]==> ((^y.(a a))(c (^z.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(c (^y.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177870/20443422. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177871/20443503. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(a a))(a b))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a b))) 5. ==[ beta ]==> ((^y.(a a))(a b)) 6. ==[ alpha ]==> ((^x.(a a))(a b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177872/20443638. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177873/20443710. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b (^y.y)) a)) 3. ==[ beta ]==> (((a a)(a a))((b (^y.y)) a)) 4. ==[ alpha ]==> (((a a)(a a))((b (^x.x)) a)) REDUCED to normal form. ------ 177874/20443737. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(a a)) b)) REDUCED to normal form. ------ 177875/20443764. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y) b) c)) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y) b) c)) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b) c)) 5. ==[ beta ]==> ((a ((a a) a))(b c)) REDUCED to normal form. ------ 177876/20444106. ------ 1. ==[ start ]==> (((a b) c)(((a a)(a a))(a a))) REDUCED to normal form. ------ 177877/20444133. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (((a a) b)(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (((a a) b)(b (a (^y.y)))) 6. ==[ alpha ]==> (((a a) b)(b (a (^x.x)))) REDUCED to normal form. ------ 177878/20444160. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 177879/20444214. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 177880/20444241. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> ((a (^x.b))((a a)((a a) a))) REDUCED to normal form. ------ 177881/20444295. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177882/20444322. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)(^z.z))) 6. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 177883/20444349. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (a a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))(b a))) REDUCED to normal form. ------ 177884/20444376. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 177885/20444403. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a (^z.z)) b)) REDUCED to normal form. ------ 177886/20444466. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 177887/20444493. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a b))(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a b))(b (^x.(^y.y)))) REDUCED to normal form. ------ 177888/20444520. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 177889/20444547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((b a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.(z z)))) 7. ==[ beta ]==> ((^y.y)((b a)(^z.(z z)))) 8. ==[ alpha ]==> ((^x.x)((b a)(^y.(y y)))) 9. ==[ beta ]==> ((b a)(^y.(y y))) 10. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 177890/20444574. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 177891/20444601. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (((a b) a)((a a)(^y.a))) 6. ==[ alpha ]==> (((a b) a)((a a)(^x.a))) REDUCED to normal form. ------ 177892/20444628. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((a b)(^z.b))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a b)(^z.b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a b)(^y.b))) REDUCED to normal form. ------ 177893/20444655. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 177894/20444682. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 177895/20444772. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) b))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177896/20444853. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 177897/20444961. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((b a)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((b a)((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 177898/20444988. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.b)(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.b))) 5. ==[ beta ]==> ((^y.b)(^z.b)) 6. ==[ alpha ]==> ((^x.b)(^y.b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177899/20445042. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 177900/20445105. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(c (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 177901/20445123. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177902/20445132. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(b ((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(b b)) REDUCED to normal form. ------ 177903/20445159. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(a ((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(a ((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 177904/20445186. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (a a))) REDUCED to normal form. ------ 177905/20445519. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(b (^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b (^z.z))) REDUCED to normal form. ------ 177906/20445528. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177907/20445609. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177908/20445690. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (b ((^x1.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177909/20445798. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177910/20445825. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 177911/20445852. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177912/20445987. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (b ((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (b ((^x.b)(^y.a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 177913/20446122. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 177914/20446167. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y) a)) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 177915/20446194. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 177916/20446248. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z)) d)) 5. ==[ beta ]==> ((a b)((^y.(^z.z)) d)) 6. ==[ alpha ]==> ((a b)((^x.(^y.y)) d)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 177917/20446401. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177918/20446446. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 177919/20446473. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(a (^z1.z1))) 3. ==[ beta ]==> ((^y.y)(a (^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(a (^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 177920/20446608. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 177921/20446716. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177922/20446770. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 177923/20446797. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(^y2.y2))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 177924/20446932. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.a)(^z.a))) 3. ==[ beta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177925/20447049. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(b (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (b a))) REDUCED to normal form. ------ 177926/20447076. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(a (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b (^y.y))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b (^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 177927/20447382. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((b a)(^x1.x1))) REDUCED to normal form. ------ 177928/20447409. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 177929/20447436. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a)(^y.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a a)(^x.a))) REDUCED to normal form. ------ 177930/20447472. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a (a a)))) 5. ==[ beta ]==> ((^y.b)(a (a a))) 6. ==[ alpha ]==> ((^x.b)(a (a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 177931/20447607. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177932/20447715. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177933/20447796. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 177934/20447823. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.b))) 5. ==[ beta ]==> ((^y.(y y))(^z.b)) 6. ==[ alpha ]==> ((^x.(x x))(^y.b)) 7. ==[ beta ]==> ((^y.b)(^y.b)) 8. ==[ alpha ]==> ((^x.b)(^y.b)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 177935/20447877. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 177936/20447940. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 177937/20447967. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.b))((a a)(a (^y.y)))) REDUCED to normal form. ------ 177938/20448021. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 177939/20448075. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (a a))((a a) a))) REDUCED to normal form. ------ 177940/20448102. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(a b))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 177941/20448129. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 177942/20448192. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 177943/20448219. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 177944/20448246. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((a b)(^x.a))) REDUCED to normal form. ------ 177945/20448273. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 177946/20448300. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((((a a) a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 177947/20448327. ------ 1. ==[ start ]==> (((a b)(a b))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a b))((a (a a))(^x.a))) REDUCED to normal form. ------ 177948/20448354. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) a)(^y.b))) 5. ==[ beta ]==> (((a a)((a a) a))(a (^y.b))) 6. ==[ alpha ]==> (((a a)((a a) a))(a (^x.b))) REDUCED to normal form. ------ 177949/20448381. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 177950/20448435. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((a a)(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z)) a)) REDUCED to normal form. ------ 177951/20448462. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((b (a (^x.x)))((a a) b)) REDUCED to normal form. ------ 177952/20448489. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a b) c)) REDUCED to normal form. ------ 177953/20448606. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.a)(^y2.b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.a)(^y2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177954/20448831. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((b c)(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> ((b c)(((^x.x) a)((a a) a))) 5. ==[ beta ]==> ((b c)(a ((a a) a))) REDUCED to normal form. ------ 177955/20448858. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x))(a b))) REDUCED to normal form. ------ 177956/20448903. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 177957/20448930. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a a))) 5. ==[ beta ]==> ((^y.(a a))(a a)) 6. ==[ alpha ]==> ((^x.(a a))(a a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177958/20449065. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)((a a) a))) 3. ==[ beta ]==> (b ((^z.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 177959/20449173. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177960/20449353. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(a a)) a)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(a a)) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a)) a)) 5. ==[ beta ]==> ((a b)((^y.(a a)) a)) 6. ==[ alpha ]==> ((a b)((^x.(a a)) a)) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 177961/20449380. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b) b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b) b)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 177962/20449407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a) c)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a) c)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a) c)) 5. ==[ beta ]==> ((b a)((^y.a) c)) 6. ==[ alpha ]==> ((b a)((^x.a) c)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 177963/20449569. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a b)(^z.z))) REDUCED to normal form. ------ 177964/20449596. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(((a a) a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 177965/20449623. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.a)) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.a)) REDUCED to normal form. ------ 177966/20449677. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 177967/20449767. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.b)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(^z.z))) 7. ==[ beta ]==> ((^y.b)(^z.z)) 8. ==[ alpha ]==> ((^x.b)(^y.y)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 177968/20449848. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> (b ((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 177969/20450073. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a ((a (^y.y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a ((a (^x.x))((^y.y)(^z.z)))) 7. ==[ beta ]==> (a ((a (^x.x))(^z.z))) 8. ==[ alpha ]==> (a ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 177970/20450091. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b (^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(b (^x1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(b (^x1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(b (^z.a))) 5. ==[ beta ]==> ((^y.y)(b (^z.a))) 6. ==[ alpha ]==> ((^x.x)(b (^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 177971/20450118. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(a (^x1.b))) 3. ==[ beta ]==> ((^y.y)(a (^x1.b))) 4. ==[ alpha ]==> ((^x.x)(a (^y.b))) 5. ==[ beta ]==> (a (^y.b)) 6. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 177972/20450172. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(a (^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(a (^z.z)))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 177973/20450253. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 177974/20450361. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(z1 z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177975/20450397. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c (a (a a)))) 3. ==[ beta ]==> ((b (^y.(y y)))(c (a (a a)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c (a (a a)))) REDUCED to normal form. ------ 177976/20450424. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (^y.y))) REDUCED to normal form. ------ 177977/20450478. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a a)) 9. ==[ beta ]==> ((^y.y)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 177978/20450622. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 177979/20450649. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 177980/20450676. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (^z.a))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.a))) REDUCED to normal form. ------ 177981/20450703. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a a))((a (^y.y))(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 177982/20450730. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 177983/20450784. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (a a)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a)) b)) REDUCED to normal form. ------ 177984/20450811. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a) c)) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a) c)) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a) c)) 5. ==[ beta ]==> ((b (a (a a)))(a c)) REDUCED to normal form. ------ 177985/20450892. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 177986/20450910. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (a a))(a a))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(a a))) REDUCED to normal form. ------ 177987/20450919. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y)) b)) 3. ==[ beta ]==> ((a (a (a (^x.x))))(b b)) REDUCED to normal form. ------ 177988/20451315. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a)((^z.z) a))) 3. ==[ beta ]==> (((^y.y) b)((a a)((^z.z) a))) 4. ==[ alpha ]==> (((^x.x) b)((a a)((^y.y) a))) 5. ==[ beta ]==> (b ((a a)((^y.y) a))) 6. ==[ alpha ]==> (b ((a a)((^x.x) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 177989/20451333. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(a (^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(y y)))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 177990/20451360. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a)(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(a a))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 177991/20451387. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177992/20451441. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a)(^y.y))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 177993/20451477. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(b (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(b (a (^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 177994/20451504. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 177995/20451522. ------ 1. ==[ start ]==> (((^a.b)(b a))(c (^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(c (^y.y))) 3. ==[ beta ]==> (b (c (^y.y))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 177996/20451585. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c a)) REDUCED to normal form. ------ 177997/20451630. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 177998/20451666. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 177999/20451693. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (a (^y.y)))) REDUCED to normal form. ------ 178000/20451747. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b a)) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178001/20451765. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 178002/20451774. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a b)) REDUCED to normal form. ------ 178003/20451792. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 178004/20451810. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y) a)) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 178005/20451836. ------ 1. ==[ start ]==> (^a.((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (^x.((x (^y.y))((^z.(^x1.x1)) x))) 3. ==[ beta ]==> (^x.((x (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (^x.((x (^y.y))(^z.z))) REDUCED to normal form. ------ 178006/20451837. ------ 1. ==[ start ]==> (a ((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (a ((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> (a ((a (^x.x))(^z.z))) 4. ==[ alpha ]==> (a ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 178007/20462865. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178008/20462913. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a)) a) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a)) a) 3. ==[ beta ]==> (((a (^x.x))(^z.z)) a) 4. ==[ alpha ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 178009/20462919. ------ 1. ==[ start ]==> ((^a.a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 178010/20462946. ------ 1. ==[ start ]==> ((^a.(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> (((a a)(a (a (^y.y))))((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 178011/20462967. ------ 1. ==[ start ]==> (((a a) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178012/20463009. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178013/20463171. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (^x.(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 178014/20463399. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 178015/20463414. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a (^z.z))) a)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 178016/20463831. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((b b)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((b b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 178017/20463840. ------ 1. ==[ start ]==> (((a (a a))(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 178018/20463864. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178019/20465403. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((((^z.z) a)((^x1.x1) b))(((^z.z) a)((^x1.x1) b)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) a)((^z.z) b))(((^x1.x1) a)((^y1.y1) b)))) 5. ==[ beta ]==> ((((^y.y) a)((^z.z) b))(((^x1.x1) a)((^y1.y1) b))) 6. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z) a)((^x1.x1) b))) 7. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)((^x1.x1) b))) 8. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((^z.z) b))) 9. ==[ beta ]==> ((a b)(((^y.y) a)((^z.z) b))) 10. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y) b))) 11. ==[ beta ]==> ((a b)(a ((^y.y) b))) 12. ==[ alpha ]==> ((a b)(a ((^x.x) b))) 13. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 178020/20467314. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 178021/20467989. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 178022/20468322. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^y.b)) REDUCED to normal form. ------ 178023/20468589. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.z))(b a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 178024/20468925. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178025/20468934. ------ 1. ==[ start ]==> (((a a)(^b.b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 178026/20469231. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 178027/20471508. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((a b)(^y.((^z.z)(y y)))) 6. ==[ alpha ]==> ((a b)(^x.((^y.y)(x x)))) 7. ==[ beta ]==> ((a b)(^x.(x x))) REDUCED to normal form. ------ 178028/20472444. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((a a) a))) REDUCED to normal form. ------ 178029/20472648. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 178030/20472750. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a)) b)(^x.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.y))) REDUCED to normal form. ------ 178031/20473047. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a a)(^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)(^x.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 178032/20473071. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a))(a a))) 3. ==[ beta ]==> (((a (a a))(a a))(((a (a a))(a a))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a (a a))(a a))(^x.x))) REDUCED to normal form. ------ 178033/20473497. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.(z z)))) REDUCED to normal form. ------ 178034/20473659. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.a))) REDUCED to normal form. ------ 178035/20473740. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.z))) REDUCED to normal form. ------ 178036/20473848. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 178037/20473902. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178038/20473929. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(a a))) REDUCED to normal form. ------ 178039/20473944. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178040/20473947. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 178041/20473965. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(y y))) REDUCED to normal form. ------ 178042/20473992. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.x1)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 178043/20474004. ------ 1. ==[ start ]==> ((a a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a a)((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a a)((a (^x.x))(^z.z))) 4. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 178044/20474022. ------ 1. ==[ start ]==> (((^a.a) a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(b (^y.(y (^z.z))))) 3. ==[ beta ]==> (a (b (^y.(y (^z.z))))) 4. ==[ alpha ]==> (a (b (^x.(x (^y.y))))) REDUCED to normal form. ------ 178045/20474031. ------ 1. ==[ start ]==> ((a (a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 178046/20474049. ------ 1. ==[ start ]==> (((a a) a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 178047/20474067. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a a))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a a)((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> ((a a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 178048/20474076. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 178049/20474094. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 178050/20474148. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178051/20474157. ------ 1. ==[ start ]==> (((a a) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 178052/20474175. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 178053/20474184. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 178054/20474211. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 178055/20474229. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((b a)(^z.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 178056/20474256. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 178057/20474292. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178058/20474337. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.a)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 178059/20474364. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178060/20474373. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 178061/20474400. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 178062/20474427. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 178063/20474454. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 178064/20474481. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((a (^x.x))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 178065/20474499. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a (^y.y))) a)) REDUCED to normal form. ------ 178066/20474724. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 178067/20474805. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 178068/20474895. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(b (^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 178069/20474913. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((b b)((^y.y)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((b b)((^x.x)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((b b)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((b b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 178070/20474922. ------ 1. ==[ start ]==> (((a (a a))(a a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(a (a (a (^x.x))))) REDUCED to normal form. ------ 178071/20474949. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 178072/20475246. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.x))((a (a a)) b)) REDUCED to normal form. ------ 178073/20475273. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 178074/20475300. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(b (^z.z)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 178075/20475327. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 178076/20475417. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.a)) 6. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 178077/20475471. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (a ((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 178078/20475552. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.(a a)))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 178079/20475579. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 178080/20475588. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 178081/20475633. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.(^y1.y1))))) 10. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 11. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 12. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 178082/20475642. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 178083/20475669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178084/20475696. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x)) a) REDUCED to normal form. ------ 178085/20475885. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 178086/20476047. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 178087/20476074. ------ 1. ==[ start ]==> (((a b) a)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a b) a)((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a b) a)((^y.y)(^y.y))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 178088/20476101. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 178089/20476299. ------ 1. ==[ start ]==> (((a a)(a b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a a)(a b))((b a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a b))((b a)(^x.x))) REDUCED to normal form. ------ 178090/20476326. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 178091/20476353. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(a b))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(a b))) 7. ==[ beta ]==> ((a (^x.x))((a a)(a b))) REDUCED to normal form. ------ 178092/20476380. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a b)(a a))) REDUCED to normal form. ------ 178093/20476407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a) a)((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(((a a) a)((a a)(^z.z)))) 6. ==[ alpha ]==> (((^x.x) a)(((a a) a)((a a)(^y.y)))) 7. ==[ beta ]==> (a (((a a) a)((a a)(^y.y)))) 8. ==[ alpha ]==> (a (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 178094/20476434. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((^z.z)(b a))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)(b a))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b a)) REDUCED to normal form. ------ 178095/20476461. ------ 1. ==[ start ]==> (((a b)(a a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a a))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 178096/20476488. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> ((a (a a))(a ((^y.y) b))) 6. ==[ alpha ]==> ((a (a a))(a ((^x.x) b))) 7. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 178097/20476578. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.y)((b (^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 7. ==[ beta ]==> ((b (^y.y))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 178098/20476659. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 178099/20476668. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a b) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) b)(^x.(^y.y))) REDUCED to normal form. ------ 178100/20476722. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 178101/20476740. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.b)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.b)) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 178102/20476749. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 178103/20476803. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 178104/20476830. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(b a))) 7. ==[ beta ]==> (((^y.(^z.z))(b a))((^y.(^z.z))(b a))) 8. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(b a))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 11. ==[ beta ]==> ((^y.(^z.z))(b a)) 12. ==[ alpha ]==> ((^x.(^y.y))(b a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178105/20476857. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 178106/20476875. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 178107/20476884. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 178108/20476911. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 178109/20477100. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178110/20477676. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 178111/20478009. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> (b ((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 178112/20478090. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z) b) b)) 3. ==[ beta ]==> (b (((^z.z) b) b)) 4. ==[ alpha ]==> (b (((^x.x) b) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 178113/20478261. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 178114/20478288. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 178115/20478342. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 178116/20478369. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 178117/20478396. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(a a))) REDUCED to normal form. ------ 178118/20478486. ------ 1. ==[ start ]==> (((a a)(b a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b a))((b a)((^x.x) a))) 3. ==[ beta ]==> (((a a)(b a))((b a) a)) REDUCED to normal form. ------ 178119/20478513. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 178120/20478540. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a (a a))((a a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a (a a))((a a)((^x.x)(^y.y)))) 9. ==[ beta ]==> ((a (a a))((a a)(^y.y))) 10. ==[ alpha ]==> ((a (a a))((a a)(^x.x))) REDUCED to normal form. ------ 178121/20478567. ------ 1. ==[ start ]==> (((a (a a))(a b))((a b)((a a) a))) REDUCED to normal form. ------ 178122/20478594. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((a a) a)(a b))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a) a)(a b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a) a)(a b))) 5. ==[ beta ]==> (((a a) a)(((a a) a)(a b))) REDUCED to normal form. ------ 178123/20478621. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)((^z.z)(a a)))) 7. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(a a))) 8. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(a a))) 9. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 178124/20478648. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 178125/20478675. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) a)(b a))) 5. ==[ beta ]==> (((a a) a)(((^y.y) a)(b a))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) a)(b a))) 7. ==[ beta ]==> (((a a) a)(a (b a))) REDUCED to normal form. ------ 178126/20478702. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 178127/20478765. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) b)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) b)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178128/20478846. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a a)(((a a)(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 178129/20478927. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(^x1.b))) 3. ==[ beta ]==> (b (((a a) a)(^x1.b))) 4. ==[ alpha ]==> (b (((a a) a)(^x.b))) REDUCED to normal form. ------ 178130/20479035. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178131/20479044. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 178132/20479062. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 178133/20479071. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((^y1.y1) b)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1) b)) 5. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 178134/20479089. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z) b) a)) 3. ==[ beta ]==> ((^y.y)(((^z.z) b) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) a)) 5. ==[ beta ]==> (((^y.y) b) a) 6. ==[ alpha ]==> (((^x.x) b) a) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178135/20479143. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((b a) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((b a) c)) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((b a) c)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((b a) c)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((b a) c)) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a) c)) 7. ==[ beta ]==> (((a a)(a a))((b a) c)) REDUCED to normal form. ------ 178136/20479179. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 178137/20479233. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 178138/20479287. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 178139/20479377. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 178140/20479404. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(a ((^y.y) b))) 3. ==[ beta ]==> (((a (^x.x))(b a))(a b)) REDUCED to normal form. ------ 178141/20479431. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 178142/20479458. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((b a)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))(a a))((b a)(a (^y.y)))) 4. ==[ alpha ]==> (((a (a a))(a a))((b a)(a (^x.x)))) REDUCED to normal form. ------ 178143/20479485. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a b)(((a a)(^y.y))((^z.z) a))) 6. ==[ alpha ]==> ((a b)(((a a)(^x.x))((^y.y) a))) 7. ==[ beta ]==> ((a b)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 178144/20479512. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a a)(a (a a)))) REDUCED to normal form. ------ 178145/20479539. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(^x.x))((a b)(^z.z))) 6. ==[ alpha ]==> (((a b)(^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 178146/20479566. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 178147/20479593. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(a b))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(a b))) 7. ==[ beta ]==> ((((a a)(^x.x)) a)(a b)) REDUCED to normal form. ------ 178148/20479647. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 178149/20479674. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.y))(b a))) 3. ==[ beta ]==> ((a b)((a (^y.y))(b a))) 4. ==[ alpha ]==> ((a b)((a (^x.x))(b a))) REDUCED to normal form. ------ 178150/20479845. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 178151/20479962. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 178152/20479989. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 178153/20480007. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((a a)(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 178154/20480016. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^x.x))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 178155/20480034. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1))) a)) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z))) a)) 5. ==[ beta ]==> ((a (^y.(^z.z))) a) 6. ==[ alpha ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 178156/20480043. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) REDUCED to normal form. ------ 178157/20480124. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.(z z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178158/20480151. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) b) REDUCED to normal form. ------ 178159/20480178. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 178160/20480205. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 178161/20480232. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 178162/20480313. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((b (^x.x))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 178163/20480349. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((b a)(a a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((b a)(a a))) 3. ==[ beta ]==> (((a a) b)((b a)(a a))) REDUCED to normal form. ------ 178164/20480376. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a)(^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 178165/20480403. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a (b a))((a a)((^y.y) a))) 6. ==[ alpha ]==> ((a (b a))((a a)((^x.x) a))) 7. ==[ beta ]==> ((a (b a))((a a) a)) REDUCED to normal form. ------ 178166/20480430. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a b)(a (a a)))) REDUCED to normal form. ------ 178167/20480457. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((a a) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)(((a a) a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a a)(((a a) a)((^x.x)(^y.y)))) 9. ==[ beta ]==> ((a a)(((a a) a)(^y.y))) 10. ==[ alpha ]==> ((a a)(((a a) a)(^x.x))) REDUCED to normal form. ------ 178168/20480484. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(^y.y))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a b))((^y.y)((a a) a))) 4. ==[ alpha ]==> ((((a a) a)(a b))((^x.x)((a a) a))) 5. ==[ beta ]==> ((((a a) a)(a b))((a a) a)) REDUCED to normal form. ------ 178169/20480511. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (a a))(a b))) REDUCED to normal form. ------ 178170/20480538. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(a ((^z.z)(a a)))) 8. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y)(a a)))) 9. ==[ beta ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 178171/20480565. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 178172/20480709. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(y y)))) 5. ==[ beta ]==> ((a b)(^y.(y y))) 6. ==[ alpha ]==> ((a b)(^x.(x x))) REDUCED to normal form. ------ 178173/20480844. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 178174/20480952. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1)(a a)) c)) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178175/20480988. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((b b)((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((b b)((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 178176/20481069. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.b)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(^x1.b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 178177/20481096. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.a)(^z1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(^y1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 178178/20481195. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z)) b)) 3. ==[ beta ]==> (b ((^y.(^z.z)) b)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178179/20481402. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 178180/20481924. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178181/20482068. ------ 1. ==[ start ]==> ((((^a.a) b) c)(d (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(d (^y.a))) 3. ==[ beta ]==> ((b c)(d (^y.a))) 4. ==[ alpha ]==> ((b c)(d (^x.a))) REDUCED to normal form. ------ 178182/20482095. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(c (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(c (^x.b))) REDUCED to normal form. ------ 178183/20482167. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.z)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.y)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 178184/20482203. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 178185/20482221. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a) a)(^y1.a))) REDUCED to normal form. ------ 178186/20482302. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 178187/20482311. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 178188/20482338. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(a b))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 178189/20482410. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a b) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a b) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178190/20482419. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 178191/20482446. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 178192/20482473. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 178193/20482536. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(c ((a a) a))) REDUCED to normal form. ------ 178194/20482563. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b (a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b (a b))) REDUCED to normal form. ------ 178195/20482590. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)(a ((^y.y)(a a)))) 6. ==[ alpha ]==> ((a b)(a ((^x.x)(a a)))) 7. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 178196/20482617. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a b)(a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a b)(a a))) REDUCED to normal form. ------ 178197/20482644. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(b a))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(b a))(((a a) a)(a (^y.y)))) 5. ==[ beta ]==> ((b a)(((a a) a)(a (^y.y)))) 6. ==[ alpha ]==> ((b a)(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 178198/20482671. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z) a)) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y) a)) 7. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) a) REDUCED to normal form. ------ 178199/20482698. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((a b)(a a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 178200/20482725. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a b))(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a)(a b))(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a a)(a b))(a (^y.y))) 8. ==[ alpha ]==> (((a a)(a b))(a (^x.x))) REDUCED to normal form. ------ 178201/20482752. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 178202/20483004. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a b) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a b) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))((a b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b) a)) 5. ==[ beta ]==> ((^y.y)((a b) a)) 6. ==[ alpha ]==> ((^x.x)((a b) a)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 178203/20483085. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (a a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a)) d)) 3. ==[ beta ]==> (b ((a (a a)) d)) REDUCED to normal form. ------ 178204/20483193. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178205/20483409. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((b b)((^y.y)(^z.(^x1.x1)))) 10. ==[ alpha ]==> ((b b)((^x.x)(^y.(^z.z)))) 11. ==[ beta ]==> ((b b)(^y.(^z.z))) 12. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 178206/20483418. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 178207/20483445. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178208/20483490. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 178209/20483499. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 178210/20483526. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.z)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)((a a) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a a) a)) REDUCED to normal form. ------ 178211/20483553. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 178212/20483607. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.a)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 178213/20483634. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 178214/20483661. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 178215/20483733. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 178216/20483751. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 178217/20483778. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a ((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a a)) REDUCED to normal form. ------ 178218/20483805. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a (^y.y))(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 178219/20483832. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a)) b)((a a)(^y.y))) 6. ==[ alpha ]==> (((a (a a)) b)((a a)(^x.x))) REDUCED to normal form. ------ 178220/20484129. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)(a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)(a ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 178221/20484156. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (a a))(a a))) REDUCED to normal form. ------ 178222/20484165. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(x1 x1)) b)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z)) b)) 5. ==[ beta ]==> (((^z.(z z)) b)(^y.y)) 6. ==[ alpha ]==> (((^x.(x x)) b)(^y.y)) 7. ==[ beta ]==> ((b b)(^y.y)) 8. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 178223/20484552. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b (^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b (^z.a))) 3. ==[ beta ]==> (((^y.y) b)(b (^z.a))) 4. ==[ alpha ]==> (((^x.x) b)(b (^y.a))) 5. ==[ beta ]==> (b (b (^y.a))) 6. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 178224/20484579. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.(y y)))) REDUCED to normal form. ------ 178225/20484597. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 178226/20484606. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a)(a a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 178227/20484624. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 178228/20484678. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y) a) a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y) a) a)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x) a) a)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 178229/20484714. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178230/20484741. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.a)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 178231/20484759. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a) a)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a) a)) 3. ==[ beta ]==> (b ((^y.a) a)) 4. ==[ alpha ]==> (b ((^x.a) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178232/20484822. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.a))) REDUCED to normal form. ------ 178233/20484867. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178234/20484903. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 178235/20484930. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 178236/20484984. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178237/20485002. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a)(^z.z))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 178238/20485011. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(a a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a a)) REDUCED to normal form. ------ 178239/20485029. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 178240/20485047. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a (a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (a a))) REDUCED to normal form. ------ 178241/20485074. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 178242/20485140. ------ 1. ==[ start ]==> ((^a.b)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 178243/20496111. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178244/20496159. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a)) b) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a)) b) 3. ==[ beta ]==> (((a (^x.x))(^z.z)) b) 4. ==[ alpha ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 178245/20496183. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178246/20496201. ------ 1. ==[ start ]==> ((^a.(a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((b (^y.(y (^z.z))))(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((b (^x.(x (^y.y))))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 178247/20496228. ------ 1. ==[ start ]==> ((^a.b)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 178248/20496231. ------ 1. ==[ start ]==> ((a b)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178249/20496498. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.b)(b a))) 3. ==[ eta ]==> ((^y.y)((^z.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 178250/20497095. ------ 1. ==[ start ]==> (((a (a a))(a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 178251/20497527. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 178252/20497932. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^z.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 178253/20498064. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) b) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1))) b) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178254/20498346. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((^x.(x x))(a (a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.(x x))(a (a a)))(^y.(^z.z))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 178255/20498451. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (^y.(((a (^z.(^x1.x1)))(a (a a)))((a (^z.(^x1.x1)))(a (a a))))) 4. ==[ alpha ]==> (^x.(((a (^y.(^z.z)))(a (a a)))((a (^x1.(^y1.y1)))(a (a a))))) REDUCED to normal form. ------ 178256/20499120. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(y (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 178257/20499333. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((((^z.b)(^x1.(a a)))((^z.b)(^x1.(a a))))(^y.y)) 4. ==[ alpha ]==> ((((^x.b)(^y.(a a)))((^z.b)(^x1.(a a))))(^y1.y1)) 5. ==[ beta ]==> ((b ((^z.b)(^x1.(a a))))(^y1.y1)) 6. ==[ alpha ]==> ((b ((^x.b)(^y.(a a))))(^z.z)) 7. ==[ beta ]==> ((b b)(^z.z)) 8. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 178258/20499507. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 178259/20500089. ------ 1. ==[ start ]==> ((^a.(b a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)((^z.z)(a a)))) 3. ==[ eta ]==> (b ((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178260/20500638. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178261/20501529. ------ 1. ==[ start ]==> ((^a.(^b.b))(c (b a))) 2. ==[ alpha ]==> ((^x.(^y.y))(c (b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178262/20501577. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 178263/20501844. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(c (^d.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(c (^z.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 178264/20502189. ------ 1. ==[ start ]==> (((a a)(^b.b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 178265/20502792. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 178266/20503845. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 178267/20503923. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178268/20504097. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (b (^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.((x x)(^y.y)))) REDUCED to normal form. ------ 178269/20504313. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.y))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.x))(^y.(a a))) REDUCED to normal form. ------ 178270/20504763. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(^z.(a a)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 178271/20504979. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 178272/20505084. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(x1 x1))(a (a a)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178273/20505366. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(z1 b))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(z1 b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178274/20505528. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.((a a) a))) 3. ==[ beta ]==> ((^y.y)(^x1.((a a) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((a a) a))) 5. ==[ beta ]==> (^y.((a a) a)) 6. ==[ alpha ]==> (^x.((a a) a)) REDUCED to normal form. ------ 178275/20505699. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.a))) REDUCED to normal form. ------ 178276/20505903. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 178277/20506302. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 178278/20506932. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.((^z.z) y))) 3. ==[ eta ]==> (((^x.b)(b a))(^z.z)) 4. ==[ alpha ]==> (((^x.b)(b a))(^y.y)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178279/20506995. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.c)) REDUCED to normal form. ------ 178280/20507157. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.y1)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.y1)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178281/20507199. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178282/20507202. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.b)) REDUCED to normal form. ------ 178283/20507220. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 178284/20507247. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 178285/20507277. ------ 1. ==[ start ]==> ((a (^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.x))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 178286/20507295. ------ 1. ==[ start ]==> ((a (a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 178287/20507304. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 178288/20507322. ------ 1. ==[ start ]==> ((a b)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 178289/20507340. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 178290/20507367. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 178291/20507394. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 178292/20507421. ------ 1. ==[ start ]==> (((a a) b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a) b)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 178293/20507448. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.(^z.z)))) REDUCED to normal form. ------ 178294/20507502. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)(^z.b))) REDUCED to normal form. ------ 178295/20507556. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 178296/20507565. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 178297/20507592. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.b)(b a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.b)(b a))) 3. ==[ beta ]==> ((a a)((^y.b)(b a))) 4. ==[ alpha ]==> ((a a)((^x.b)(b a))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 178298/20507637. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 178299/20507745. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 178300/20507781. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a a) a)((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> (((a a) a)((^z.z)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 178301/20508186. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 178302/20508222. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178303/20508249. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 178304/20508303. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (a a)))) 7. ==[ beta ]==> (((^y.y) b)(a (a a))) 8. ==[ alpha ]==> (((^x.x) b)(a (a a))) 9. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 178305/20508357. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b a)((a a) a))) 5. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 7. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 178306/20508384. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))(a b)) 6. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 178307/20508438. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 178308/20508618. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a a))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a a))(a (^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(y (^z.z))))) 6. ==[ alpha ]==> ((a a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 178309/20508771. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((b a)(^z.a))) 3. ==[ beta ]==> (((^y.y) b)((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.x) b)((b a)(^y.a))) 5. ==[ beta ]==> (b ((b a)(^y.a))) 6. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 178310/20508798. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a) a)(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 178311/20508852. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 178312/20508906. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (a a))(^x.a))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 178313/20508933. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (a a))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178314/20508996. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 178315/20509023. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 178316/20509131. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.(y y))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(x x))) REDUCED to normal form. ------ 178317/20509158. ------ 1. ==[ start ]==> ((a (a b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 178318/20509437. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a (^y.y))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 178319/20509518. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (b (((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (b (((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (b (b ((^y.y) a))) 6. ==[ alpha ]==> (b (b ((^x.x) a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 178320/20509545. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 178321/20509761. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178322/20509788. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 178323/20509932. ------ 1. ==[ start ]==> (((a b) b)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b) b)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 178324/20509959. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) a)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 178325/20509986. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 178326/20510013. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a a)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a)(^z.b))) REDUCED to normal form. ------ 178327/20510067. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 178328/20510121. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178329/20510148. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 178330/20510211. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 178331/20510292. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.a)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.a)) REDUCED to normal form. ------ 178332/20510319. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 178333/20510373. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 178334/20510400. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.b))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 178335/20510427. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 178336/20510598. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(a (b (^z.z)))) 3. ==[ beta ]==> (b (a (b (^z.z)))) 4. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 178337/20510607. ------ 1. ==[ start ]==> (((a b) c)((^d.(^a.a)) a)) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y)) a)) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 178338/20510634. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(a a)) b)) 3. ==[ beta ]==> (((a a) b)((^y.(a a)) b)) 4. ==[ alpha ]==> (((a a) b)((^x.(a a)) b)) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 178339/20510661. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y) c)) 3. ==[ beta ]==> ((((a a)(^x.x)) a) c) REDUCED to normal form. ------ 178340/20510679. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 178341/20510706. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((b a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((b a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((b a)(a (a a)))) 5. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 178342/20510760. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a a)((a a) a))) REDUCED to normal form. ------ 178343/20510841. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b ((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (b ((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 178344/20510940. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 178345/20510994. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))(a a))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))(a a))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))(a a))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 178346/20511021. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(a (^x.x))) REDUCED to normal form. ------ 178347/20511048. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) a)) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a)) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178348/20511102. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 178349/20511129. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(a a))((a a) a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 178350/20511156. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.b)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) b) REDUCED to normal form. ------ 178351/20511183. ------ 1. ==[ start ]==> ((a (b a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 178352/20511624. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(c (a (^y.(^z.z))))) 3. ==[ beta ]==> (b (c (a (^y.(^z.z))))) 4. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 178353/20511732. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.(^y1.y1)))(a (^z1.z1)))) REDUCED to normal form. ------ 178354/20512308. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 178355/20512335. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a a)(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 178356/20512416. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((b a) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((b a) c)) REDUCED to normal form. ------ 178357/20512623. ------ 1. ==[ start ]==> ((a (^b.b))(c (b a))) 2. ==[ alpha ]==> ((a (^x.x))(c (b a))) REDUCED to normal form. ------ 178358/20512641. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 178359/20512668. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 178360/20512938. ------ 1. ==[ start ]==> ((a ((^a.a) b))(c (^d.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(c (^y.a))) 3. ==[ beta ]==> ((a b)(c (^y.a))) 4. ==[ alpha ]==> ((a b)(c (^x.a))) REDUCED to normal form. ------ 178361/20512947. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(b a))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(b a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(b a))) 5. ==[ beta ]==> ((a (^y.y))(b a)) 6. ==[ alpha ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 178362/20512974. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 178363/20513226. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 178364/20513280. ------ 1. ==[ start ]==> (((a a)(^b.b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178365/20513307. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1))) a)) REDUCED to normal form. ------ 178366/20513883. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 178367/20514378. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(c ((^y.y)(a a)))) 3. ==[ beta ]==> (((b a)(b a))(c ((^y.y)(a a)))) 4. ==[ alpha ]==> (((b a)(b a))(c ((^x.x)(a a)))) 5. ==[ beta ]==> (((b a)(b a))(c (a a))) REDUCED to normal form. ------ 178368/20514459. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a)(^y.y))(a a))) 3. ==[ beta ]==> (b (((a a)(^y.y))(a a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a a))) REDUCED to normal form. ------ 178369/20514468. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 178370/20514567. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178371/20514666. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 178372/20514747. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))(b a))(a a)) REDUCED to normal form. ------ 178373/20514774. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 178374/20514828. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 178375/20514855. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(y y))((a a) a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(y y))((a a) a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(x x))((a a) a))) 5. ==[ beta ]==> (((a a)((a a) a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 178376/20514882. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.a)(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 178377/20514936. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)(^z.z))) REDUCED to normal form. ------ 178378/20514963. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 178379/20514990. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a a)) REDUCED to normal form. ------ 178380/20515017. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.b)(^z.a))) 3. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 178381/20515188. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(a ((a a)(^z.z)))) 3. ==[ beta ]==> (b (a ((a a)(^z.z)))) 4. ==[ alpha ]==> (b (a ((a a)(^x.x)))) REDUCED to normal form. ------ 178382/20515296. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(^z1.z1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178383/20515404. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b (^y.y))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b (^x.x))((a a)(a a))) REDUCED to normal form. ------ 178384/20515467. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 178385/20515494. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((a a) a)(^x1.a))) REDUCED to normal form. ------ 178386/20515575. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a (^z.a))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(a (^y.a))) REDUCED to normal form. ------ 178387/20515602. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 178388/20515683. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a b) b)) REDUCED to normal form. ------ 178389/20515710. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((a a) a) c)) 3. ==[ beta ]==> ((b (^y.a))(((a a) a) c)) 4. ==[ alpha ]==> ((b (^x.a))(((a a) a) c)) REDUCED to normal form. ------ 178390/20515800. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 178391/20515827. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 178392/20515854. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.(a a)))) 7. ==[ beta ]==> ((a b)(^y.(a a))) 8. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 178393/20516070. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a (^z.(a a)))) REDUCED to normal form. ------ 178394/20516097. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.b)(a a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.b)(a a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.b)(a a))) 5. ==[ beta ]==> ((b a)((^y.b)(a a))) 6. ==[ alpha ]==> ((b a)((^x.b)(a a))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 178395/20516178. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))((a (a a))(a (a a)))) REDUCED to normal form. ------ 178396/20516457. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(a (a b))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178397/20516592. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 178398/20516619. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a a)((a a) a))) 3. ==[ beta ]==> ((^y.y)((a a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a a)((a a) a))) 5. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 178399/20516682. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 178400/20516709. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a (a a))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (a a))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (a a))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (a a))(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))(^x1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178401/20516763. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 178402/20516790. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a a)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.a))) REDUCED to normal form. ------ 178403/20516817. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((a a) a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((a a) a) a)) REDUCED to normal form. ------ 178404/20516871. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a)) c)) REDUCED to normal form. ------ 178405/20516997. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(a a))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 178406/20517096. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b (^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 178407/20517150. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(a a))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 178408/20517177. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 178409/20517204. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.a)((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 178410/20517231. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 178411/20517285. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 178412/20517312. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b (a (a a)))(^y.y)) 8. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 178413/20517339. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(^y.a))) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 178414/20517393. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 178415/20517411. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 178416/20517429. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (a a))(a a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (a a))(a a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))(a a))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 178417/20517816. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) c)) 5. ==[ beta ]==> (b ((^y.(^z.z)) c)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178418/20517834. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a)((^x1.x1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a))) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 178419/20517870. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a (^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a (^z.z))) REDUCED to normal form. ------ 178420/20517978. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z)) b)) 5. ==[ beta ]==> ((^y.y)((a (^z.z)) b)) 6. ==[ alpha ]==> ((^x.x)((a (^y.y)) b)) 7. ==[ beta ]==> ((a (^y.y)) b) 8. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 178421/20518023. ------ 1. ==[ start ]==> (((^a.b)(b a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))(a ((^y.y) a))) 3. ==[ beta ]==> (b (a ((^y.y) a))) 4. ==[ alpha ]==> (b (a ((^x.x) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 178422/20518086. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) c) REDUCED to normal form. ------ 178423/20518131. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b b)) 3. ==[ beta ]==> ((^y.(^z.z))(b b)) 4. ==[ alpha ]==> ((^x.(^y.y))(b b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178424/20518167. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1)) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1)) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 178425/20518194. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a) b)) REDUCED to normal form. ------ 178426/20518248. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178427/20518266. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b a)) 3. ==[ beta ]==> (((a a)(^y.y))(b a)) 4. ==[ alpha ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 178428/20518275. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 178429/20518293. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a b)) REDUCED to normal form. ------ 178430/20518311. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 178431/20518338. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a (^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 178432/20518854. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 178433/20529384. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178434/20529522. ------ 1. ==[ start ]==> (((^a.a)(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178435/20529546. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178436/20529591. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> (((b (^z.z))(^x1.a))(^y.y)) 4. ==[ alpha ]==> (((b (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 178437/20529951. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 178438/20529954. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 178439/20530275. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178440/20530401. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178441/20530833. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((((^y.(^z.z)) a)(^x1.x1))(((^y.(^z.z)) a)(^x1.x1)))(((^y.(^z.z)) a)(^x1.x1))) 4. ==[ alpha ]==> (((((^x.(^y.y)) a)(^z.z))(((^x1.(^y1.y1)) a)(^z1.z1)))(((^x2.(^y2.y2)) a)(^z2.z2))) 5. ==[ beta ]==> ((((^y.y)(^z.z))(((^x1.(^y1.y1)) a)(^z1.z1)))(((^x2.(^y2.y2)) a)(^z2.z2))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(((^z.(^x1.x1)) a)(^y1.y1)))(((^z1.(^x2.x2)) a)(^y2.y2))) 7. ==[ beta ]==> (((^y.y)(((^z.(^x1.x1)) a)(^y1.y1)))(((^z1.(^x2.x2)) a)(^y2.y2))) 8. ==[ alpha ]==> (((^x.x)(((^y.(^z.z)) a)(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.x2))) 9. ==[ beta ]==> ((((^y.(^z.z)) a)(^x1.x1))(((^y1.(^z1.z1)) a)(^x2.x2))) 10. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.(^y1.y1)) a)(^z1.z1))) 11. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(^y1.y1)) a)(^z1.z1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 13. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.y1))) 14. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.x1))) 15. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.x1)) 16. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z)) 17. ==[ beta ]==> ((^y.y)(^z.z)) 18. ==[ alpha ]==> ((^x.x)(^y.y)) 19. ==[ beta ]==> (^y.y) 20. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178442/20531166. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 178443/20531637. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a (a a))(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 178444/20532798. ------ 1. ==[ start ]==> (((a b) c)(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(b (^y.y)))) REDUCED to normal form. ------ 178445/20533371. ------ 1. ==[ start ]==> ((^a.(b a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(((a a) a)(^y.(a a)))) 3. ==[ eta ]==> (b (((a a) a)(^y.(a a)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 178446/20533878. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((x1 x1)(x1 x1)))) REDUCED to normal form. ------ 178447/20534544. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.(^y.y))(b a))(^x1.x1)) 4. ==[ alpha ]==> (((^x.(^y.y))(b a))(^z.z)) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178448/20535489. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(^y1.(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^y1.(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(a (^y.(^z.z)))) REDUCED to normal form. ------ 178449/20536125. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((((a a)(^y.y))(^z.(^x1.x1)))(((a a)(^y.y))(^z.(^x1.x1))))((((a a)(^y.y))(^z.(^x1.x1)))(((a a)(^y.y))(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1))))((((a a)(^x2.x2))(^y2.(^z2.z2)))(((a a)(^x3.x3))(^y3.(^z3.z3))))) REDUCED to normal form. ------ 178450/20536632. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^a.(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(b y))) 3. ==[ eta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 178451/20537205. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a b) c)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a b) c)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178452/20537379. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 178453/20538366. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (a a))(^x1.(x1 x1)))) 3. ==[ eta ]==> ((^y.(^z.z))((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178454/20538459. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(a z))) 3. ==[ eta ]==> (((^x.(x x))(^y.y)) a) 4. ==[ beta ]==> (((^y.y)(^y.y)) a) 5. ==[ alpha ]==> (((^x.x)(^y.y)) a) 6. ==[ beta ]==> ((^y.y) a) 7. ==[ alpha ]==> ((^x.x) a) 8. ==[ beta ]==> a REDUCED to normal form. ------ 178455/20538648. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178456/20539170. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(^x1.((x1 x1) x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((x1 x1) x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((z z) z))) 5. ==[ beta ]==> ((^y.y)(^z.((z z) z))) 6. ==[ alpha ]==> ((^x.x)(^y.((y y) y))) 7. ==[ beta ]==> (^y.((y y) y)) 8. ==[ alpha ]==> (^x.((x x) x)) REDUCED to normal form. ------ 178457/20539602. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 178458/20539608. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((^z.(^x1.x1)) a)(((^z.(^x1.x1)) a)(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.(^x1.x1)) a)(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.x1))) 7. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.x1)) 8. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178459/20540052. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 178460/20540133. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^x.a)) REDUCED to normal form. ------ 178461/20540214. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.a))) 3. ==[ beta ]==> (b (^y.(^z.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 178462/20540277. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 178463/20540358. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 178464/20540457. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 178465/20540481. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178466/20540484. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(a a))) REDUCED to normal form. ------ 178467/20540529. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.a)) REDUCED to normal form. ------ 178468/20540577. ------ 1. ==[ start ]==> (((^a.a) a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x) a)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (a ((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (a ((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> (a ((a (^x.x))(^z.z))) 6. ==[ alpha ]==> (a ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 178469/20540595. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 178470/20540604. ------ 1. ==[ start ]==> (((a a) a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 178471/20540622. ------ 1. ==[ start ]==> (((^a.a)(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 178472/20540649. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 178473/20540667. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 178474/20540694. ------ 1. ==[ start ]==> ((a (a (^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 178475/20540757. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 178476/20540784. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178477/20540829. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 178478/20540892. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.b)(b a))) 3. ==[ beta ]==> ((^y.a)((^z.b)(b a))) 4. ==[ alpha ]==> ((^x.a)((^y.b)(b a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 178479/20540973. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> (a ((^y.(y y))((a a)(a a)))) 6. ==[ alpha ]==> (a ((^x.(x x))((a a)(a a)))) 7. ==[ beta ]==> (a (((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 178480/20541000. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 178481/20541054. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a (^x.(x x)))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a (a (^y.y)))) REDUCED to normal form. ------ 178482/20541072. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (a (^y.y))) a)) 3. ==[ beta ]==> (((a a) a)((a (a (^y.y))) a)) 4. ==[ alpha ]==> (((a a) a)((a (a (^x.x))) a)) REDUCED to normal form. ------ 178483/20541099. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 178484/20541126. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((b (^y.y)) c)) 3. ==[ beta ]==> ((a (a a))((b (^y.y)) c)) 4. ==[ alpha ]==> ((a (a a))((b (^x.x)) c)) REDUCED to normal form. ------ 178485/20541189. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178486/20541297. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178487/20541378. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 178488/20541468. ------ 1. ==[ start ]==> (((^a.(a a)) b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((b b)(b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((b b)(b ((^x.(^y.y)) a))) 5. ==[ beta ]==> ((b b)(b (^y.y))) 6. ==[ alpha ]==> ((b b)(b (^x.x))) REDUCED to normal form. ------ 178489/20541504. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 178490/20541603. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> (((a (a a)) b)(b (a (a a)))) REDUCED to normal form. ------ 178491/20541630. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (a ((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (a ((a (^x.(^y.y)))(^x1.x1))) 8. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 178492/20541657. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)((a a) a))) REDUCED to normal form. ------ 178493/20541684. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 178494/20541711. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.a))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.a))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.a))((a a)(a a))) REDUCED to normal form. ------ 178495/20541738. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 178496/20541765. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(b a))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(b a))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(b a))) 7. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 178497/20541936. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.(^y.y)) a)(^z.z))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 178498/20542026. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.z)(a (a a)))) 5. ==[ beta ]==> (a ((^z.z)(a (a a)))) 6. ==[ alpha ]==> (a ((^x.x)(a (a a)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 178499/20542134. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178500/20542269. ------ 1. ==[ start ]==> ((a (^a.b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 178501/20542341. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((a (a (a a)))(((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.(^y.y)) a) a)) 5. ==[ beta ]==> ((a (a (a a)))((^y.y) a)) 6. ==[ alpha ]==> ((a (a (a a)))((^x.x) a)) 7. ==[ beta ]==> ((a (a (a a))) a) REDUCED to normal form. ------ 178502/20542368. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((b (^y.y)) b)) 3. ==[ beta ]==> (((a (a a)) a)((b (^y.y)) b)) 4. ==[ alpha ]==> (((a (a a)) a)((b (^x.x)) b)) REDUCED to normal form. ------ 178503/20542458. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 178504/20542539. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))(^x1.(a a)))) IRREDUCIBLE: cycle. ------ 178505/20542620. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178506/20542647. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((a b)((^y.(y y))(^z.z))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(^y.y))) 5. ==[ beta ]==> ((a b)((^y.y)(^y.y))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 178507/20542674. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(a a))) 6. ==[ alpha ]==> ((^x.a)(^y.(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 178508/20542710. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (b (^z.z)))) REDUCED to normal form. ------ 178509/20542737. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 178510/20542764. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z))(a a))) 5. ==[ beta ]==> ((^y.a)((b (^z.z))(a a))) 6. ==[ alpha ]==> ((^x.a)((b (^y.y))(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 178511/20542791. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 178512/20542818. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.x))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a b)(^x.x))(b ((^y.y) a))) 5. ==[ beta ]==> (((a b)(^x.x))(b a)) REDUCED to normal form. ------ 178513/20543007. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (b ((^y.y)(b a))) 6. ==[ alpha ]==> (b ((^x.x)(b a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 178514/20543079. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(c (^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(c (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(a a)))) 5. ==[ beta ]==> (c (^y.(a a))) 6. ==[ alpha ]==> (c (^x.(a a))) REDUCED to normal form. ------ 178515/20543214. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (b ((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178516/20543295. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178517/20543349. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)((^z1.z1)(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)((^z1.z1)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)((^y1.y1)(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)((^y1.y1)(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)((^x1.x1)(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.b)((^x1.x1)(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(a a)))) 11. ==[ beta ]==> ((^y.b)((^z.z)(a a))) 12. ==[ alpha ]==> ((^x.b)((^y.y)(a a))) 13. ==[ beta ]==> b REDUCED to normal form. ------ 178518/20543430. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 178519/20543529. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((b (^y.y)) a)) REDUCED to normal form. ------ 178520/20543556. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((a a)(a a)) b)) 3. ==[ beta ]==> ((a ((a a) a))(((a a)(a a)) b)) REDUCED to normal form. ------ 178521/20543583. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((^z.z) b) c)) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z) b) c)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) b) c)) 5. ==[ beta ]==> (((a (a a))(^x.x))(b c)) REDUCED to normal form. ------ 178522/20543754. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 178523/20543898. ------ 1. ==[ start ]==> (((a b) c)(a (b (^a.a)))) 2. ==[ alpha ]==> (((a b) c)(a (b (^x.x)))) REDUCED to normal form. ------ 178524/20543925. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a)(a a))(a a))) 3. ==[ beta ]==> (((a a) b)(((a a)(a a))(a a))) REDUCED to normal form. ------ 178525/20543952. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (a (^y.y)))) REDUCED to normal form. ------ 178526/20544006. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((b a)(a (a a)))) REDUCED to normal form. ------ 178527/20544033. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b))(((a a)(^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 178528/20544087. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a b)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178529/20544114. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(((a a) a)(a a))) REDUCED to normal form. ------ 178530/20544141. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(^x.a))((a a)(^z.z))) 6. ==[ alpha ]==> (((a b)(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 178531/20544168. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (a a))(b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (a a))(b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))(b a))) REDUCED to normal form. ------ 178532/20544195. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 178533/20544285. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(a a))(^y.y))) 3. ==[ beta ]==> ((a (a b))(((a a)(a a))(^y.y))) 4. ==[ alpha ]==> ((a (a b))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 178534/20544312. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 178535/20544339. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(^z1.a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.a))) 7. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.a))) 8. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.a))) 9. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.a)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 178536/20544366. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((b a)(^x.(x x)))) REDUCED to normal form. ------ 178537/20544393. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 178538/20544447. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a b)(^y.b))) REDUCED to normal form. ------ 178539/20544474. ------ 1. ==[ start ]==> ((a (b a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (b a))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 178540/20544564. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (b ((^z.a)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b ((^x.a)(a (^y.(^z.z))))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178541/20544645. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 178542/20544753. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 178543/20544780. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((^y.(a a))(^z.a)) 6. ==[ alpha ]==> ((^x.(a a))(^y.a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178544/20544834. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 178545/20544915. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178546/20544924. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 178547/20544951. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(b ((^z.z) b))) 3. ==[ beta ]==> (((a a)(^y.a))(b ((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.a))(b ((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.a))(b b)) REDUCED to normal form. ------ 178548/20544978. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a ((a a)(a a)))) REDUCED to normal form. ------ 178549/20545041. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.(^z.z))) c)) 3. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 178550/20545302. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178551/20545482. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)((a a) a))) 3. ==[ beta ]==> (b ((^x1.b)((a a) a))) 4. ==[ alpha ]==> (b ((^x.b)((a a) a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 178552/20545590. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178553/20545617. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 178554/20545644. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((^y.y)((^z.z) b)) 6. ==[ alpha ]==> ((^x.x)((^y.y) b)) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 178555/20545698. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 9. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 10. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 178556/20545779. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 178557/20545986. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.z) a)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.z) a)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y) a)) 5. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 178558/20546013. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 178559/20546193. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178560/20546238. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(c (^d.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.a))) 3. ==[ beta ]==> ((^y.y)(c (^z.a))) 4. ==[ alpha ]==> ((^x.x)(c (^y.a))) 5. ==[ beta ]==> (c (^y.a)) 6. ==[ alpha ]==> (c (^x.a)) REDUCED to normal form. ------ 178561/20546265. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(b (^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(b (^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 178562/20546400. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (b ((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 178563/20546508. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(z1 z1))((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178564/20546562. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(b a))) 5. ==[ beta ]==> (b ((^y.(^z.z))(b a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178565/20546589. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.y1)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 178566/20546724. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 178567/20546832. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178568/20546868. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(b (b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(b (b a))) 3. ==[ beta ]==> ((b (^y.y))(b (b a))) 4. ==[ alpha ]==> ((b (^x.x))(b (b a))) REDUCED to normal form. ------ 178569/20546904. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 178570/20546958. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y)) c)) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 178571/20547201. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((b a)(^y.y))) 3. ==[ beta ]==> ((b (a a))((b a)(^y.y))) 4. ==[ alpha ]==> ((b (a a))((b a)(^x.x))) REDUCED to normal form. ------ 178572/20547228. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 178573/20547264. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(a a))((^y.y) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178574/20547399. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178575/20547507. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178576/20547615. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178577/20547669. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 178578/20547732. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(a (b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a (b a))) REDUCED to normal form. ------ 178579/20547759. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 178580/20547813. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b) a)) REDUCED to normal form. ------ 178581/20547867. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 178582/20547894. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a))((a a) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a))((a a) a))) REDUCED to normal form. ------ 178583/20547921. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y) a)(a b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a (a b))) REDUCED to normal form. ------ 178584/20548011. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 178585/20548038. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(b a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 178586/20548065. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.a))) REDUCED to normal form. ------ 178587/20548092. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a) a)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)(^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 178588/20548119. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 178589/20548173. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.b))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.b))) REDUCED to normal form. ------ 178590/20548254. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((a a)(^z.z)) a)) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a)(^z.z)) a)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 178591/20548281. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x)(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a a) b)) REDUCED to normal form. ------ 178592/20548308. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a b) c)) 2. ==[ alpha ]==> ((a (b (^x.x)))((a b) c)) REDUCED to normal form. ------ 178593/20548479. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 178594/20548623. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b c)((a (a a))((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b c)((a (a a))((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b c)((a (a a))(^y.y))) 6. ==[ alpha ]==> ((b c)((a (a a))(^x.x))) REDUCED to normal form. ------ 178595/20548650. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x) a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a ((a a) a))) REDUCED to normal form. ------ 178596/20548695. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(b (^z.(a a)))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 178597/20548776. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b)(a (^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 178598/20548857. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> (b ((^y.y)(^z.z))) 10. ==[ alpha ]==> (b ((^x.x)(^y.y))) 11. ==[ beta ]==> (b (^y.y)) 12. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178599/20548965. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178600/20549172. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 178601/20549199. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.b) b)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.b) b)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.b) b)) 5. ==[ beta ]==> ((b a)((^y.b) b)) 6. ==[ alpha ]==> ((b a)((^x.b) b)) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 178602/20549388. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a b)(^z.z))) 3. ==[ beta ]==> ((b ((^y.y) a))((a b)(^z.z))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a b)(^y.y))) 5. ==[ beta ]==> ((b a)((a b)(^y.y))) 6. ==[ alpha ]==> ((b a)((a b)(^x.x))) REDUCED to normal form. ------ 178603/20549415. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 178604/20549469. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 178605/20549559. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a b))) 5. ==[ beta ]==> ((^y.y)((^z.z)(a b))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a b))) 7. ==[ beta ]==> ((^y.y)(a b)) 8. ==[ alpha ]==> ((^x.x)(a b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 178606/20549640. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178607/20549748. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178608/20549865. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> (a (((^y.y) a)(a (a a)))) 6. ==[ alpha ]==> (a (((^x.x) a)(a (a a)))) 7. ==[ beta ]==> (a (a (a (a a)))) REDUCED to normal form. ------ 178609/20549910. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(b (^x1.a))) 3. ==[ beta ]==> ((^y.y)(b (^x1.a))) 4. ==[ alpha ]==> ((^x.x)(b (^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 178610/20549964. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(a a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(a a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(a a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(a a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(a a))) 7. ==[ beta ]==> ((b b)((^y.a)(a a))) 8. ==[ alpha ]==> ((b b)((^x.a)(a a))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 178611/20550045. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (b ((^z.a)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.a)(a (a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178612/20550153. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178613/20550216. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (a (a a)))) REDUCED to normal form. ------ 178614/20550270. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(a ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((a a) a))) 5. ==[ beta ]==> ((^y.y)(a ((a a) a))) 6. ==[ alpha ]==> ((^x.x)(a ((a a) a))) 7. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 178615/20550306. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 178616/20550333. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z)) c)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(c c)) REDUCED to normal form. ------ 178617/20550441. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 178618/20550468. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 178619/20550495. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.a))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^y.a))) 7. ==[ beta ]==> (((a a)(a a))(a (^y.a))) 8. ==[ alpha ]==> (((a a)(a a))(a (^x.a))) REDUCED to normal form. ------ 178620/20550522. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 178621/20550576. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1)(^z1.z1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(^y1.y1)) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1) a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1) a)) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 178622/20550603. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (a a)) b)) 3. ==[ beta ]==> ((b (a (a a)))((a (a a)) b)) REDUCED to normal form. ------ 178623/20550702. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 178624/20550711. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 178625/20551107. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b ((a (^y.y))(a (^z.z)))) 6. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 178626/20551125. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b (^x1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(b (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.a))) 5. ==[ beta ]==> ((^y.y)(b (^z.a))) 6. ==[ alpha ]==> ((^x.x)(b (^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 178627/20551134. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a)((^y.y) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((a a) a)) REDUCED to normal form. ------ 178628/20551152. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(a (^z.(z z)))) 3. ==[ beta ]==> ((a (a (^y.y)))(a (^z.(z z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 178629/20551179. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a)(a a))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a a))) 5. ==[ beta ]==> ((^y.a)(a a)) 6. ==[ alpha ]==> ((^x.a)(a a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 178630/20551233. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y) a)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x) a)) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 178631/20551269. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c (a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(c (a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c (a a))) 5. ==[ beta ]==> ((^y.y)(c (a a))) 6. ==[ alpha ]==> ((^x.x)(c (a a))) 7. ==[ beta ]==> (c (a a)) REDUCED to normal form. ------ 178632/20551296. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b (a (^x1.x1)))) REDUCED to normal form. ------ 178633/20551314. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y)(^z.a))) 3. ==[ beta ]==> (b ((^y.y)(^z.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 178634/20551377. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a)(a (^z.z)))) REDUCED to normal form. ------ 178635/20551422. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178636/20551458. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a c)) REDUCED to normal form. ------ 178637/20551485. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b (a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b (a a))) REDUCED to normal form. ------ 178638/20551539. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178639/20551557. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 178640/20551566. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b a)) REDUCED to normal form. ------ 178641/20551584. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(a a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 178642/20551602. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a) a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a) a)) REDUCED to normal form. ------ 178643/20551629. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 178644/20551655. ------ 1. ==[ start ]==> (^a.(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (^x.(((^y.y) x)(b (^z.z)))) 3. ==[ beta ]==> (^x.(x (b (^z.z)))) 4. ==[ alpha ]==> (^x.(x (b (^y.y)))) REDUCED to normal form. ------ 178645/20551656. ------ 1. ==[ start ]==> (a (((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (a (((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> (a (a (b (^y.y)))) 4. ==[ alpha ]==> (a (a (b (^x.x)))) REDUCED to normal form. ------ 178646/20551713. ------ 1. ==[ start ]==> ((^a.b)(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 178647/20552604. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178648/20561811. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^z.((^x1.x1)(^y1.y1)))((^z.((^x1.x1)(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.((^y1.y1)(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178649/20562684. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178650/20562759. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a))) a) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y))) a) 3. ==[ beta ]==> ((a (b (^y.y))) a) 4. ==[ alpha ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 178651/20562765. ------ 1. ==[ start ]==> ((^a.a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 4. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 5. ==[ beta ]==> (a (b (^y.y))) 6. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 178652/20562792. ------ 1. ==[ start ]==> ((^a.(a a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x x))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^y.y))((^z.(^x1.x1)) a))((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1))((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))((a (^z.z))(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 178653/20562819. ------ 1. ==[ start ]==> ((^a.b)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)((a a)(a (a (^y.y))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 178654/20562822. ------ 1. ==[ start ]==> ((a b)(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 178655/20562840. ------ 1. ==[ start ]==> (((a a)(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 178656/20562855. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178657/20563017. ------ 1. ==[ start ]==> ((^a.(^b.a))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.x))((b a)(^z.b))) 3. ==[ beta ]==> (^y.((b a)(^z.b))) 4. ==[ alpha ]==> (^x.((b a)(^y.b))) REDUCED to normal form. ------ 178658/20563260. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 178659/20563710. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(a (a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178660/20563713. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 178661/20564475. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 178662/20565249. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(((a (a a))(a (^z.(^x1.x1))))((a (a a))(a (^z.(^x1.x1)))))) 4. ==[ alpha ]==> ((^x.x)(((a (a a))(a (^y.(^z.z))))((a (a a))(a (^x1.(^y1.y1)))))) 5. ==[ beta ]==> (((a (a a))(a (^y.(^z.z))))((a (a a))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (a a))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 178663/20566107. ------ 1. ==[ start ]==> (((a b) c)(^b.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 178664/20567187. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.(a a)))) REDUCED to normal form. ------ 178665/20567229. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.b) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178666/20567517. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a a)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)((^x1.x1) b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(^z.z))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 178667/20567853. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178668/20568195. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.((^z.z) b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 178669/20568435. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 178670/20568807. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(a (^z1.(^x2.x2))))) REDUCED to normal form. ------ 178671/20569113. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 178672/20570193. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 178673/20571381. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^z.(z z))) REDUCED to normal form. ------ 178674/20571768. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.b))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.b))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 7. ==[ beta ]==> (^y.(^z.b)) 8. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 178675/20572317. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((a a) a))) REDUCED to normal form. ------ 178676/20572479. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.a))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 7. ==[ beta ]==> (^y.(^z.a)) 8. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 178677/20572911. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 178678/20572917. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^z.z)(^x1.x1)))((a ((^z.z)(^x1.x1)))(^y.y))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a ((^z.z)(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((a (^y.y))((a ((^z.z)(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.x))((a ((^y.y)(^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((a (^x.x))((a (^z.z))(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 178679/20572920. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 178680/20573370. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 178681/20573523. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.c)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.y)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178682/20573667. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 178683/20573766. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.z)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 178684/20573775. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 178685/20573790. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(^y1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178686/20573793. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 178687/20573811. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.b)) REDUCED to normal form. ------ 178688/20573838. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(x1 x1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 178689/20573865. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.z)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 178690/20573877. ------ 1. ==[ start ]==> ((a a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a a)(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> ((a a)(a (b (^y.y)))) 4. ==[ alpha ]==> ((a a)(a (b (^x.x)))) REDUCED to normal form. ------ 178691/20573904. ------ 1. ==[ start ]==> ((a (a a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a a))((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a a))((a (^x.x))(^z.z))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 178692/20573922. ------ 1. ==[ start ]==> (((a a) a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 178693/20573931. ------ 1. ==[ start ]==> ((a b)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a b)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 178694/20573949. ------ 1. ==[ start ]==> (((a a)(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178695/20573967. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 178696/20573976. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (b ((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> (b ((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 178697/20574021. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178698/20574048. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 178699/20574075. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 178700/20574084. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 178701/20574111. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 178702/20574129. ------ 1. ==[ start ]==> ((a (^b.a))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.a))((b a)(^y.b))) REDUCED to normal form. ------ 178703/20574165. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178704/20574237. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 178705/20574246. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 178706/20574273. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 178707/20574300. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 178708/20574327. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 178709/20574354. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 178710/20574372. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 178711/20574543. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 178712/20574624. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 178713/20574795. ------ 1. ==[ start ]==> (((a (a a))(a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a a))(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a (a a))(a a))(b (^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))(b (^x.x))) REDUCED to normal form. ------ 178714/20574822. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((a (^y.y))(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((a (^x.x))(a (a (a (^y.y))))) REDUCED to normal form. ------ 178715/20574831. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 (^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178716/20575119. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 178717/20575146. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a (a a)) b)) REDUCED to normal form. ------ 178718/20575173. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)((a a)(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)((a a)(a a)))) 7. ==[ beta ]==> ((a a)(a ((a a)(a a)))) REDUCED to normal form. ------ 178719/20575200. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 178720/20575227. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((a a)((^y.(^z.z)) a))) 6. ==[ alpha ]==> ((a a)((a a)((^x.(^y.y)) a))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 178721/20575290. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 178722/20575344. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (a (((^z.z) b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (a (((^x.x) b)(^y.(y y)))) 7. ==[ beta ]==> (a (b (^y.(y y)))) 8. ==[ alpha ]==> (a (b (^x.(x x)))) REDUCED to normal form. ------ 178723/20575380. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 178724/20575425. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 178725/20575452. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(a a))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(a a))) 7. ==[ beta ]==> ((a a)(^y.(a a))) 8. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 178726/20575461. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 178727/20575488. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 178728/20575515. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a)(b a))) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 178729/20575542. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178730/20575569. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(b ((^z.z) b))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(b ((^y.y) b))) 7. ==[ beta ]==> ((((a a) a)(^x.x))(b b)) REDUCED to normal form. ------ 178731/20575587. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.b))(a (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(a (^y.(a a)))) REDUCED to normal form. ------ 178732/20575758. ------ 1. ==[ start ]==> (((^a.b) a)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 178733/20575920. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.a)(^d.a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 178734/20575947. ------ 1. ==[ start ]==> (((a b) a)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 178735/20575974. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 178736/20576127. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(a a)) c)) 3. ==[ beta ]==> (b ((^y.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 178737/20576172. ------ 1. ==[ start ]==> (((a a)(a b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a a)(a b))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 178738/20576199. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((b a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((b a)(^y.y))) REDUCED to normal form. ------ 178739/20576226. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))((a a) a))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 178740/20576253. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(a a))(a b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(a b))) REDUCED to normal form. ------ 178741/20576280. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((a b)((^y.y)(a a)))) 7. ==[ beta ]==> (a ((a b)((^y.y)(a a)))) 8. ==[ alpha ]==> (a ((a b)((^x.x)(a a)))) 9. ==[ beta ]==> (a ((a b)(a a))) REDUCED to normal form. ------ 178742/20576307. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 178743/20576334. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)(b a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)(b a))) 5. ==[ beta ]==> (((a b)(a a))(b a)) REDUCED to normal form. ------ 178744/20576361. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (a a))((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (a a))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 178745/20576532. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (b (((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.a))) 5. ==[ beta ]==> (b (b (^y.a))) 6. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 178746/20576541. ------ 1. ==[ start ]==> (((a b) b)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b) b)((^x.x)((^y.y) a))) 3. ==[ beta ]==> (((a b) b)((^y.y) a)) 4. ==[ alpha ]==> (((a b) b)((^x.x) a)) 5. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 178747/20576568. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 178748/20576586. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)((b a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 178749/20576613. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 178750/20576622. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 178751/20576667. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)(^y1.(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)(^y1.(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(^x1.(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.(a a)))) 9. ==[ beta ]==> ((^y.y)((a b)(^z.(a a)))) 10. ==[ alpha ]==> ((^x.x)((a b)(^y.(a a)))) 11. ==[ beta ]==> ((a b)(^y.(a a))) 12. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 178752/20576676. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 178753/20576730. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 178754/20576748. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 178755/20576757. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 178756/20576784. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 178757/20576973. ------ 1. ==[ start ]==> (((^a.b) c)((^d.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 178758/20577216. ------ 1. ==[ start ]==> (((a b) c)((^a.a)(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 178759/20577288. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.z) c)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z) c)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y) c)) 5. ==[ beta ]==> (((a a)(^x.x)) c) REDUCED to normal form. ------ 178760/20577549. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 178761/20577576. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 178762/20577882. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b (a (^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> (b (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 178763/20577963. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a)(a a)) a)) 3. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 178764/20578026. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 178765/20578134. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.b)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.b)(^z.b))) 5. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 178766/20578161. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 178767/20578242. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 178768/20578269. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 178769/20578341. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.b) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1) b)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 178770/20578359. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 178771/20578386. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((b a) a)) REDUCED to normal form. ------ 178772/20578413. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(^y.y))(a (a a)))) 5. ==[ beta ]==> ((a (a a))(((a a)(^y.y))(a (a a)))) 6. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 178773/20578440. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x)(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a b))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a b))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a))(a b))((a a)(^y.y))) 6. ==[ alpha ]==> (((a (a a))(a b))((a a)(^x.x))) REDUCED to normal form. ------ 178774/20578467. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a b)((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a b)((a a) a))) 5. ==[ beta ]==> (((a a) a)((a b)((a a) a))) REDUCED to normal form. ------ 178775/20578494. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((a a) a)(a b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((a a) a)(a b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a) a)(a b))) REDUCED to normal form. ------ 178776/20578521. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(a (a a)))((^y.y)(a a))) 6. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(a a))) 7. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 178777/20578548. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (a a))((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)((a (a a))((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a) a)((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 178778/20578575. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a (b a))) REDUCED to normal form. ------ 178779/20578620. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(b (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(b (^x1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178780/20578629. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)((^z.z) b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a) b)) REDUCED to normal form. ------ 178781/20578719. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((b a)(^z.a))) 5. ==[ beta ]==> ((a a)((b a)(^z.a))) 6. ==[ alpha ]==> ((a a)((b a)(^x.a))) REDUCED to normal form. ------ 178782/20578800. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> (b ((a b)(^x1.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 178783/20578917. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 178784/20578935. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 178785/20578944. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 178786/20578962. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a a)(^z.z))) 3. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 178787/20579016. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.(^x1.x1))) b)) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.(^z.z))) b)) 7. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z))) b)) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 178788/20579025. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 178789/20579106. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 178790/20579133. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 178791/20579160. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 178792/20579277. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 178793/20579304. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(a ((^z.z) b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a ((^y.y) b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a b)) REDUCED to normal form. ------ 178794/20579331. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> (((a (a a))(a a))((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> (((a (a a))(a a))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 178795/20579358. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((b a)(a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a b))((b a)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a b))((b a)(a (^y.y)))) 5. ==[ beta ]==> ((a b)((b a)(a (^y.y)))) 6. ==[ alpha ]==> ((a b)((b a)(a (^x.x)))) REDUCED to normal form. ------ 178796/20579385. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(^x.x))((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 178797/20579412. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (((a b)(^x.x))((a a)(a (a a)))) REDUCED to normal form. ------ 178798/20579439. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(a (a a)))((a b)(^y.y))) 6. ==[ alpha ]==> (((a a)(a (a a)))((a b)(^x.x))) REDUCED to normal form. ------ 178799/20579466. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 178800/20579520. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a (a a))(a a))) REDUCED to normal form. ------ 178801/20579547. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a b)(((^y.y) a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a b)(((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)(a ((a a)(^y.y)))) 6. ==[ alpha ]==> ((a b)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 178802/20579718. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> (b ((a a)(^y.(y y)))) 6. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 178803/20579826. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (a a))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178804/20579835. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a)(a a))) REDUCED to normal form. ------ 178805/20579862. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((b a)((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((b a)((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 178806/20579889. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 178807/20579907. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 178808/20579916. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a (^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) REDUCED to normal form. ------ 178809/20579961. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((b a) b)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((b a) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((b a) b)) REDUCED to normal form. ------ 178810/20579997. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178811/20580024. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a a)) REDUCED to normal form. ------ 178812/20580051. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 178813/20580078. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 178814/20580105. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 178815/20580159. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 178816/20580222. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a) b)(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a) b)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 178817/20580249. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((b a)(a a))) REDUCED to normal form. ------ 178818/20580276. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((a (b a))(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 178819/20580303. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)((^y.y) a))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 178820/20580330. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((a b)(a (a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a b)(a (a a)))) 7. ==[ beta ]==> ((a a)((a b)(a (a a)))) REDUCED to normal form. ------ 178821/20580357. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((a a) a)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a b))(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((((a a) a)(a b))(((a a) a)(^x.x))) REDUCED to normal form. ------ 178822/20580384. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b)((a a) a))((^y.y)((a a) a))) 4. ==[ alpha ]==> (((a b)((a a) a))((^x.x)((a a) a))) 5. ==[ beta ]==> (((a b)((a a) a))((a a) a)) REDUCED to normal form. ------ 178823/20580411. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a (a a))(a b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (a a))(a b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (a a))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))((a (a a))(a b))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(a b))) REDUCED to normal form. ------ 178824/20580438. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a (a a))) REDUCED to normal form. ------ 178825/20580492. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(b a))) REDUCED to normal form. ------ 178826/20580582. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.a)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.a)) 7. ==[ beta ]==> ((a a)(^y.a)) 8. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 178827/20580717. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (b (a (^y.(a a)))) 6. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 178828/20580825. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((a a)(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178829/20580861. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((b b)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((b b)((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 178830/20580888. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b)(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 178831/20580942. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 178832/20580969. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))(^y1.b))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.b)(^y1.b))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)(^y1.b))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 178833/20581275. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a (^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a (^x.x))(a a))) REDUCED to normal form. ------ 178834/20581302. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 178835/20582076. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(a a))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a a))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 178836/20582094. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a b)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 178837/20582103. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 178838/20582175. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 178839/20582184. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(^z.z))) 9. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 10. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 178840/20582211. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)((a a) a))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 178841/20582283. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1)(a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178842/20582292. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a a)) REDUCED to normal form. ------ 178843/20582319. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 178844/20582463. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b (a b))) 3. ==[ beta ]==> ((a ((^y.y) b))(b (a b))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b (a b))) 5. ==[ beta ]==> ((a b)(b (a b))) REDUCED to normal form. ------ 178845/20582490. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 178846/20582517. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a b)(a a))) 3. ==[ beta ]==> (((^y.y)(b a))((a b)(a a))) 4. ==[ alpha ]==> (((^x.x)(b a))((a b)(a a))) 5. ==[ beta ]==> ((b a)((a b)(a a))) REDUCED to normal form. ------ 178847/20582544. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 178848/20582571. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a b)(a a))((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (((a b)(a a))((^x.x)((^y.y) a))) 7. ==[ beta ]==> (((a b)(a a))((^y.y) a)) 8. ==[ alpha ]==> (((a b)(a a))((^x.x) a)) 9. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 178849/20582598. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(a b))((a (a a))(a (a a)))) REDUCED to normal form. ------ 178850/20582625. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a (^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a (^y.y))) REDUCED to normal form. ------ 178851/20582679. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a a)(a b))) REDUCED to normal form. ------ 178852/20582877. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(^z.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)(^z.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.b))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.b))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.b))) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 178853/20582958. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1)) c)) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1)) c)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) c)) 5. ==[ beta ]==> (b ((^y.y) c)) 6. ==[ alpha ]==> (b ((^x.x) c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 178854/20583282. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((a a) a)(^z.z))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((a a) a)(^z.z))) 5. ==[ beta ]==> ((b ((^y.y) b))(((a a) a)(^z.z))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((a a) a)(^y.y))) 7. ==[ beta ]==> ((b b)(((a a) a)(^y.y))) 8. ==[ alpha ]==> ((b b)(((a a) a)(^x.x))) REDUCED to normal form. ------ 178855/20583291. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^c.a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 178856/20583318. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178857/20583363. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> (b (a (^y.(y y)))) 6. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 178858/20583372. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 178859/20583399. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 178860/20583426. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a a) a)) REDUCED to normal form. ------ 178861/20583471. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1)(^x2.x2)) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178862/20583480. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 178863/20583507. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.a)(^z.a))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(^z.a))) 7. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 178864/20583534. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 178865/20583624. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 178866/20583651. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (a a))(a (^z.z)))) REDUCED to normal form. ------ 178867/20583678. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a ((^y.y) a))) 6. ==[ alpha ]==> ((a ((a a)(a a)))(a ((^x.x) a))) 7. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 178868/20583705. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y))(a (a a)))) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 178869/20583732. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 178870/20583840. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c d)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c d)) REDUCED to normal form. ------ 178871/20584002. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b (a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (a (a a)))) 5. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 178872/20584020. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 178873/20584029. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a (^z.z))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.y))) REDUCED to normal form. ------ 178874/20584038. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (((^z.(^x1.x1)) a)(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178875/20584425. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(c (^y.(^z.z)))) 5. ==[ beta ]==> (b (c (^y.(^z.z)))) 6. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 178876/20584452. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b (^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b (^y.a))) REDUCED to normal form. ------ 178877/20584479. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a (^z.(z z)))) REDUCED to normal form. ------ 178878/20584497. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1) a)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((^y.y) a)(^z.z)) 6. ==[ alpha ]==> (((^x.x) a)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 178879/20584551. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(^y.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)(^x.a))) REDUCED to normal form. ------ 178880/20584587. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 7. ==[ beta ]==> ((^y.a)(^z.z)) 8. ==[ alpha ]==> ((^x.a)(^y.y)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 178881/20584614. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 178882/20584632. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a) c)) 2. ==[ alpha ]==> (((^x.b)(b a))((a a) c)) 3. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 178883/20584695. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 178884/20584740. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178885/20584776. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 178886/20584803. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 178887/20584857. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b (^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178888/20584875. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z) b)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 178889/20584884. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 178890/20584902. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 178891/20584920. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a b)) REDUCED to normal form. ------ 178892/20584947. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a (a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a (a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 178893/20584974. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a a)) 3. ==[ beta ]==> ((a (b (^y.y)))(a a)) 4. ==[ alpha ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 178894/20585931. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178895/20586363. ------ 1. ==[ start ]==> ((^a.((a a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.(^z.(z (^x1.x1))))(^y.(^z.(z (^x1.x1)))))(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.(^y.(y (^z.z))))(^x1.(^y1.(y1 (^z1.z1)))))(^x2.(^y2.(y2 (^z2.z2))))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^x2.(^y2.(y2 (^z2.z2))))) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 7. ==[ beta ]==> ((^z.(^x1.(x1 (^y1.y1))))(^y.y)) 8. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.x1)) 9. ==[ beta ]==> (^y.(y (^z.z))) 10. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 178896/20594715. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^a.((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.((x1 x1) x1))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 178897/20595138. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^z.(^x1.(^y1.y1)))((^z.(^x1.(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178898/20596086. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a))) b) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y))) b) 3. ==[ beta ]==> ((a (b (^y.y))) b) 4. ==[ alpha ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 178899/20596110. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178900/20596155. ------ 1. ==[ start ]==> ((^a.b)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)(b (^y.(y (^z.z))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 178901/20596425. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ eta ]==> ((^y.y)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178902/20596617. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(a (a (^z.z))))) 3. ==[ beta ]==> (((a a) a)(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> (((a a) a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 178903/20597046. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178904/20597049. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 178905/20597058. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (z (^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178906/20597478. ------ 1. ==[ start ]==> ((^a.((a a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))(a (^y.(y (^z.z))))) 3. ==[ beta ]==> (((a (^y.(y (^z.z))))(a (^y.(y (^z.z)))))(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a (^x.(x (^y.y))))(a (^z.(z (^x1.x1)))))(a (^y1.(y1 (^z1.z1))))) REDUCED to normal form. ------ 178907/20597481. ------ 1. ==[ start ]==> ((a ((a a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 178908/20597886. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a (a a)))(^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a (a a)))(^x.(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 178909/20597991. ------ 1. ==[ start ]==> ((^a.(a b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z))) b) 4. ==[ alpha ]==> (((^x.x)(^y.(y y))) b) 5. ==[ beta ]==> ((^y.(y y)) b) 6. ==[ alpha ]==> ((^x.(x x)) b) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 178910/20598378. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (^y.((((^z.z) b)((^x1.x1) a))(((^z.z) b)((^x1.x1) a)))) 4. ==[ alpha ]==> (^x.((((^y.y) b)((^z.z) a))(((^x1.x1) b)((^y1.y1) a)))) 5. ==[ beta ]==> (^x.((b ((^z.z) a))(((^x1.x1) b)((^y1.y1) a)))) 6. ==[ alpha ]==> (^x.((b ((^y.y) a))(((^z.z) b)((^x1.x1) a)))) 7. ==[ beta ]==> (^x.((b a)(((^z.z) b)((^x1.x1) a)))) 8. ==[ alpha ]==> (^x.((b a)(((^y.y) b)((^z.z) a)))) 9. ==[ beta ]==> (^x.((b a)(b ((^z.z) a)))) 10. ==[ alpha ]==> (^x.((b a)(b ((^y.y) a)))) 11. ==[ beta ]==> (^x.((b a)(b a))) REDUCED to normal form. ------ 178911/20598678. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(b (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(^y1.(b (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 7. ==[ beta ]==> (^y.(b (^z.z))) 8. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 178912/20599074. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(y (^z.z)))) REDUCED to normal form. ------ 178913/20599260. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((((^z.(a a))(^x1.b))((^z.(a a))(^x1.b)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(a a))(^y.b))((^z.(a a))(^x1.b)))(^y1.y1)) 5. ==[ beta ]==> (((a a)((^z.(a a))(^x1.b)))(^y1.y1)) 6. ==[ alpha ]==> (((a a)((^x.(a a))(^y.b)))(^z.z)) 7. ==[ beta ]==> (((a a)(a a))(^z.z)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 178914/20600016. ------ 1. ==[ start ]==> ((^a.(b a))((^a.b)(a b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.b)(a b))) 3. ==[ eta ]==> (b ((^y.b)(a b))) 4. ==[ alpha ]==> (b ((^x.b)(a b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 178915/20600565. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) b)(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178916/20600853. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(b (^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(b (^x1.x1))) 3. ==[ beta ]==> ((b (^x1.x1))(^y.(^z.z))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 178917/20601531. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 178918/20602449. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178919/20602746. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178920/20603295. ------ 1. ==[ start ]==> (((^a.b)(a b))(^a.(b a))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(b y))) 3. ==[ eta ]==> (((^x.b)(a b)) b) 4. ==[ beta ]==> (b b) REDUCED to normal form. ------ 178921/20603799. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 178922/20603850. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 178923/20604717. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 178924/20604933. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.(y y)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(y y)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(x x)))) REDUCED to normal form. ------ 178925/20605011. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178926/20605653. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.a))) REDUCED to normal form. ------ 178927/20605830. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a ((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a ((a a) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 178928/20605833. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.((z z) z))) REDUCED to normal form. ------ 178929/20605986. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.x))) REDUCED to normal form. ------ 178930/20606121. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 178931/20606253. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^x1.(^y1.y1)))(((^z.z)(^x1.(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.(^z1.z1)))(^x2.x2))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.(^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178932/20606256. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 178933/20606265. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^z.((^x1.x1)(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.x1)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178934/20607003. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 178935/20607111. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 178936/20607126. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 178937/20607147. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(a a))) REDUCED to normal form. ------ 178938/20607174. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 178939/20607201. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 178940/20607231. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a (^x.x))(a (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 178941/20607258. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 178942/20607276. ------ 1. ==[ start ]==> ((a b)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a b)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 178943/20607285. ------ 1. ==[ start ]==> (((^a.a)(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((a a)((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> ((a a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 178944/20607321. ------ 1. ==[ start ]==> (((^a.a) b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x) b)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> (b ((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> (b ((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 178945/20607330. ------ 1. ==[ start ]==> (((a a)(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(a a))((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> (((a a)(a a))((a a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 178946/20607348. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 178947/20607375. ------ 1. ==[ start ]==> (((a a) b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a) b)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 178948/20607402. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 178949/20607429. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 178950/20607510. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 178951/20607546. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 178952/20607591. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 178953/20607618. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 178954/20607645. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 178955/20607735. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a a) a)((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> (((a a) a)(a (a (^y.y)))) 6. ==[ alpha ]==> (((a a) a)(a (a (^x.x)))) REDUCED to normal form. ------ 178956/20607762. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^y1.y1)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 178957/20607807. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x)) a)((b (^y.y)) c)) 3. ==[ beta ]==> ((a a)((b (^y.y)) c)) 4. ==[ alpha ]==> ((a a)((b (^x.x)) c)) REDUCED to normal form. ------ 178958/20608059. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 178959/20608167. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a (^x.x))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 178960/20608176. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (a (^z.z))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178961/20608203. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a)(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a a)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a a)) 7. ==[ beta ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178962/20608257. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 8. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 178963/20608266. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.(a a)) d)) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(a a)) d)) 3. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 178964/20608311. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 178965/20608338. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 5. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 178966/20608392. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)(a a))) REDUCED to normal form. ------ 178967/20608599. ------ 1. ==[ start ]==> ((a ((a a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 178968/20608725. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 178969/20608752. ------ 1. ==[ start ]==> ((((a a) a) a)((b a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a) a)((b a)(^x.a))) REDUCED to normal form. ------ 178970/20608806. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.(a a)))) REDUCED to normal form. ------ 178971/20608833. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 178972/20608887. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 178973/20608914. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 178974/20608950. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 178975/20608977. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 178976/20609004. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a (a a)))((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a (a (a a)))(^y.y)) 8. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 178977/20609112. ------ 1. ==[ start ]==> ((a (a b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> ((a (a b))(^y.(y y))) 4. ==[ alpha ]==> ((a (a b))(^x.(x x))) REDUCED to normal form. ------ 178978/20609391. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(b (b (^y.y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(b (b (^y.y)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(b (b (^x.x)))) REDUCED to normal form. ------ 178979/20609472. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> (b (((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> (b (((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 178980/20609481. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a)) c)) 3. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 178981/20609499. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> ((a (^x.(a a)))(b ((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b ((^y.y) a))) 5. ==[ beta ]==> ((a (^x.(a a)))(b a)) REDUCED to normal form. ------ 178982/20609715. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.(a a))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.(a a))((a (a a))(a (^y.(^z.z))))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 178983/20609742. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (((^y.y) a)((^z.z) b)) 6. ==[ alpha ]==> (((^x.x) a)((^y.y) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 178984/20609796. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(b (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a a)(b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 178985/20609886. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a b) b)(((^x.x) b)(^y.a))) 3. ==[ beta ]==> (((a b) b)(b (^y.a))) 4. ==[ alpha ]==> (((a b) b)(b (^x.a))) REDUCED to normal form. ------ 178986/20609913. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 178987/20609940. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 178988/20609967. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 178989/20610021. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a b)(^z.(a a)))) REDUCED to normal form. ------ 178990/20610102. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 178991/20610129. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 178992/20610165. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 178993/20610192. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(b (^y.y))) REDUCED to normal form. ------ 178994/20610273. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.a))) 7. ==[ beta ]==> ((a (a a))(^y.a)) 8. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 178995/20610300. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((a a) a) a)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 178996/20610381. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 178997/20610552. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 178998/20610633. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (a (^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (a (^y.y)))) REDUCED to normal form. ------ 178999/20610660. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 179000/20610714. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 179001/20610795. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (b (((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 179002/20610921. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(b (^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.(a a)))) REDUCED to normal form. ------ 179003/20611002. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(a (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(a (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a (^x1.x1)))) 7. ==[ beta ]==> ((^y.y)((^z.z)(a (^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z)))) 9. ==[ beta ]==> ((^y.y)(a (^z.z))) 10. ==[ alpha ]==> ((^x.x)(a (^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 179004/20611029. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 179005/20611110. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 179006/20611137. ------ 1. ==[ start ]==> ((a (b a))((^a.b)(a b))) 2. ==[ alpha ]==> ((a (b a))((^x.b)(a b))) 3. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 179007/20611371. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 179008/20611686. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b (a a))) REDUCED to normal form. ------ 179009/20611974. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(b (^b.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b (^z.z))) REDUCED to normal form. ------ 179010/20611983. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)((^x1.x1) b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179011/20612289. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 179012/20612370. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 179013/20612397. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((b a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((b a) c)) 3. ==[ beta ]==> (((^y.y)(^z.b))((b a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((b a) c)) 5. ==[ beta ]==> ((^y.b)((b a) c)) 6. ==[ alpha ]==> ((^x.b)((b a) c)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 179014/20612622. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 179015/20612649. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 179016/20612901. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y) a)((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x) a)((a a)(^y.y))) 7. ==[ beta ]==> (a ((a a)(^y.y))) 8. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 179017/20612928. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.z1))(b a))) 3. ==[ beta ]==> ((^y.y)((a (^z1.z1))(b a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(b a))) 5. ==[ beta ]==> ((a (^y.y))(b a)) 6. ==[ alpha ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 179018/20613180. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 179019/20613207. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b a)(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 179020/20613261. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 179021/20613342. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((a a)(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a)(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z)) c)) 5. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z)) c)) 6. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y)) c)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 179022/20613567. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) b)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 179023/20613864. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b (a a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b (a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 179024/20614206. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(a a)) c)) 3. ==[ beta ]==> ((b b)(((^y.y)(a a)) c)) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a)) c)) 5. ==[ beta ]==> ((b b)((a a) c)) REDUCED to normal form. ------ 179025/20614413. ------ 1. ==[ start ]==> (((^a.b)(a b))(a (b a))) 2. ==[ alpha ]==> (((^x.b)(a b))(a (b a))) 3. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 179026/20614476. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 179027/20614521. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179028/20614647. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.(^z.z)))) REDUCED to normal form. ------ 179029/20614701. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 179030/20614728. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 179031/20614755. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.b)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 179032/20614782. ------ 1. ==[ start ]==> (((a b)(a b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(a (a a)))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 179033/20614809. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 179034/20614836. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(((a a) a)((a a) a))) REDUCED to normal form. ------ 179035/20614890. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 179036/20614917. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((b (a (^x.x)))((a a)(^z.z))) 6. ==[ alpha ]==> ((b (a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 179037/20614971. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 179038/20615142. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (b (b ((^z.z)(a a)))) 4. ==[ alpha ]==> (b (b ((^x.x)(a a)))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 179039/20615250. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((a a) a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179040/20615358. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (^z.z))(a b))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(a b))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 179041/20615385. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)((^y.y)(a a))) 6. ==[ alpha ]==> ((a a)((^x.x)(a a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 179042/20615421. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 179043/20615448. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 179044/20615529. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 179045/20615556. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.b))(a (^z.a))) 6. ==[ alpha ]==> (((a a)(^x.b))(a (^y.a))) REDUCED to normal form. ------ 179046/20615637. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(a a)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a) a)) REDUCED to normal form. ------ 179047/20615664. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a b) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a b) b)) 3. ==[ beta ]==> ((b (^y.a))((a b) b)) 4. ==[ alpha ]==> ((b (^x.a))((a b) b)) REDUCED to normal form. ------ 179048/20615754. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 179049/20615781. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 179050/20615808. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.b))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 179051/20615835. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.(a a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 179052/20616024. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(b (^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(b (^z.b))) REDUCED to normal form. ------ 179053/20616051. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(a (^z.(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))(a (^z.(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(a (^y.(a a)))) 5. ==[ beta ]==> ((b a)(a (^y.(a a)))) 6. ==[ alpha ]==> ((b a)(a (^x.(a a)))) REDUCED to normal form. ------ 179054/20616078. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.b)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 179055/20616132. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 179056/20616411. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(b ((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179057/20616546. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1) a)(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (a a)))) 7. ==[ beta ]==> (((^y.y) a)(a (a a))) 8. ==[ alpha ]==> (((^x.x) a)(a (a a))) 9. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 179058/20616573. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 179059/20616636. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 179060/20616663. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.(^z2.z2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179061/20616717. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 179062/20616744. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 179063/20616771. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)(^z.a))) REDUCED to normal form. ------ 179064/20616825. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 179065/20616852. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (a a)) c)) 3. ==[ beta ]==> ((b (^y.(y y)))((a (a a)) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (a a)) c)) REDUCED to normal form. ------ 179066/20616951. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a ((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a ((a a) a))) REDUCED to normal form. ------ 179067/20617050. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c (^y.(y y)))) 3. ==[ beta ]==> (((a (a a)) b)(c (^y.(y y)))) 4. ==[ alpha ]==> (((a (a a)) b)(c (^x.(x x)))) REDUCED to normal form. ------ 179068/20617077. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 179069/20617104. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (^c.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.a))) REDUCED to normal form. ------ 179070/20617131. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 179071/20617158. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y))(a (^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(a (^y.y)))) 7. ==[ beta ]==> (((a a)(a a))((a (^y.y))(a (^y.y)))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 179072/20617185. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 179073/20617239. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.y1)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 179074/20617266. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 179075/20617293. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 179076/20617347. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 179077/20617374. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 179078/20617383. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((^z.z)(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.z)) 7. ==[ beta ]==> ((a (^y.y))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 179079/20617770. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a) b)) 3. ==[ beta ]==> (((^y.y) b)((^z.a) b)) 4. ==[ alpha ]==> (((^x.x) b)((^y.a) b)) 5. ==[ beta ]==> (b ((^y.a) b)) 6. ==[ alpha ]==> (b ((^x.a) b)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179080/20617788. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a (^y.y))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 179081/20617815. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a a)((^z.z) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)((^y.y) a))) 5. ==[ beta ]==> ((a (a (^x.x)))((a a) a)) REDUCED to normal form. ------ 179082/20617896. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b c)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b c)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b c)) REDUCED to normal form. ------ 179083/20617932. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a) a)) 5. ==[ beta ]==> ((^y.y)(((^z.z) a) a)) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a) a)) 7. ==[ beta ]==> (((^y.y) a) a) 8. ==[ alpha ]==> (((^x.x) a) a) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 179084/20617959. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1)) b)) REDUCED to normal form. ------ 179085/20617977. ------ 1. ==[ start ]==> (((^a.b)(b a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(b (a (^y.y)))) 3. ==[ beta ]==> (b (b (a (^y.y)))) 4. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 179086/20618040. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 179087/20618121. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 179088/20618148. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y)) a)) REDUCED to normal form. ------ 179089/20618202. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1)) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179090/20618220. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a)(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 179091/20618229. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z) b)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) b) REDUCED to normal form. ------ 179092/20618247. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 179093/20618265. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)(a a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a a)) REDUCED to normal form. ------ 179094/20618292. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 179095/20618319. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a (^z.z))) 3. ==[ beta ]==> ((a (b (^y.y)))(a (^z.z))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 179096/20618430. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179097/20628069. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 179098/20629365. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179099/20629440. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a))) c) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y))) c) 3. ==[ beta ]==> ((a (b (^y.y))) c) 4. ==[ alpha ]==> ((a (b (^x.x))) c) REDUCED to normal form. ------ 179100/20629554. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179101/20629557. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 179102/20629599. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^z.(^x1.x1)) a)(^y1.(^z1.z1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.y1)) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179103/20629716. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (^y.((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179104/20629959. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 179105/20630058. ------ 1. ==[ start ]==> ((^a.(a (a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(x (x x)))((b (^y.y)) c)) 3. ==[ beta ]==> (((b (^y.y)) c)(((b (^y.y)) c)((b (^y.y)) c))) 4. ==[ alpha ]==> (((b (^x.x)) c)(((b (^y.y)) c)((b (^z.z)) c))) REDUCED to normal form. ------ 179106/20630283. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179107/20630421. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179108/20631174. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 179109/20631672. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.a))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(^y1.y1))) 5. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 179110/20632437. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 179111/20632806. ------ 1. ==[ start ]==> (((a b) c)(^d.((a a)(a a)))) 2. ==[ alpha ]==> (((a b) c)(^x.((a a)(a a)))) REDUCED to normal form. ------ 179112/20632833. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.(b (^z.z)))) 3. ==[ beta ]==> (((a a) b)(^y.(b (^z.z)))) 4. ==[ alpha ]==> (((a a) b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 179113/20633379. ------ 1. ==[ start ]==> ((^a.(b a))((a b)(^a.b))) 2. ==[ alpha ]==> ((^x.(b x))((a b)(^y.b))) 3. ==[ eta ]==> (b ((a b)(^y.b))) 4. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 179114/20633553. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.((a a)(a a)))) 3. ==[ beta ]==> (b (^z.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 179115/20634819. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179116/20636133. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((b a)(^y.y))) 3. ==[ beta ]==> ((((b a)(^y.y))((b a)(^y.y)))(((b a)(^y.y))((b a)(^y.y)))) 4. ==[ alpha ]==> ((((b a)(^x.x))((b a)(^y.y)))(((b a)(^z.z))((b a)(^x1.x1)))) REDUCED to normal form. ------ 179117/20636667. ------ 1. ==[ start ]==> (((a b)(^a.b))(^a.(b a))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(b y))) 3. ==[ eta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 179118/20637162. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 179119/20637213. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179120/20637873. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179121/20638374. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179122/20638872. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.b))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.b))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.b))) 7. ==[ beta ]==> ((b b)(^y.(^z.b))) 8. ==[ alpha ]==> ((b b)(^x.(^y.b))) REDUCED to normal form. ------ 179123/20639196. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.a))) REDUCED to normal form. ------ 179124/20639628. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^z.(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179125/20640087. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 5. ==[ beta ]==> (^y.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 179126/20640330. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(^y1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179127/20640447. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179128/20640489. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179129/20640492. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 179130/20640564. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.a)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.a)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.a)) REDUCED to normal form. ------ 179131/20640612. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (a (((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> (a (((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> (a (a (b (^y.y)))) 6. ==[ alpha ]==> (a (a (b (^x.x)))) REDUCED to normal form. ------ 179132/20640639. ------ 1. ==[ start ]==> (((a a) a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a) a)((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a) a)((a (^x.x))(^z.z))) 4. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 179133/20640657. ------ 1. ==[ start ]==> (((^a.a)(a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a a)(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 179134/20640666. ------ 1. ==[ start ]==> (((a a)(^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 179135/20640684. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 179136/20640702. ------ 1. ==[ start ]==> (((a a)(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(a a))((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 179137/20640729. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 179138/20640819. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179139/20640846. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 179140/20640864. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((b a)(^y.b))) REDUCED to normal form. ------ 179141/20640891. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 179142/20640927. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.a)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 179143/20640954. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^y1.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 179144/20641008. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (a ((^y.(^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((^z.z) b))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 179145/20641035. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 179146/20641089. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 179147/20641107. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a) a)((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a a) a)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 179148/20641134. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 179149/20641161. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a (a a))(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 179150/20641188. ------ 1. ==[ start ]==> ((a (a (a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (a (a a)))((b (^x.x)) c)) REDUCED to normal form. ------ 179151/20641224. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(z z))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(y y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 179152/20641413. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 179153/20641503. ------ 1. ==[ start ]==> (((^a.(a a)) b)(c (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(c (b (^y.y)))) 3. ==[ beta ]==> ((b b)(c (b (^y.y)))) 4. ==[ alpha ]==> ((b b)(c (b (^x.x)))) REDUCED to normal form. ------ 179154/20641548. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179155/20641638. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a)) b)(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> (((a (a a)) b)(((a a)(a a)) a)) REDUCED to normal form. ------ 179156/20641665. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (a (((^y.y) b)(a (a a)))) 6. ==[ alpha ]==> (a (((^x.x) b)(a (a a)))) 7. ==[ beta ]==> (a (b (a (a a)))) REDUCED to normal form. ------ 179157/20641692. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^z1.z1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 179158/20641719. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b a)((a a) a))) REDUCED to normal form. ------ 179159/20641746. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((a (^y.a))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 179160/20641773. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 179161/20641800. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.y)((a b)((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 7. ==[ beta ]==> ((a b)((a a)(^y.y))) 8. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 179162/20642061. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> (a ((^z.(a a))((^x1.x1) a))) 6. ==[ alpha ]==> (a ((^x.(a a))((^y.y) a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 179163/20642223. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> ((a a)((^y.b)((a a)(^z.z)))) 8. ==[ alpha ]==> ((a a)((^x.b)((a a)(^y.y)))) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 179164/20642304. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((a (^x.b))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.b))(b ((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.b))(b ((^y.y) b))) 7. ==[ beta ]==> ((a (^x.b))(b b)) REDUCED to normal form. ------ 179165/20642403. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a (a a)) a)(((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.(^y.y)) a) a)) 5. ==[ beta ]==> (((a (a a)) a)((^y.y) a)) 6. ==[ alpha ]==> (((a (a a)) a)((^x.x) a)) 7. ==[ beta ]==> (((a (a a)) a) a) REDUCED to normal form. ------ 179166/20642430. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((b (^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b (^z.z)) b)) 5. ==[ beta ]==> ((a (^y.y))((b (^z.z)) b)) 6. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) b)) REDUCED to normal form. ------ 179167/20642493. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.b)((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(z z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 179168/20642655. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b ((^z.a)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179169/20642682. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 179170/20642709. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((^y.(y y))(^z.z)) 6. ==[ alpha ]==> ((^x.(x x))(^y.y)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179171/20642745. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(c ((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(c ((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(c ((a a)(a a)))) REDUCED to normal form. ------ 179172/20642772. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(b (b (^y.y)))) REDUCED to normal form. ------ 179173/20642799. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.a)(a ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((^x.a)(a ((^y.(^z.z)) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 179174/20642826. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b (^z.z))(a a))) REDUCED to normal form. ------ 179175/20642853. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 179176/20643042. ------ 1. ==[ start ]==> (((^a.b) b)(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> (b (((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> (b (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 179177/20643249. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 179178/20643303. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 179179/20643384. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(a a))(a b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(a b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))(a b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(a b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(a b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(a b))) 9. ==[ beta ]==> ((^y.y)((^z.(a a))(a b))) 10. ==[ alpha ]==> ((^x.x)((^y.(a a))(a b))) 11. ==[ beta ]==> ((^y.(a a))(a b)) 12. ==[ alpha ]==> ((^x.(a a))(a b)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 179180/20643465. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179181/20643591. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((b (^y.y)) a)) 3. ==[ beta ]==> ((a ((a a) a))((b (^y.y)) a)) 4. ==[ alpha ]==> ((a ((a a) a))((b (^x.x)) a)) REDUCED to normal form. ------ 179182/20643618. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a (a a))(^y.y))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((a a)(a a)) b)) REDUCED to normal form. ------ 179183/20643645. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z) b) c)) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z) b) c)) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) b) c)) 5. ==[ beta ]==> ((a (a a))(((^y.y) b) c)) 6. ==[ alpha ]==> ((a (a a))(((^x.x) b) c)) 7. ==[ beta ]==> ((a (a a))(b c)) REDUCED to normal form. ------ 179184/20643789. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(a a)))) 5. ==[ beta ]==> ((^y.b)(^z.(a a))) 6. ==[ alpha ]==> ((^x.b)(^y.(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 179185/20643924. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179186/20643933. ------ 1. ==[ start ]==> (((a b) c)(b ((a a)(a a)))) REDUCED to normal form. ------ 179187/20643960. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(a (b (^y.y)))) 3. ==[ beta ]==> (((a a) b)(a (b (^y.y)))) 4. ==[ alpha ]==> (((a a) b)(a (b (^x.x)))) REDUCED to normal form. ------ 179188/20643987. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(a a))(a a))) REDUCED to normal form. ------ 179189/20644041. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 179190/20644068. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((b a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.b))((b a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.b))((b a)(a (a a)))) REDUCED to normal form. ------ 179191/20644122. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179192/20644149. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a b)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a b)(a b))) REDUCED to normal form. ------ 179193/20644176. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(((a a) a)(a a))) REDUCED to normal form. ------ 179194/20644203. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)((a a)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((a a)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 179195/20644230. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a))(b a))) REDUCED to normal form. ------ 179196/20644347. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 179197/20644374. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 9. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 10. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 11. ==[ beta ]==> (b (^y.(^z.z))) 12. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 179198/20644401. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 179199/20644428. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((b a)(^y.(y y)))) 3. ==[ beta ]==> (((a b) a)((b a)(^y.(y y)))) 4. ==[ alpha ]==> (((a b) a)((b a)(^x.(x x)))) REDUCED to normal form. ------ 179200/20644455. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 179201/20644509. ------ 1. ==[ start ]==> ((a (b a))((a b)(^a.b))) 2. ==[ alpha ]==> ((a (b a))((a b)(^x.b))) REDUCED to normal form. ------ 179202/20644599. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(z z))(b a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(z z))(b a))) 5. ==[ beta ]==> (b ((^z.(z z))(b a))) 6. ==[ alpha ]==> (b ((^x.(x x))(b a))) 7. ==[ beta ]==> (b ((b a)(b a))) REDUCED to normal form. ------ 179203/20644680. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (b ((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 179204/20644869. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.b)(^z.b))) 3. ==[ beta ]==> (((a b)(a b))((^y.b)(^z.b))) 4. ==[ alpha ]==> (((a b)(a b))((^x.b)(^y.b))) 5. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 179205/20644986. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.a))(c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.a))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 179206/20645013. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b ((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b b)) REDUCED to normal form. ------ 179207/20645076. ------ 1. ==[ start ]==> (((a a)(b a))((^b.b) b)) 2. ==[ alpha ]==> (((a a)(b a))((^x.x) b)) 3. ==[ beta ]==> (((a a)(b a)) b) REDUCED to normal form. ------ 179208/20645337. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179209/20645355. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(b (^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179210/20645436. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(a (^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 179211/20645517. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 179212/20645625. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(y1 y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179213/20645652. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(b a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 179214/20645679. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179215/20645733. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 179216/20645814. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179217/20645922. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179218/20645949. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 179219/20646048. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.b) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.y) a)) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y) a)) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x) a)) 5. ==[ beta ]==> (((a (a a))(a a)) a) REDUCED to normal form. ------ 179220/20646075. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1))) b)) 6. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z))) b)) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 179221/20646129. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z)) d)) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 179222/20646228. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179223/20646435. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179224/20646543. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179225/20646597. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> (b ((^y.a)((a a)(^z.z)))) 6. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179226/20646624. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(b a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179227/20646678. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 179228/20646759. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 179229/20646867. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(y1 y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179230/20646903. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(c ((a a)(^z.z)))) 3. ==[ beta ]==> ((b (^y.y))(c ((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))(c ((a a)(^y.y)))) REDUCED to normal form. ------ 179231/20646966. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 179232/20647263. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((b a)(^x.x))) REDUCED to normal form. ------ 179233/20647299. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179234/20647434. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(z z))(a b))) 3. ==[ beta ]==> (b ((^z.(z z))(a b))) 4. ==[ alpha ]==> (b ((^x.(x x))(a b))) 5. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 179235/20647623. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 179236/20647650. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 179237/20647704. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((b a)(b a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> (((b a)(b a))((^y.b)(^y.b))) 6. ==[ alpha ]==> (((b a)(b a))((^x.b)(^y.b))) 7. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 179238/20647767. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(b ((a a)(^y.y)))) REDUCED to normal form. ------ 179239/20647794. ------ 1. ==[ start ]==> (((a b)(^a.b))(a (b a))) 2. ==[ alpha ]==> (((a b)(^x.b))(a (b a))) REDUCED to normal form. ------ 179240/20647848. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 179241/20647902. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 179242/20647929. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 179243/20647956. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (a a))((a a) a))) REDUCED to normal form. ------ 179244/20648073. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(b a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 179245/20648100. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 179246/20648127. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a b)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(a a))((a b)(^y.a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a b)(^x.a))) REDUCED to normal form. ------ 179247/20648154. ------ 1. ==[ start ]==> (((a b)(a b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 179248/20648181. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)((a a) a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)((a a) a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 179249/20648262. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 179250/20648289. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 179251/20648316. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 179252/20648343. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(a a)) b)) 3. ==[ beta ]==> ((a (b (^x.x)))((a a) b)) REDUCED to normal form. ------ 179253/20648433. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.(^x3.x3)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))(^z2.(^x3.x3)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179254/20648514. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179255/20648658. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y))(a (a a)))) 5. ==[ beta ]==> ((b c)((^y.y)(a (a a)))) 6. ==[ alpha ]==> ((b c)((^x.x)(a (a a)))) 7. ==[ beta ]==> ((b c)(a (a a))) REDUCED to normal form. ------ 179256/20648685. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (a a))((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a (a a))(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((a (a a))(^x.x))) REDUCED to normal form. ------ 179257/20648730. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c (^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(c (^z.b))) 3. ==[ beta ]==> ((b (^y.y))(c (^z.b))) 4. ==[ alpha ]==> ((b (^x.x))(c (^y.b))) REDUCED to normal form. ------ 179258/20648757. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(b (^z.(a a)))) 3. ==[ beta ]==> ((^y.y)(b (^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 179259/20648811. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(a a))(a a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(a a))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(a a))(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 179260/20648892. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179261/20649000. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179262/20649234. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(a a)) a)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a)) a)) 5. ==[ beta ]==> ((b a)((^y.(a a)) a)) 6. ==[ alpha ]==> ((b a)((^x.(a a)) a)) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 179263/20649261. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.b) b)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 179264/20649288. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.a) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a) c)) 3. ==[ beta ]==> (((a b)(a a))((^y.a) c)) 4. ==[ alpha ]==> (((a b)(a a))((^x.a) c)) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 179265/20649450. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 179266/20649504. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.a))) 7. ==[ beta ]==> ((a (^x.x))(^z.a)) 8. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 179267/20649594. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 7. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179268/20649675. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179269/20649783. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179270/20649900. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (((^x.x) a)((a (a a))((^y.y) a))) 5. ==[ beta ]==> (a ((a (a a))((^y.y) a))) 6. ==[ alpha ]==> (a ((a (a a))((^x.x) a))) 7. ==[ beta ]==> (a ((a (a a)) a)) REDUCED to normal form. ------ 179271/20649945. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(^z.z)))) 5. ==[ beta ]==> (c (^y.(^z.z))) 6. ==[ alpha ]==> (c (^x.(^y.y))) REDUCED to normal form. ------ 179272/20649999. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(a (^z.b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(a (^z.b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(a (^z.b))) 5. ==[ beta ]==> ((b ((^y.y) b))(a (^z.b))) 6. ==[ alpha ]==> ((b ((^x.x) b))(a (^y.b))) 7. ==[ beta ]==> ((b b)(a (^y.b))) 8. ==[ alpha ]==> ((b b)(a (^x.b))) REDUCED to normal form. ------ 179273/20650080. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> (b (((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> (b (((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> (b (a ((^y.y) a))) 8. ==[ alpha ]==> (b (a ((^x.x) a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 179274/20650089. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d d)) REDUCED to normal form. ------ 179275/20650305. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(b ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b ((^y.y)(^z.z)))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179276/20650368. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 179277/20650503. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 179278/20650530. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((a (a a))(^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 179279/20650557. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a (^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.a))) REDUCED to normal form. ------ 179280/20650611. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 179281/20650638. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x)(^y.y)) a)) 5. ==[ beta ]==> ((b (a (a a)))((^y.y) a)) 6. ==[ alpha ]==> ((b (a (a a)))((^x.x) a)) 7. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 179282/20650665. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (a a)) b)) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (a a)) b)) REDUCED to normal form. ------ 179283/20650737. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b (a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(b (a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(b (a (a a)))) REDUCED to normal form. ------ 179284/20650755. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^z.z)(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179285/20651142. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a)(a a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(a a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(a a))) 5. ==[ beta ]==> (b (((^y.y) a)(a a))) 6. ==[ alpha ]==> (b (((^x.x) a)(a a))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 179286/20651169. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 179287/20651187. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b (^z.a))) 3. ==[ beta ]==> ((a (a (^y.y)))(b (^z.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 179288/20651196. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((a a) a)) REDUCED to normal form. ------ 179289/20651214. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(a (^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(a (^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(y y)))) 5. ==[ beta ]==> (a (^y.(y y))) 6. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 179290/20651268. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 179291/20651349. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179292/20651412. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z))(a a))) REDUCED to normal form. ------ 179293/20651457. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(a (^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179294/20651493. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 179295/20651574. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179296/20651592. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b (^z.z))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 179297/20651601. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 179298/20651619. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 179299/20651637. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(^y.y))) REDUCED to normal form. ------ 179300/20651664. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a) a)) REDUCED to normal form. ------ 179301/20651691. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z) a)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z) a)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y) a)) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 179302/20651717. ------ 1. ==[ start ]==> (^a.((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (^x.((x (x x))((x x)(x x)))) REDUCED to normal form. ------ 179303/20651718. ------ 1. ==[ start ]==> (a ((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 179304/20662746. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179305/20662848. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 179306/20662854. ------ 1. ==[ start ]==> ((^a.a)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 179307/20662881. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)(b (^z.z)))(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(((^z.z) a)(b (^x1.x1)))) 5. ==[ beta ]==> ((a (b (^y.y)))(((^z.z) a)(b (^x1.x1)))) 6. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(b (^z.z)))) 7. ==[ beta ]==> ((a (b (^x.x)))(a (b (^z.z)))) 8. ==[ alpha ]==> ((a (b (^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 179308/20662908. ------ 1. ==[ start ]==> ((^a.b)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.b)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 179309/20662956. ------ 1. ==[ start ]==> (((^a.a) b)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 179310/20663106. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (^y.((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (^x.((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 179311/20663799. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179312/20664231. ------ 1. ==[ start ]==> ((^a.((a a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((x x) x))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a)((^y.(^z.z)) a))((a a)((^y.(^z.z)) a)))((a a)((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((((a a)((^x.(^y.y)) a))((a a)((^z.(^x1.x1)) a)))((a a)((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((((a a)(^y.y))((a a)((^z.(^x1.x1)) a)))((a a)((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)((^y.(^z.z)) a)))((a a)((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^z.z)))((a a)((^x1.(^y1.y1)) a))) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)((^z.(^x1.x1)) a))) 9. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^x1.x1))) 10. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 179313/20664564. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (a a))(^z.z))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 179314/20665131. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(a a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a)) c)) 3. ==[ beta ]==> (^y.(((^z.(a a)) c)((^z.(a a)) c))) 4. ==[ alpha ]==> (^x.(((^y.(a a)) c)((^z.(a a)) c))) 5. ==[ beta ]==> (^x.((a a)((^z.(a a)) c))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a)) c))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 179315/20665338. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.y)((((^z.z)(^x1.x1))(b a))(((^z.z)(^x1.x1))(b a)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y)(^z.z))(b a))(((^x1.x1)(^y1.y1))(b a)))) 5. ==[ beta ]==> ((((^y.y)(^z.z))(b a))(((^x1.x1)(^y1.y1))(b a))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))(b a))) 7. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(b a))) 8. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(b a))) 9. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(b a))) 10. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(b a))) 11. ==[ beta ]==> ((b a)((^y.y)(b a))) 12. ==[ alpha ]==> ((b a)((^x.x)(b a))) 13. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 179316/20666583. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.((a a)(a a)))) 3. ==[ beta ]==> ((a (a b))(^y.((a a)(a a)))) 4. ==[ alpha ]==> ((a (a b))(^x.((a a)(a a)))) REDUCED to normal form. ------ 179317/20666943. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 179318/20667606. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x1.x1))(a (^y1.(^z1.z1))))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 179319/20668311. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.((^y.y) b))) 5. ==[ beta ]==> (((a (a a))(a a))(^x.b)) REDUCED to normal form. ------ 179320/20668524. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 179321/20669229. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(x1 (^y1.(^z1.z1))))) REDUCED to normal form. ------ 179322/20669499. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(b a))) 3. ==[ beta ]==> ((b (a a))(^y.(b a))) 4. ==[ alpha ]==> ((b (a a))(^x.(b a))) REDUCED to normal form. ------ 179323/20671056. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 179324/20671272. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(a a))) REDUCED to normal form. ------ 179325/20671497. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((b a)(^y.((^z.z)(y y)))) 6. ==[ alpha ]==> ((b a)(^x.((^y.y)(x x)))) 7. ==[ beta ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 179326/20671686. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(a b))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(a b))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(a b))) 5. ==[ beta ]==> ((b a)(^y.(a b))) 6. ==[ alpha ]==> ((b a)(^x.(a b))) REDUCED to normal form. ------ 179327/20672271. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 179328/20672604. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.((z z) z))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.((z z) z))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.((y y) y))) REDUCED to normal form. ------ 179329/20672739. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 179330/20673006. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b (a (a a)))) 3. ==[ beta ]==> ((b (a (a a)))((b (a (a a)))(^y.y))) 4. ==[ alpha ]==> ((b (a (a a)))((b (a (a a)))(^x.x))) REDUCED to normal form. ------ 179331/20673567. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a))) 7. ==[ beta ]==> (^y.((^z.z) a)) 8. ==[ alpha ]==> (^x.((^y.y) a)) 9. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 179332/20673720. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.c)) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.c)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179333/20673783. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 179334/20673837. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179335/20673879. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179336/20673882. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 179337/20673927. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.b)) REDUCED to normal form. ------ 179338/20673954. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(z z))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(z z))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 179339/20673981. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.a)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 179340/20673993. ------ 1. ==[ start ]==> ((a a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 179341/20674020. ------ 1. ==[ start ]==> ((a (a a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a a))(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> ((a (a a))(a (b (^y.y)))) 4. ==[ alpha ]==> ((a (a a))(a (b (^x.x)))) REDUCED to normal form. ------ 179342/20674047. ------ 1. ==[ start ]==> ((a b)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a b)((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a b)((a (^x.x))(^z.z))) 4. ==[ alpha ]==> ((a b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 179343/20674065. ------ 1. ==[ start ]==> (((a a)(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 179344/20674092. ------ 1. ==[ start ]==> (((^a.a) b)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (b (a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 179345/20674119. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 179346/20674137. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179347/20674164. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 179348/20674191. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 179349/20674218. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 179350/20674227. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 179351/20674245. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 179352/20674326. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 179353/20674362. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)(b a))) 3. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 179354/20674407. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.z))) 7. ==[ beta ]==> (a ((^y.y)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 179355/20674416. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 179356/20674443. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 179357/20674470. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 179358/20674596. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z)) c)) 3. ==[ beta ]==> ((^y.(y y))((b (^z.z)) c)) 4. ==[ alpha ]==> ((^x.(x x))((b (^y.y)) c)) 5. ==[ beta ]==> (((b (^y.y)) c)((b (^y.y)) c)) 6. ==[ alpha ]==> (((b (^x.x)) c)((b (^y.y)) c)) REDUCED to normal form. ------ 179359/20674659. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 179360/20674740. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 179361/20674767. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 179362/20674938. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.y))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.x))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 179363/20674974. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((^y.(y (^z.z))) a) 6. ==[ alpha ]==> ((^x.(x (^y.y))) a) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 179364/20675235. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a) a)(b a))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(b a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(b a))) REDUCED to normal form. ------ 179365/20675262. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 179366/20675289. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a a)((a (a a))((^y.y) b))) 6. ==[ alpha ]==> ((a a)((a (a a))((^x.x) b))) 7. ==[ beta ]==> ((a a)((a (a a)) b)) REDUCED to normal form. ------ 179367/20675316. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(a ((a a)(a a)))) REDUCED to normal form. ------ 179368/20675343. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(b (^z.z)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 179369/20675370. ------ 1. ==[ start ]==> ((a ((a a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((a a) a))((a a)((^x.(^y.y)) a))) 3. ==[ beta ]==> ((a ((a a) a))((a a)(^y.y))) 4. ==[ alpha ]==> ((a ((a a) a))((a a)(^x.x))) REDUCED to normal form. ------ 179370/20675406. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a)(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.x1)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179371/20675460. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(a a))(^z.a))) 5. ==[ beta ]==> (a (((a a)(a a))(^z.a))) 6. ==[ alpha ]==> (a (((a a)(a a))(^x.a))) REDUCED to normal form. ------ 179372/20675496. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.z)(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(a (a a)))) 5. ==[ beta ]==> (b ((^y.y)(a (a a)))) 6. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 179373/20675523. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 179374/20675541. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((b a)(^y.a))) 3. ==[ beta ]==> (((a a) a)((b a)(^y.a))) 4. ==[ alpha ]==> (((a a) a)((b a)(^x.a))) REDUCED to normal form. ------ 179375/20675568. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 179376/20675577. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 179377/20675604. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 179378/20675622. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a b)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)((a b)(^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 179379/20675631. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.a)) b) REDUCED to normal form. ------ 179380/20675685. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 179381/20675703. ------ 1. ==[ start ]==> ((a (^a.b))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.b))((a (a a))(^y.y))) REDUCED to normal form. ------ 179382/20675874. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(a a))(^z.a))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 179383/20676036. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a) b) b) REDUCED to normal form. ------ 179384/20676063. ------ 1. ==[ start ]==> (((a b) a)((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a b) a)((^x.a)(^y.a))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 179385/20676090. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 179386/20676144. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 179387/20676270. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(a a)) c)) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a)) c)) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 179388/20676288. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) b)((^y.y) a))) 3. ==[ beta ]==> (((a a)(a b))(b ((^y.y) a))) 4. ==[ alpha ]==> (((a a)(a b))(b ((^x.x) a))) 5. ==[ beta ]==> (((a a)(a b))(b a)) REDUCED to normal form. ------ 179389/20676315. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 179390/20676342. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((b a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((b a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a (^x.x))((b a)(^z.z))) 8. ==[ alpha ]==> ((a (^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 179391/20676369. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 179392/20676396. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))(a b))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(a b))) 7. ==[ beta ]==> (a (((^y.y)(a a))(a b))) 8. ==[ alpha ]==> (a (((^x.x)(a a))(a b))) 9. ==[ beta ]==> (a ((a a)(a b))) REDUCED to normal form. ------ 179393/20676423. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((a b)(a a))) REDUCED to normal form. ------ 179394/20676450. ------ 1. ==[ start ]==> (((a b)(a a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 179395/20676477. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> ((a (a a))((^y.y)(b a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(b a))) 7. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 179396/20676648. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 179397/20676657. ------ 1. ==[ start ]==> (((a b) b)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 179398/20676684. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a a) a)((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y) a))) 5. ==[ beta ]==> (((a a) a)((^y.y) a)) 6. ==[ alpha ]==> (((a a) a)((^x.x) a)) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 179399/20676702. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 179400/20676711. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 179401/20676729. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 179402/20676783. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(a a))(^z1.b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(a a))(^z1.b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.b))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))(^y1.b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.b))) 9. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.b))) 10. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.b))) 11. ==[ beta ]==> (((^y.y)(a a))(^z.b)) 12. ==[ alpha ]==> (((^x.x)(a a))(^y.b)) 13. ==[ beta ]==> ((a a)(^y.b)) 14. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 179403/20676792. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 179404/20676819. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.b)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.b)((^z.z)(a a)))) 7. ==[ beta ]==> (((^y.b)((^z.z)(a a)))((^y.b)((^z.z)(a a)))) 8. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b)((^x1.x1)(a a)))) 9. ==[ beta ]==> (b ((^z.b)((^x1.x1)(a a)))) 10. ==[ alpha ]==> (b ((^x.b)((^y.y)(a a)))) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 179405/20676846. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 179406/20676873. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 179407/20676900. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 179408/20677089. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 179409/20677332. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 179410/20677431. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.x1) c)) 3. ==[ beta ]==> ((^y.y)((^x1.x1) c)) 4. ==[ alpha ]==> ((^x.x)((^y.y) c)) 5. ==[ beta ]==> ((^y.y) c) 6. ==[ alpha ]==> ((^x.x) c) 7. ==[ beta ]==> c REDUCED to normal form. ------ 179411/20677665. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 179412/20677692. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x))(a a))((a (^y.y)) b)) REDUCED to normal form. ------ 179413/20677719. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a a)((a a)(a a)))) 3. ==[ beta ]==> ((a (a b))((a a)((a a)(a a)))) REDUCED to normal form. ------ 179414/20678079. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a a)(^z.(a a)))) 3. ==[ beta ]==> (b ((a a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 179415/20678142. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 179416/20678250. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 179417/20678277. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.b)(^z.b))) 3. ==[ beta ]==> (((a (a a))(^x.b)) b) REDUCED to normal form. ------ 179418/20678331. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 179419/20678385. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 179420/20678412. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 179421/20678475. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) b)(a a))) 3. ==[ beta ]==> (((a a)(b a))(b (a a))) REDUCED to normal form. ------ 179422/20678502. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 179423/20678529. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((b a)((^z.z) a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((b a)((^z.z) a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((b a)((^y.y) a))) 5. ==[ beta ]==> ((a (a a))((b a)((^y.y) a))) 6. ==[ alpha ]==> ((a (a a))((b a)((^x.x) a))) 7. ==[ beta ]==> ((a (a a))((b a) a)) REDUCED to normal form. ------ 179424/20678556. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 179425/20678583. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a) a)((a a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> (((a a) a)((a a)((^x.x)(^y.y)))) 9. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 10. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 179426/20678610. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a b)((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a b)((a a) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a b)((a a) a))) REDUCED to normal form. ------ 179427/20678637. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((a a) a)(a b))) REDUCED to normal form. ------ 179428/20678664. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a) a)((^y.y)((^z.z)(a a)))) 8. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y)(a a)))) 9. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 10. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 11. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 179429/20678691. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a (a a))((a a)(^z.z)))) REDUCED to normal form. ------ 179430/20678745. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 179431/20678835. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a a)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 179432/20678916. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 179433/20679033. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a)(^x1.x1))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 179434/20679060. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.a)(b a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 179435/20679078. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 179436/20679132. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z) b) a)) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z) b) a)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) b) a)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) b) a)) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) b) a)) 7. ==[ beta ]==> (((a a)(a a))(((^y.y) b) a)) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x) b) a)) 9. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 179437/20679141. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 179438/20679168. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 179439/20679222. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 179440/20679249. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 179441/20679276. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) b) REDUCED to normal form. ------ 179442/20679330. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 179443/20679393. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(c (b a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(c (b a))) REDUCED to normal form. ------ 179444/20679420. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 179445/20679447. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(a ((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(a a))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a (a a))(a a))(a ((^x.x) b))) 5. ==[ beta ]==> (((a (a a))(a a))(a b)) REDUCED to normal form. ------ 179446/20679474. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(a a))) 6. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 179447/20679501. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((b a)(a (^x.x)))) REDUCED to normal form. ------ 179448/20679528. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a b)(^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 179449/20679555. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))((a a)(a (a a)))) REDUCED to normal form. ------ 179450/20679582. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((a b)(^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)(^y.y))) REDUCED to normal form. ------ 179451/20679636. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((^x1.x1)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a b)) REDUCED to normal form. ------ 179452/20679663. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((a b)((a (a a))((^y.y)(a a)))) 4. ==[ alpha ]==> ((a b)((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> ((a b)((a (a a))(a a))) REDUCED to normal form. ------ 179453/20679834. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 179454/20679942. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(^y2.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(^y2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179455/20679951. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 179456/20679978. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((b a)((^y.(y y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((b a)((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)(((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((b a)((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> ((b a)((a a)((^x.x)(a a)))) 9. ==[ beta ]==> ((b a)((a a)(a a))) REDUCED to normal form. ------ 179457/20679996. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (((^y.y) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 179458/20680005. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 179459/20680032. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 179460/20680077. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 179461/20680140. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 179462/20680167. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 179463/20680194. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 179464/20680275. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.(a a))(^z1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(a a))(^z1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 179465/20680302. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 179466/20680338. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(b (b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(b (b a))) 3. ==[ beta ]==> (((a a) b)(b (b a))) REDUCED to normal form. ------ 179467/20680365. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 179468/20680392. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((b a)(a a))) 3. ==[ beta ]==> ((a (b a))((b a)(a a))) REDUCED to normal form. ------ 179469/20680419. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 179470/20680446. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))((^x1.x1) a))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))((^z.z) a))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))((^z.z) a))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y) a))) 9. ==[ beta ]==> ((a a)((a a)((^y.y) a))) 10. ==[ alpha ]==> ((a a)((a a)((^x.x) a))) 11. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 179471/20680473. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a b)(a (a a)))) REDUCED to normal form. ------ 179472/20680500. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a) a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a b)((a a) a))(((a a) a)(^y.y))) 4. ==[ alpha ]==> (((a b)((a a) a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 179473/20680527. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((a a) a))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)((a a) a))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a) a))) 9. ==[ beta ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 179474/20680554. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a (a a))(a b))) REDUCED to normal form. ------ 179475/20680608. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 179476/20680635. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a a)(b a))) 3. ==[ beta ]==> ((b (a a))((a a)(b a))) REDUCED to normal form. ------ 179477/20680698. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 179478/20680833. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a (a a))(^z.b))) 3. ==[ beta ]==> (b ((a (a a))(^z.b))) 4. ==[ alpha ]==> (b ((a (a a))(^x.b))) REDUCED to normal form. ------ 179479/20680941. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((b a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((b a) a)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179480/20680977. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 179481/20681004. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(a a))(^y.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 179482/20681058. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 179483/20681085. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 179484/20681166. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 179485/20681391. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x) a)(a b))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a (a b))) REDUCED to normal form. ------ 179486/20681418. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)((a (^y.y))(a a))) REDUCED to normal form. ------ 179487/20681445. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 179488/20682021. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.b) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179489/20682192. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 179490/20682210. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.z1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^y1.y1))) REDUCED to normal form. ------ 179491/20682219. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(a a))(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 179492/20682291. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 179493/20682300. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 179494/20682327. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.b))((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (((a a)(^x.b))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.z))) 11. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 12. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 179495/20682399. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179496/20682408. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a a)) REDUCED to normal form. ------ 179497/20682435. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.a))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((b (^x.a))(a a)) REDUCED to normal form. ------ 179498/20682462. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 179499/20682579. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(c ((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) b))(c ((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(c ((a a) a))) 5. ==[ beta ]==> ((a b)(c ((a a) a))) REDUCED to normal form. ------ 179500/20682606. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b (a b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b (a b))) REDUCED to normal form. ------ 179501/20682633. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)(a ((^y.y)(a a)))) 6. ==[ alpha ]==> ((b a)(a ((^x.x)(a a)))) 7. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 179502/20682660. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a b)(a a))) REDUCED to normal form. ------ 179503/20682687. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((a a) a)(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a a))(((a a) a)(a (^y.y)))) 4. ==[ alpha ]==> (((a b)(a a))(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 179504/20682714. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(a b))((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(a b))((^x.x)((^y.y) a))) 7. ==[ beta ]==> (((a a)(a b))((^y.y) a)) 8. ==[ alpha ]==> (((a a)(a b))((^x.x) a)) 9. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 179505/20682741. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 179506/20682795. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 179507/20682822. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a a)(a b))) 3. ==[ beta ]==> ((b ((^y.y) a))((a a)(a b))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a a)(a b))) 5. ==[ beta ]==> ((b a)((a a)(a b))) REDUCED to normal form. ------ 179508/20682993. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.a))) 7. ==[ beta ]==> ((a (^y.y))(^z.a)) 8. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 179509/20683074. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a) b)) 3. ==[ beta ]==> (b (((a a) a) b)) REDUCED to normal form. ------ 179510/20683407. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(a (^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.b))) REDUCED to normal form. ------ 179511/20683479. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (a a))(^z.a))) 3. ==[ beta ]==> (b ((a (a a))(^z.a))) 4. ==[ alpha ]==> (b ((a (a a))(^x.a))) REDUCED to normal form. ------ 179512/20683488. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(((^x1.x1) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a ((^x1.x1) a))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((^z.z) a))) 7. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 179513/20683515. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 179514/20683542. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 179515/20683587. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((a a) a) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179516/20683596. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 179517/20683623. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 179518/20683650. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 179519/20683704. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179520/20683740. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a ((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(a ((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))(a ((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(a ((a a) a))) REDUCED to normal form. ------ 179521/20683767. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a a)) REDUCED to normal form. ------ 179522/20683794. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a (a a))(a (^y.y)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a (a a))(a (^y.y)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 179523/20683821. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> (((a (a a)) b)(a ((^y.y) a))) 6. ==[ alpha ]==> (((a (a a)) b)(a ((^x.x) a))) 7. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 179524/20683848. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 179525/20683875. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a a)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(b a))((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a) a)(b a))((a a)(^x.x))) REDUCED to normal form. ------ 179526/20684136. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 179527/20684145. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (a (a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (a (a a)))) REDUCED to normal form. ------ 179528/20684559. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a) b)) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) b)) 5. ==[ beta ]==> ((^y.y)((^z.a) b)) 6. ==[ alpha ]==> ((^x.x)((^y.a) b)) 7. ==[ beta ]==> ((^y.a) b) 8. ==[ alpha ]==> ((^x.a) b) 9. ==[ beta ]==> a REDUCED to normal form. ------ 179529/20684595. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b (^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b (^z.a))) REDUCED to normal form. ------ 179530/20684667. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 179531/20684703. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((^y.y)((^z.z) a)) 8. ==[ alpha ]==> ((^x.x)((^y.y) a)) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 179532/20684730. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 179533/20684748. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y)) b)) 3. ==[ beta ]==> (b ((a (^y.y)) b)) 4. ==[ alpha ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 179534/20684811. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c (^z.z))) REDUCED to normal form. ------ 179535/20684892. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 179536/20684919. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 179537/20684973. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179538/20684991. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 179539/20685000. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b (^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b (^z.z))) REDUCED to normal form. ------ 179540/20685018. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1) b)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 179541/20685036. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b a)) REDUCED to normal form. ------ 179542/20685063. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a b)) REDUCED to normal form. ------ 179543/20685090. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a (a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a (a a))) 3. ==[ beta ]==> ((a (b (^y.y)))(a (a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (a a))) REDUCED to normal form. ------ 179544/20685117. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 179545/20689593. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.((y1 y1)(y1 y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179546/20691798. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1)))))((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1)))))) 4. ==[ alpha ]==> (((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2)))))((^z2.(^x3.(^y3.(^z3.z3))))(^x4.(^y4.(^z4.(^x5.x5)))))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^z2.(^x3.(^y3.(^z3.z3))))(^x4.(^y4.(^z4.(^x5.x5)))))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.(^x2.x2))))(^y2.(^z2.(^x3.(^y3.y3)))))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179547/20696154. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179548/20696256. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a))) b) REDUCED to normal form. ------ 179549/20696280. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179550/20696361. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179551/20696382. ------ 1. ==[ start ]==> (((a a)(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 179552/20696406. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (((^z.(z (^x1.x1)))(a a))(^y.y)) 4. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.z)) 5. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 179553/20696814. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 179554/20697255. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.(x1 (x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 (x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 5. ==[ beta ]==> (^y.(y (y (^z.z)))) 6. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 179555/20698083. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a)) a)(^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a (a a)) a)(^x.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 179556/20698161. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((^y.(a a))(^z.a)) b) 4. ==[ alpha ]==> (((^x.(a a))(^y.a)) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 179557/20698548. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> (^y.((((a a)(a a))(a (^z.z)))(((a a)(a a))(a (^z.z))))) 4. ==[ alpha ]==> (^x.((((a a)(a a))(a (^y.y)))(((a a)(a a))(a (^z.z))))) REDUCED to normal form. ------ 179558/20699271. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(y (^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 179559/20700186. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(a a))((a a) a))) 3. ==[ eta ]==> (b ((^y.(a a))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((a a) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 179560/20700735. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a ((a a)(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179561/20700738. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((x1 x1)(x1 x1)))) REDUCED to normal form. ------ 179562/20701728. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(^y.(^z.z))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 179563/20702646. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 179564/20702940. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^y.(^z.(^x1.x1))))(a (^y.(^z.(^x1.x1)))))((a (^y.(^z.(^x1.x1))))(a (^y.(^z.(^x1.x1)))))) 4. ==[ alpha ]==> (((a (^x.(^y.(^z.z))))(a (^x1.(^y1.(^z1.z1)))))((a (^x2.(^y2.(^z2.z2))))(a (^x3.(^y3.(^z3.z3)))))) REDUCED to normal form. ------ 179565/20702943. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 179566/20703996. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 179567/20704020. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179568/20704914. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(a a)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(a a)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 179569/20705130. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 179570/20705679. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((a a) a))) 7. ==[ beta ]==> ((b b)(^y.((a a) a))) 8. ==[ alpha ]==> ((b b)(^x.((a a) a))) REDUCED to normal form. ------ 179571/20706000. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 179572/20706021. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.(^c.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 179573/20706183. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(^c.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 179574/20706318. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))(^x.(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 179575/20706423. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y1.(y1 y1)))(((^z.(^x1.x1))(^y1.(y1 y1)))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.(^y1.y1))(^z1.(z1 z1)))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.(z1 z1)))(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.(x1 x1)))(^y1.y1))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(x1 x1)))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.x1)) 9. ==[ beta ]==> ((^y.y)(^x1.x1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179576/20706984. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.a))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 7. ==[ beta ]==> (^y.(^z.a)) 8. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 179577/20707272. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 179578/20707296. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179579/20707299. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(a a))) REDUCED to normal form. ------ 179580/20707317. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 179581/20707344. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(a a))) REDUCED to normal form. ------ 179582/20707371. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 179583/20707398. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 179584/20707428. ------ 1. ==[ start ]==> ((a (^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 179585/20707455. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 179586/20707482. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a a)((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a a)((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 179587/20707509. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a (a (^z.z))))) REDUCED to normal form. ------ 179588/20707527. ------ 1. ==[ start ]==> (((a a)(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 179589/20707545. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 179590/20707554. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a (a (^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 179591/20707572. ------ 1. ==[ start ]==> (((a a) b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 179592/20707599. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y))(^z.a))) REDUCED to normal form. ------ 179593/20707626. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a))(^z.(z z)))) REDUCED to normal form. ------ 179594/20707653. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 179595/20707689. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 179596/20707707. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((b a)(^z.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 179597/20707815. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 179598/20707842. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 179599/20707932. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 179600/20707959. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 179601/20707986. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (a a))((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a a))((^z.z)(^y.y))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 179602/20708004. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> ((a a)((^y.y) b)) 6. ==[ alpha ]==> ((a a)((^x.x) b)) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 179603/20708283. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 179604/20708373. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179605/20708400. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(a (a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(a (a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(a (a (a (^y.y))))) 5. ==[ beta ]==> (a (a (a (^y.y)))) 6. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 179606/20708454. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((b (^y1.y1))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((b (^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 179607/20708508. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) b)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (a a)))) 7. ==[ beta ]==> (((^y.y) b)(a (a a))) 8. ==[ alpha ]==> (((^x.x) b)(a (a a))) 9. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 179608/20708535. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 179609/20708589. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 179610/20708922. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (b (((^y.y) b)(^z.(z z)))) 6. ==[ alpha ]==> (b (((^x.x) b)(^y.(y y)))) 7. ==[ beta ]==> (b (b (^y.(y y)))) 8. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 179611/20708949. ------ 1. ==[ start ]==> ((((a a) a) a)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 179612/20709003. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.b))) REDUCED to normal form. ------ 179613/20709030. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))((a a)(^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.(x x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 179614/20709057. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 179615/20709111. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 179616/20709147. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(x x))((^y.y) b))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> (((a a)((a a) a))(b ((^y.y) b))) 6. ==[ alpha ]==> (((a a)((a a) a))(b ((^x.x) b))) 7. ==[ beta ]==> (((a a)((a a) a))(b b)) REDUCED to normal form. ------ 179617/20709174. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 179618/20709201. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 179619/20709228. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a (a a)) a)((^y.(^z.z)) a)) 6. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y)) a)) 7. ==[ beta ]==> (((a (a a)) a)(^y.y)) 8. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 179620/20709300. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b) a)(((a a)(a a)) c)) 3. ==[ beta ]==> (b (((a a)(a a)) c)) REDUCED to normal form. ------ 179621/20709309. ------ 1. ==[ start ]==> ((a (a b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.a))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 179622/20709669. ------ 1. ==[ start ]==> (((^a.b)(a a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a a))((b (^y.y))(a a))) 3. ==[ beta ]==> (b ((b (^y.y))(a a))) 4. ==[ alpha ]==> (b ((b (^x.x))(a a))) REDUCED to normal form. ------ 179623/20709696. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 179624/20709912. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 179625/20709939. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 179626/20709993. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.y1))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(a a)))) 7. ==[ beta ]==> ((a (^y.y))((a a)(a a))) 8. ==[ alpha ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 179627/20710083. ------ 1. ==[ start ]==> (((a b) b)(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 179628/20710110. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a a) a)(((^y.y) b)(^z.a))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b)(^y.a))) 5. ==[ beta ]==> (((a a) a)(b (^y.a))) 6. ==[ alpha ]==> (((a a) a)(b (^x.a))) REDUCED to normal form. ------ 179629/20710137. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 179630/20710164. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 179631/20710218. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a a)(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 179632/20710245. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)(^z.(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a b)(^z.(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((a b)(^y.(a a)))) 7. ==[ beta ]==> (((a b)(^y.(a a)))((a b)(^y.(a a)))) 8. ==[ alpha ]==> (((a b)(^x.(a a)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 179633/20710272. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 179634/20710326. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 179635/20710362. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)((^y.y) b))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 179636/20710389. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 179637/20710416. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(b (^y.y)))) 5. ==[ beta ]==> ((a ((a a) a))(b (^y.y))) 6. ==[ alpha ]==> ((a ((a a) a))(b (^x.x))) REDUCED to normal form. ------ 179638/20710497. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(^z.a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)(^y.a))) 5. ==[ beta ]==> ((((a a) a) a)(^y.a)) 6. ==[ alpha ]==> ((((a a) a) a)(^x.a)) REDUCED to normal form. ------ 179639/20710515. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.(^a.a))) d)) 2. ==[ alpha ]==> (((^x.b) c)((a (^y.(^z.z))) d)) 3. ==[ beta ]==> (b ((a (^y.(^z.z))) d)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) d)) REDUCED to normal form. ------ 179640/20710524. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 179641/20710749. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c ((^z.z) b))) 3. ==[ beta ]==> (b (c ((^z.z) b))) 4. ==[ alpha ]==> (b (c ((^x.x) b))) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 179642/20710830. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))(a a))) REDUCED to normal form. ------ 179643/20710857. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1) b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 6. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 179644/20710866. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) c) REDUCED to normal form. ------ 179645/20710911. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((b a)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((b a)(a (a a)))) REDUCED to normal form. ------ 179646/20710992. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a b)(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a b)(a b))) 3. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 179647/20711145. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(b (^y.(a a)))) 3. ==[ beta ]==> ((a (a b))(b (^y.(a a)))) 4. ==[ alpha ]==> ((a (a b))(b (^x.(a a)))) REDUCED to normal form. ------ 179648/20711226. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(a (^y.y))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 179649/20711253. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 179650/20711334. ------ 1. ==[ start ]==> ((a (b a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((a (b a))((^x.(a a))((a a) a))) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 179651/20711568. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) b) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(b b)) REDUCED to normal form. ------ 179652/20711883. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((a a)(a a)))) REDUCED to normal form. ------ 179653/20712180. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179654/20712567. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y) b) a)) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(b a)) REDUCED to normal form. ------ 179655/20712594. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1))) b)) 6. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z))) b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 179656/20712846. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 179657/20712873. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 179658/20713098. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(a a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(a a))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 179659/20713125. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1) a)((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1) a)((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y) a)((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x) a)((a a)(^y.y))) 7. ==[ beta ]==> (a ((a a)(^y.y))) 8. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 179660/20713377. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(^x1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.b)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.b)) REDUCED to normal form. ------ 179661/20713404. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (a a))(^y.(a a)))) 3. ==[ beta ]==> ((b a)((a (a a))(^y.(a a)))) 4. ==[ alpha ]==> ((b a)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 179662/20713431. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 179663/20713539. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((b a) b)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((b a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a) b)) 5. ==[ beta ]==> ((^y.(a a))((b a) b)) 6. ==[ alpha ]==> ((^x.(a a))((b a) b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 179664/20713566. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 179665/20713593. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(a a)) d)) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a)) d)) 3. ==[ beta ]==> (((a b)(^x.a))((a a) d)) REDUCED to normal form. ------ 179666/20713791. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 179667/20714088. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 179668/20714403. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a)(^y.y)) b)) 3. ==[ beta ]==> ((b b)(((a a)(^y.y)) b)) 4. ==[ alpha ]==> ((b b)(((a a)(^x.x)) b)) REDUCED to normal form. ------ 179669/20714610. ------ 1. ==[ start ]==> (((^a.b)(a b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(b ((a a)(^y.y)))) 3. ==[ beta ]==> (b (b ((a a)(^y.y)))) 4. ==[ alpha ]==> (b (b ((a a)(^x.x)))) REDUCED to normal form. ------ 179670/20714673. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 179671/20714718. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a b)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179672/20714844. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(c (^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(c (^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(c (^y.(a a)))) REDUCED to normal form. ------ 179673/20714871. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 179674/20714952. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 179675/20714979. ------ 1. ==[ start ]==> (((a b)(a b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.b)((^y.y) a))) 3. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 179676/20715033. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 179677/20715087. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.a)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 179678/20715114. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 179679/20715141. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.x)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))((a a)(^x.x))) REDUCED to normal form. ------ 179680/20715168. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 179681/20715339. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c (a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(c (a b))) 3. ==[ beta ]==> (b (c (a b))) REDUCED to normal form. ------ 179682/20715447. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179683/20715483. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a) d)) 3. ==[ beta ]==> ((b c)((^y.a) d)) 4. ==[ alpha ]==> ((b c)((^x.a) d)) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 179684/20715555. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((b (^x.x))(a ((a a) a))) REDUCED to normal form. ------ 179685/20715582. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a (^z.z))(a b))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(a b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a b))) 5. ==[ beta ]==> ((a (^y.y))(a b)) 6. ==[ alpha ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 179686/20715645. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 179687/20715726. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a b)(^x.(a a)))(^z.(z z))) 6. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(y y))) REDUCED to normal form. ------ 179688/20715753. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 179689/20715834. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(^x1.(a a)))) REDUCED to normal form. ------ 179690/20715861. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(a a)) a)) 5. ==[ beta ]==> ((b (^x.a))((a a) a)) REDUCED to normal form. ------ 179691/20715888. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a b) b)) REDUCED to normal form. ------ 179692/20715951. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 179693/20715978. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 179694/20716005. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.a))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 179695/20716032. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 179696/20716059. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.(a a)))) 7. ==[ beta ]==> ((b a)(^y.(a a))) 8. ==[ alpha ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 179697/20716248. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(b (^z.b))) 3. ==[ beta ]==> ((b ((^y.y) a))(b (^z.b))) 4. ==[ alpha ]==> ((b ((^x.x) a))(b (^y.b))) 5. ==[ beta ]==> ((b a)(b (^y.b))) 6. ==[ alpha ]==> ((b a)(b (^x.b))) REDUCED to normal form. ------ 179698/20716275. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 179699/20716608. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c ((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179700/20716725. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z)) c)) 5. ==[ beta ]==> (a ((^y.(^z.z)) c)) 6. ==[ alpha ]==> (a ((^x.(^y.y)) c)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 179701/20716743. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a (a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a (a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) a))) 7. ==[ beta ]==> ((a (a a))((^y.y) a)) 8. ==[ alpha ]==> ((a (a a))((^x.x) a)) 9. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 179702/20716770. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1) a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> (((^y.y) a)(a (a a))) 6. ==[ alpha ]==> (((^x.x) a)(a (a a))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 179703/20716824. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)((a a) a))) 7. ==[ beta ]==> ((b b)((a a)((a a) a))) REDUCED to normal form. ------ 179704/20716860. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((a a) a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a)(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(^x1.x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179705/20716914. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(^z.a))) REDUCED to normal form. ------ 179706/20716941. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a (^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.(y y)))) REDUCED to normal form. ------ 179707/20716968. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 179708/20717022. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a) a) a)) REDUCED to normal form. ------ 179709/20717049. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z) b)) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y) b)) 7. ==[ beta ]==> ((b (^x.(x x))) b) REDUCED to normal form. ------ 179710/20717076. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (a a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (a a)) c)) REDUCED to normal form. ------ 179711/20717148. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(b (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (^z.z))) REDUCED to normal form. ------ 179712/20717301. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 179713/20717328. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (^c.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.a))) REDUCED to normal form. ------ 179714/20717355. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(a a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a a))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 179715/20717382. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 179716/20717436. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 179717/20717463. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> ((b (a (a a)))(^y.y)) 8. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 179718/20717490. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 179719/20717544. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a a)((^y.a)(^z.a))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.a))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 179720/20717571. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 179721/20717580. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(b (a (a a)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(b (a (a a)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(b (a (a a)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 179722/20717967. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(z z)) a)) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z)) a)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y)) a)) 5. ==[ beta ]==> (b ((^y.(y y)) a)) 6. ==[ alpha ]==> (b ((^x.(x x)) a)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 179723/20717985. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a a))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a))) 7. ==[ beta ]==> (((^y.y) a)(a a)) 8. ==[ alpha ]==> (((^x.x) a)(a a)) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 179724/20717994. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a) b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a) b)) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 179725/20718012. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 179726/20718039. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a))) 5. ==[ beta ]==> ((a a)((^y.y) a)) 6. ==[ alpha ]==> ((a a)((^x.x) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 179727/20718129. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.a))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.a))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.a))) 7. ==[ beta ]==> ((a a)(^y.a)) 8. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 179728/20718156. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1) a) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 179729/20718174. ------ 1. ==[ start ]==> (((^a.b)(b a))(c (a a))) 2. ==[ alpha ]==> (((^x.b)(b a))(c (a a))) 3. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 179730/20718237. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 179731/20718282. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179732/20718318. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 179733/20718345. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 179734/20718399. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a) b)) 5. ==[ beta ]==> ((^y.(^z.z))((a a) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179735/20718417. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 179736/20718426. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 179737/20718444. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 179738/20718462. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (^y.(^z.z)))) REDUCED to normal form. ------ 179739/20718489. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 179740/20718516. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 179741/20718543. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a (^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (^x.x))) REDUCED to normal form. ------ 179742/20723028. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179743/20729805. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179744/20729817. ------ 1. ==[ start ]==> (((^a.a) b)(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> (b (^y.(a (a (^z.z))))) 4. ==[ alpha ]==> (b (^x.(a (a (^y.y))))) REDUCED to normal form. ------ 179745/20729850. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a (a (^z.z)))(^x1.x1))(^y.y)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 179746/20729967. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (^x.((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^x.((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179747/20730039. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ eta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 179748/20730210. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 179749/20730309. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((((^y.(^z.z)) a) b)((((^y.(^z.z)) a) b)(((^y.(^z.z)) a) b))) 4. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((((^z.(^x1.x1)) a) b)(((^y1.(^z1.z1)) a) b))) 5. ==[ beta ]==> (((^y.y) b)((((^z.(^x1.x1)) a) b)(((^y1.(^z1.z1)) a) b))) 6. ==[ alpha ]==> (((^x.x) b)((((^y.(^z.z)) a) b)(((^x1.(^y1.y1)) a) b))) 7. ==[ beta ]==> (b ((((^y.(^z.z)) a) b)(((^x1.(^y1.y1)) a) b))) 8. ==[ alpha ]==> (b ((((^x.(^y.y)) a) b)(((^z.(^x1.x1)) a) b))) 9. ==[ beta ]==> (b (((^y.y) b)(((^z.(^x1.x1)) a) b))) 10. ==[ alpha ]==> (b (((^x.x) b)(((^y.(^z.z)) a) b))) 11. ==[ beta ]==> (b (b (((^y.(^z.z)) a) b))) 12. ==[ alpha ]==> (b (b (((^x.(^y.y)) a) b))) 13. ==[ beta ]==> (b (b ((^y.y) b))) 14. ==[ alpha ]==> (b (b ((^x.x) b))) 15. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 179750/20730699. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 179751/20731131. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 179752/20731425. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 179753/20731605. ------ 1. ==[ start ]==> ((^a.(a b))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((^x.(x b))(((a a)(a a)) c)) 3. ==[ beta ]==> ((((a a)(a a)) c) b) REDUCED to normal form. ------ 179754/20731950. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 179755/20733111. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(b (^z.z)))) REDUCED to normal form. ------ 179756/20733630. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y)(a a))(^z.a))) 3. ==[ eta ]==> (b (((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (b ((a a)(^y.a))) 6. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 179757/20734182. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(a a)))) REDUCED to normal form. ------ 179758/20734857. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.(x x))((^y.y)(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.z)) 5. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.z)) 6. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.z)) 7. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.z)) 8. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.y)) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 179759/20735070. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179760/20735802. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 179761/20736666. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^b.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.(y1 a))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(y1 a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179762/20737464. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a)(^z.z)) a)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179763/20737917. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 179764/20738625. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^y.(^z.z))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179765/20739132. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.((a a) a))) REDUCED to normal form. ------ 179766/20739312. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179767/20739444. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 179768/20739762. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 179769/20740266. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(z (z z)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(z (z z)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(y (y y)))) 5. ==[ beta ]==> (b (^y.(y (y y)))) 6. ==[ alpha ]==> (b (^x.(x (x x)))) REDUCED to normal form. ------ 179770/20740536. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 179771/20740716. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 179772/20740725. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 179773/20740740. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (^y1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179774/20740761. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 179775/20740815. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.a)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.a)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.a)) REDUCED to normal form. ------ 179776/20740842. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.a)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.a)) REDUCED to normal form. ------ 179777/20740890. ------ 1. ==[ start ]==> (((^a.a) a)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x) a)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (a ((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 179778/20740917. ------ 1. ==[ start ]==> (((a a) a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> (((a a) a)(a (b (^y.y)))) 4. ==[ alpha ]==> (((a a) a)(a (b (^x.x)))) REDUCED to normal form. ------ 179779/20740944. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.x))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 179780/20740962. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 179781/20740971. ------ 1. ==[ start ]==> (((^a.a) b)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)((a a)(a (a (^y.y))))) 3. ==[ beta ]==> (b ((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> (b ((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 179782/20741007. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 179783/20741016. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 (^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179784/20741124. ------ 1. ==[ start ]==> ((a (^b.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 179785/20741169. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b a)(^y.b))) REDUCED to normal form. ------ 179786/20741196. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 179787/20741205. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 179788/20741232. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 179789/20741313. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179790/20741367. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a (^x.(x x))) a) REDUCED to normal form. ------ 179791/20741412. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 179792/20741439. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a (a (^y.y))) a)) 3. ==[ beta ]==> ((a (a a))((a (a (^y.y))) a)) 4. ==[ alpha ]==> ((a (a a))((a (a (^x.x))) a)) REDUCED to normal form. ------ 179793/20741466. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> ((a (a (a a)))((^y.y) b)) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x) b)) 5. ==[ beta ]==> ((a (a (a a))) b) REDUCED to normal form. ------ 179794/20741556. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179795/20741664. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 179796/20741853. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 7. ==[ beta ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 179797/20741916. ------ 1. ==[ start ]==> (((a (a a)) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 179798/20741943. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (a (((a a)(a a))((^y.y) a))) 6. ==[ alpha ]==> (a (((a a)(a a))((^x.x) a))) 7. ==[ beta ]==> (a (((a a)(a a)) a)) REDUCED to normal form. ------ 179799/20741970. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (a (a a)))) REDUCED to normal form. ------ 179800/20741997. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((a (^z.(^x1.x1)))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 179801/20742024. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b a)((a a) a))) 3. ==[ beta ]==> ((a (^y.a))((b a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.a))((b a)((a a) a))) REDUCED to normal form. ------ 179802/20742051. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 179803/20742078. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 179804/20742285. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(y (^z.z))))) 5. ==[ beta ]==> (a (^y.(y (^z.z)))) 6. ==[ alpha ]==> (a (^x.(x (^y.y)))) REDUCED to normal form. ------ 179805/20742420. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 179806/20742501. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)((^y.(a a))((^z.z)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))((^y.y)(a a)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 179807/20742582. ------ 1. ==[ start ]==> ((a (^a.b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 179808/20742600. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (a a))(^x.x))) REDUCED to normal form. ------ 179809/20742708. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a) a)) 6. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a) a)) 7. ==[ beta ]==> ((a (^x.x))((^z.z) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 179810/20742735. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(a a))((b (^x.x)) b)) REDUCED to normal form. ------ 179811/20742762. ------ 1. ==[ start ]==> ((a (a b))(((a a)(a a)) c)) REDUCED to normal form. ------ 179812/20742771. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 179813/20742933. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 179814/20742960. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.a))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 179815/20742987. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179816/20743041. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 179817/20743077. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(b (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(b (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(b (b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (b (^z.z)))) 6. ==[ alpha ]==> ((^x.a)(b (b (^y.y)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 179818/20743104. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 179819/20743131. ------ 1. ==[ start ]==> (((a b)(^a.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.x))((b (^y.y))(a a))) REDUCED to normal form. ------ 179820/20743167. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a)) c)) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 179821/20743320. ------ 1. ==[ start ]==> (((^a.b) b)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (b ((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 179822/20743446. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(c (^x1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(c (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c (^y1.(a a)))) 5. ==[ beta ]==> ((^y.y)(c (^y1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(c (^y.(a a)))) 7. ==[ beta ]==> (c (^y.(a a))) 8. ==[ alpha ]==> (c (^x.(a a))) REDUCED to normal form. ------ 179823/20743581. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a a)((^y.y)((^z.z) a))) 6. ==[ alpha ]==> ((a a)((^x.x)((^y.y) a))) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 179824/20743608. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179825/20743743. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179826/20743815. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^y.y))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 179827/20743842. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 179828/20743896. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((b (^z.z)) a)) 3. ==[ beta ]==> (((a (a a))(^y.y))((b (^z.z)) a)) 4. ==[ alpha ]==> (((a (a a))(^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 179829/20743923. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(a a)) b)) 5. ==[ beta ]==> ((a (a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 179830/20743950. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((^y.y) b) c)) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y) b) c)) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x) b) c)) 5. ==[ beta ]==> ((((a a) a) a)(b c)) REDUCED to normal form. ------ 179831/20744067. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.b))) 5. ==[ beta ]==> ((^y.(a a))(^z.b)) 6. ==[ alpha ]==> ((^x.(a a))(^y.b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 179832/20744202. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179833/20744211. ------ 1. ==[ start ]==> (((a b) c)(c ((^a.a) b))) 2. ==[ alpha ]==> (((a b) c)(c ((^x.x) b))) 3. ==[ beta ]==> (((a b) c)(c b)) REDUCED to normal form. ------ 179834/20744238. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(b ((a a)(a a)))) 3. ==[ beta ]==> (((a a) b)(b ((a a)(a a)))) REDUCED to normal form. ------ 179835/20744265. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(a (b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(a (b (^y.y)))) REDUCED to normal form. ------ 179836/20744319. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(b (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(b (a (^z.z)))) REDUCED to normal form. ------ 179837/20744346. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.b))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 179838/20744400. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179839/20744427. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)((a a) a))) REDUCED to normal form. ------ 179840/20744454. ------ 1. ==[ start ]==> (((a b)(^b.a))((a b)(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)(a b))) REDUCED to normal form. ------ 179841/20744481. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 179842/20744508. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 179843/20744652. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(a a))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(a a))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.z))) 7. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.z))) 8. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.y))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 179844/20744679. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 179845/20744706. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a b) a)((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 179846/20744733. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 179847/20744760. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 179848/20744787. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((a (b a))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> ((a (b a))((a a)(^y.a))) 4. ==[ alpha ]==> ((a (b a))((a a)(^x.a))) REDUCED to normal form. ------ 179849/20744877. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179850/20744958. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179851/20745066. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 179852/20745147. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(a b))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 179853/20745228. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179854/20745354. ------ 1. ==[ start ]==> (((a a)(b a))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a a)(b a))((^x.(a a)) a)) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 179855/20745381. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z) b)) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 179856/20745615. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1) a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179857/20745714. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z)(a a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z)(a a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z)(a a))) 5. ==[ beta ]==> ((a a)((^z.z)(a a))) 6. ==[ alpha ]==> ((a a)((^x.x)(a a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 179858/20745795. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179859/20745903. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.z1))((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179860/20745930. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(((a a)(^x1.x1))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 179861/20745957. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.a)(b a))) 3. ==[ beta ]==> ((^y.y)((^z.a)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b a))) 5. ==[ beta ]==> ((^y.a)(b a)) 6. ==[ alpha ]==> ((^x.a)(b a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 179862/20746011. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)((^x1.x1) b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)((^z.z) b))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z) b))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y) b))) 9. ==[ beta ]==> (((a a)(a a))((^y.y) b)) 10. ==[ alpha ]==> (((a a)(a a))((^x.x) b)) 11. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 179863/20746227. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 179864/20746353. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.z) a)) 3. ==[ beta ]==> (((^y.y)(a b))((^z.z) a)) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.y) a)) 5. ==[ beta ]==> ((a b)((^y.y) a)) 6. ==[ alpha ]==> ((a b)((^x.x) a)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 179865/20746380. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.(^z.z))) b)) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 179866/20746506. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((a a) a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179867/20746713. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^d.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179868/20746875. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.(y y))((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(a a)))) 7. ==[ beta ]==> (b (((^y.y)(a a))((^y.y)(a a)))) 8. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(a a)))) 9. ==[ beta ]==> (b ((a a)((^y.y)(a a)))) 10. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 11. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 179869/20746902. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.a)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.a)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.a)((a a)(^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 179870/20746956. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 179871/20747037. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179872/20747145. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179873/20747271. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a (b a))((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 179874/20747712. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179875/20747820. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.y1)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179876/20747901. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 179877/20747928. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(z z)))) 5. ==[ beta ]==> ((^y.b)(^z.(z z))) 6. ==[ alpha ]==> ((^x.b)(^y.(y y))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 179878/20747982. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 179879/20748045. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(c (a a))) REDUCED to normal form. ------ 179880/20748063. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179881/20748072. ------ 1. ==[ start ]==> (((a b)(^a.b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(b ((a a)(^y.y)))) REDUCED to normal form. ------ 179882/20748126. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(a a))) REDUCED to normal form. ------ 179883/20748180. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a b) a)) REDUCED to normal form. ------ 179884/20748207. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 179885/20748234. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((((a a)(a a))(^x.x))(^z.z)) 8. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 179886/20748378. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 179887/20748405. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 179888/20748432. ------ 1. ==[ start ]==> (((a b)(a b))((a b)(^b.a))) 2. ==[ alpha ]==> (((a b)(a b))((a b)(^x.a))) REDUCED to normal form. ------ 179889/20748459. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((a a) a)(^y.(y y)))) 3. ==[ beta ]==> (((a a)((a a) a))(((a a) a)(^y.(y y)))) 4. ==[ alpha ]==> (((a a)((a a) a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 179890/20748486. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 179891/20748540. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (^x1.b))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(a (^z.b))) REDUCED to normal form. ------ 179892/20748567. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 179893/20748621. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 179894/20748792. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (b ((^z.a)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.a)(^y.b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179895/20748936. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((b c)(((a a) a)((^y.y) a))) 4. ==[ alpha ]==> ((b c)(((a a) a)((^x.x) a))) 5. ==[ beta ]==> ((b c)(((a a) a) a)) REDUCED to normal form. ------ 179896/20748963. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(^y.y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a)) b)(a (a a))) REDUCED to normal form. ------ 179897/20749071. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 179898/20749170. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179899/20749278. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179900/20749539. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(a a)) a)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 179901/20749566. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.b) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.b) b)) 3. ==[ beta ]==> (((a b)(a a))((^y.b) b)) 4. ==[ alpha ]==> (((a b)(a a))((^x.b) b)) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 179902/20749593. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a) c)) 3. ==[ beta ]==> (((a a)(a b))((^y.a) c)) 4. ==[ alpha ]==> (((a a)(a b))((^x.a) c)) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 179903/20749782. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 179904/20749872. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 179905/20749953. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (b ((^x1.b)(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.b)(^y.y))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 179906/20750061. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179907/20750178. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (a ((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> (a ((^x.x)(a (^y.y)))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 179908/20750277. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b (^z.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b (^z.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b (^z.a))) 5. ==[ beta ]==> ((b ((^y.y) b))(b (^z.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(b (^y.a))) 7. ==[ beta ]==> ((b b)(b (^y.a))) 8. ==[ alpha ]==> ((b b)(b (^x.a))) REDUCED to normal form. ------ 179909/20750286. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)((a a) a))) REDUCED to normal form. ------ 179910/20750358. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179911/20750466. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.z1)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179912/20750601. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 179913/20750646. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a) a)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 179914/20750673. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z)) b)) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y)) b)) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 179915/20750700. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y)) c)) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y)) c)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x)) c)) 5. ==[ beta ]==> (((a (a a)) b)(c c)) REDUCED to normal form. ------ 179916/20750808. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 179917/20750835. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 179918/20750889. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(^y1.(y1 y1)))) REDUCED to normal form. ------ 179919/20750916. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a a)(^y.(^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 179920/20750943. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(^y.y)) a)) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.y) a)) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x) a)) 7. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 179921/20751033. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((^z.(^x1.x1))(^y1.(y1 y1)))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.x1)) 7. ==[ beta ]==> ((^y.y)(^x1.x1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179922/20751420. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(a (a (a a)))) 3. ==[ beta ]==> (((^y.y) b)(a (a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)(a (a (a a)))) 5. ==[ beta ]==> (b (a (a (a a)))) REDUCED to normal form. ------ 179923/20751447. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y) a)(a a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a (a a))) REDUCED to normal form. ------ 179924/20751474. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 179925/20751492. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b (^y1.a))) 3. ==[ beta ]==> ((^y.y)(b (^y1.a))) 4. ==[ alpha ]==> ((^x.x)(b (^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 179926/20751546. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a)(a a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a)(a a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a)(a a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 179927/20751582. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b c)) 3. ==[ beta ]==> (((^y.y)(^z.z))(b c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b c)) 5. ==[ beta ]==> ((^y.y)(b c)) 6. ==[ alpha ]==> ((^x.x)(b c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 179928/20751627. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a)(^z.z))) 3. ==[ beta ]==> (b ((^y.a)(^z.z))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179929/20751690. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 179930/20751735. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179931/20751771. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c a)) REDUCED to normal form. ------ 179932/20751798. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b b)) REDUCED to normal form. ------ 179933/20751852. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b (a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (a a))) 5. ==[ beta ]==> ((^y.(^z.z))(b (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179934/20751870. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 179935/20751879. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (a (^z.z)))) REDUCED to normal form. ------ 179936/20751897. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.x1))) REDUCED to normal form. ------ 179937/20751915. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a) b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y) b)) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) b) REDUCED to normal form. ------ 179938/20751942. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 179939/20751969. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a) a)) 3. ==[ beta ]==> ((a (b (^y.y)))((a a) a)) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a) a)) REDUCED to normal form. ------ 179940/20751996. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x) a)) 3. ==[ beta ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 179941/20752022. ------ 1. ==[ start ]==> (^a.(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (^x.(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (^x.((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (^x.((^y.y)((^z.z) b))) 5. ==[ beta ]==> (^x.((^z.z) b)) 6. ==[ alpha ]==> (^x.((^y.y) b)) 7. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 179942/20752023. ------ 1. ==[ start ]==> (a (((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (a (((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> (a ((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (a ((^x.x)((^y.y) b))) 5. ==[ beta ]==> (a ((^y.y) b)) 6. ==[ alpha ]==> (a ((^x.x) b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 179943/20763180. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b)) a) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b)) a) 3. ==[ beta ]==> (((^y.y)((^z.z) b)) a) 4. ==[ alpha ]==> (((^x.x)((^y.y) b)) a) 5. ==[ beta ]==> (((^y.y) b) a) 6. ==[ alpha ]==> (((^x.x) b) a) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 179944/20763186. ------ 1. ==[ start ]==> ((^a.a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 5. ==[ beta ]==> ((^y.y)((^z.z) b)) 6. ==[ alpha ]==> ((^x.x)((^y.y) b)) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 179945/20763213. ------ 1. ==[ start ]==> ((^a.(a a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x x))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 179946/20763240. ------ 1. ==[ start ]==> ((^a.b)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 179947/20763315. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 179948/20763438. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^x.(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(b (^y.(^z.z)))) REDUCED to normal form. ------ 179949/20764563. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((((a (^y.y))(b (^z.z)))((a (^y.y))(b (^z.z))))((a (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> ((((a (^x.x))(b (^y.y)))((a (^z.z))(b (^x1.x1))))((a (^y1.y1))(b (^z1.z1)))) REDUCED to normal form. ------ 179950/20764896. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 179951/20765670. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)((((a a) a)((a a)(^z.z)))(((a a) a)((a a)(^z.z))))) 4. ==[ alpha ]==> ((^x.x)((((a a) a)((a a)(^y.y)))(((a a) a)((a a)(^z.z))))) 5. ==[ beta ]==> ((((a a) a)((a a)(^y.y)))(((a a) a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 179952/20767671. ------ 1. ==[ start ]==> (((a a)(b a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.((x x)(x x)))) REDUCED to normal form. ------ 179953/20767938. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> ((((^x1.x1) a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(^z.z))) 5. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 179954/20768337. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 179955/20768670. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.((^z.z) b))) 5. ==[ beta ]==> ((a b)(^y.((^z.z) b))) 6. ==[ alpha ]==> ((a b)(^x.((^y.y) b))) 7. ==[ beta ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 179956/20768856. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 179957/20769588. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))(^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 179958/20769855. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a a)(b a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a a)(b a))) 3. ==[ beta ]==> ((((a a)(b a))((a a)(b a)))(((a a)(b a))((a a)(b a)))) REDUCED to normal form. ------ 179959/20770137. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179960/20770668. ------ 1. ==[ start ]==> (((a (a a))(b a))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 179961/20771631. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.a))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.a))(^y.(a a))) REDUCED to normal form. ------ 179962/20771856. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^y.(y y))) REDUCED to normal form. ------ 179963/20772630. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179964/20772792. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((a a) a))) REDUCED to normal form. ------ 179965/20772963. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.((z z) z))) REDUCED to normal form. ------ 179966/20773098. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 179967/20773737. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z)))) 5. ==[ beta ]==> (b (^y.(^z.(z z)))) 6. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 179968/20773926. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 179969/20774007. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.a))) REDUCED to normal form. ------ 179970/20774088. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 179971/20774196. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 179972/20774211. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 179973/20774286. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.b)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.b)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.b)) REDUCED to normal form. ------ 179974/20774313. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(x x))) REDUCED to normal form. ------ 179975/20774340. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.x1)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.x1)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.z)) 5. ==[ beta ]==> (((^y.y) b)(^z.z)) 6. ==[ alpha ]==> (((^x.x) b)(^y.y)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 179976/20774352. ------ 1. ==[ start ]==> ((a a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a a)((^y.y)((^z.z) b))) 4. ==[ alpha ]==> ((a a)((^x.x)((^y.y) b))) 5. ==[ beta ]==> ((a a)((^y.y) b)) 6. ==[ alpha ]==> ((a a)((^x.x) b)) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 179977/20774379. ------ 1. ==[ start ]==> ((a (a a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 179978/20774406. ------ 1. ==[ start ]==> ((a b)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> ((a b)(a (b (^y.y)))) 4. ==[ alpha ]==> ((a b)(a (b (^x.x)))) REDUCED to normal form. ------ 179979/20774451. ------ 1. ==[ start ]==> (((^a.a) b)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(b (^y.(y (^z.z))))) 3. ==[ beta ]==> (b (b (^y.(y (^z.z))))) 4. ==[ alpha ]==> (b (b (^x.(x (^y.y))))) REDUCED to normal form. ------ 179980/20774460. ------ 1. ==[ start ]==> (((a a)(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 179981/20774478. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 179982/20774496. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a (^z.z)))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179983/20774505. ------ 1. ==[ start ]==> (((a a) b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a) b)((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> (((a a) b)((a a)(^y.y))) 4. ==[ alpha ]==> (((a a) b)((a a)(^x.x))) REDUCED to normal form. ------ 179984/20774523. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179985/20774550. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 179986/20774577. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 179987/20774604. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 179988/20774640. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 179989/20774685. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.a)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 179990/20774721. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 179991/20774748. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.b)(b a))) 3. ==[ beta ]==> ((a a)((^y.b)(b a))) 4. ==[ alpha ]==> ((a a)((^x.b)(b a))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 179992/20774766. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (((a a) a)(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (a (((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 179993/20774775. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 179994/20774793. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 179995/20774802. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 179996/20774829. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 179997/20774937. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a a)((^z.z)(^y.y))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 179998/20774955. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((^y.(y y))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> ((((^y.(^z.z)) a) b)(((^y.(^z.z)) a) b)) 6. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.(^x1.x1)) a) b)) 7. ==[ beta ]==> (((^y.y) b)(((^z.(^x1.x1)) a) b)) 8. ==[ alpha ]==> (((^x.x) b)(((^y.(^z.z)) a) b)) 9. ==[ beta ]==> (b (((^y.(^z.z)) a) b)) 10. ==[ alpha ]==> (b (((^x.(^y.y)) a) b)) 11. ==[ beta ]==> (b ((^y.y) b)) 12. ==[ alpha ]==> (b ((^x.x) b)) 13. ==[ beta ]==> (b b) REDUCED to normal form. ------ 179999/20774982. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((b (^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 5. ==[ beta ]==> ((b (^y.y)) c) 6. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 180000/20775018. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 180001/20775045. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 180002/20775153. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 180003/20775261. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((b b)((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> ((b b)((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> ((b b)((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 180004/20775594. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 180005/20775621. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((a a) a)(b a))) REDUCED to normal form. ------ 180006/20775648. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)((^y.y)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 9. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 10. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 180007/20775675. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 180008/20775702. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)((a a)(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)((a a)(a a)))) 7. ==[ beta ]==> ((a a)(a ((a a)(a a)))) REDUCED to normal form. ------ 180009/20775729. ------ 1. ==[ start ]==> ((a ((a a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 180010/20775819. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a ((b (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a ((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 180011/20775855. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> (b ((^y.(a a))((^z.z) a))) 6. ==[ alpha ]==> (b ((^x.(a a))((^y.y) a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 180012/20775882. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.x)(a (a a)))) 3. ==[ beta ]==> ((((a a) a) a)(a (a a))) REDUCED to normal form. ------ 180013/20775900. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 180014/20775927. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((b a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 180015/20775981. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.(a a)))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(a a)))) 9. ==[ beta ]==> ((a a)((a a)(^y.(a a)))) 10. ==[ alpha ]==> ((a a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 180016/20775990. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a a)) REDUCED to normal form. ------ 180017/20776017. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.b)((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.b)((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)((a a)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((a a)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180018/20776062. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.b))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 180019/20776251. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(a a)) c)) 3. ==[ beta ]==> ((^y.b)(((a a)(a a)) c)) 4. ==[ alpha ]==> ((^x.b)(((a a)(a a)) c)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 180020/20776395. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 180021/20776422. ------ 1. ==[ start ]==> (((a b) a)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 180022/20776449. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 180023/20776503. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 180024/20776530. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x))) a) REDUCED to normal form. ------ 180025/20776647. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 180026/20776674. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(b ((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(b a)) REDUCED to normal form. ------ 180027/20776701. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 180028/20776728. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b a)(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)(^x.x))) REDUCED to normal form. ------ 180029/20776755. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))((a a) a))) 6. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))((a a) a))) 7. ==[ beta ]==> (a (((a a)(^y.y))((a a) a))) 8. ==[ alpha ]==> (a (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 180030/20776782. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((a a)(a b))) REDUCED to normal form. ------ 180031/20776809. ------ 1. ==[ start ]==> (((a b)(a a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a b)(a a))((a b)(a a))) REDUCED to normal form. ------ 180032/20776836. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> ((a (a a))(((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((a (a a))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 180033/20777007. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (b ((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 180034/20777061. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)(^z.a))) 5. ==[ beta ]==> ((a a)(((^y.y) b)(^z.a))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.a))) 7. ==[ beta ]==> ((a a)(b (^y.a))) 8. ==[ alpha ]==> ((a a)(b (^x.a))) REDUCED to normal form. ------ 180035/20777070. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) a)) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 180036/20777088. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 180037/20777097. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 180038/20777151. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 180039/20777178. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))(a b))) 5. ==[ beta ]==> ((^y.(y y))((^z.(a a))(a b))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(a b))) 7. ==[ beta ]==> (((^y.(a a))(a b))((^y.(a a))(a b))) 8. ==[ alpha ]==> (((^x.(a a))(a b))((^y.(a a))(a b))) 9. ==[ beta ]==> ((a a)((^y.(a a))(a b))) 10. ==[ alpha ]==> ((a a)((^x.(a a))(a b))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 180040/20777205. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) b) REDUCED to normal form. ------ 180041/20777223. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 180042/20777232. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 180043/20777259. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(b a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 180044/20777448. ------ 1. ==[ start ]==> (((^a.b) c)((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.y)(^z.a))) 3. ==[ beta ]==> (b ((^y.y)(^z.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 180045/20777691. ------ 1. ==[ start ]==> (((a b) c)((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(^y.y))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 180046/20777718. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 180047/20778024. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (a a))(b a))) REDUCED to normal form. ------ 180048/20778051. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 180049/20778078. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a (a b))((a (^y.y))((^z.z) b))) 4. ==[ alpha ]==> ((a (a b))((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> ((a (a b))((a (^x.x)) b)) REDUCED to normal form. ------ 180050/20778105. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 180051/20778357. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> (b (^y.(^z.z))) 10. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180052/20778438. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 180053/20778501. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 180054/20778546. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.(^z.z))) c)) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z))) c)) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 180055/20778609. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 180056/20778636. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 180057/20778690. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 180058/20778717. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 180059/20778771. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 180060/20778834. ------ 1. ==[ start ]==> (((a a)(b a))(a ((a a)(a a)))) REDUCED to normal form. ------ 180061/20778861. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(b (a a))) REDUCED to normal form. ------ 180062/20778888. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 180063/20778915. ------ 1. ==[ start ]==> (((a (a a))(a b))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a b))((b a)((^x.x) a))) 3. ==[ beta ]==> (((a (a a))(a b))((b a) a)) REDUCED to normal form. ------ 180064/20778942. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(a (a a)))) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 180065/20778969. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((((a a) a)(^x.x))((a a)(^z.z))) 8. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 180066/20778996. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a b)((a a) a))) REDUCED to normal form. ------ 180067/20779023. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((a a) a)(a b))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((a a) a)(a b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((a a) a)(a b))) 5. ==[ beta ]==> (((a a) a)(((a a) a)(a b))) REDUCED to normal form. ------ 180068/20779050. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 180069/20779104. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (b a))) REDUCED to normal form. ------ 180070/20779194. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> ((a a)(((^z.z) b)(^x1.x1))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.y))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 180071/20779275. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 180072/20779383. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1)(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180073/20779392. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 180074/20779419. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(((a a)(^y1.y1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((a a)(^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 180075/20779491. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a a)(^z.z))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a a)(^z.z))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)(^z.z))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)(^y.y))) 7. ==[ beta ]==> (((a a)(a a))((a a)(^y.y))) 8. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 180076/20779500. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.z) b)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y) b)) 5. ==[ beta ]==> (((a (a a))(^x.(a a))) b) REDUCED to normal form. ------ 180077/20779527. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((^y.b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 180078/20779572. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((b a) c)) 3. ==[ beta ]==> (b ((b a) c)) REDUCED to normal form. ------ 180079/20779635. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 180080/20779806. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(b (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a (a a))(a a))(b (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a (a a))(a a))(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 180081/20779833. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(a ((^z.z) b))) 3. ==[ beta ]==> (((^y.y)(a b))(a ((^z.z) b))) 4. ==[ alpha ]==> (((^x.x)(a b))(a ((^y.y) b))) 5. ==[ beta ]==> ((a b)(a ((^y.y) b))) 6. ==[ alpha ]==> ((a b)(a ((^x.x) b))) 7. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 180082/20779860. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 180083/20779887. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((b a)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^y.y))((b a)(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.x))((b a)(a (^y.y)))) REDUCED to normal form. ------ 180084/20779914. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a (a a)))(((a a)(^x.x)) a)) REDUCED to normal form. ------ 180085/20779941. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(a (a a)))) REDUCED to normal form. ------ 180086/20779995. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 180087/20780022. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(a b))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(a b))) 5. ==[ beta ]==> ((a b)((^y.y)(a b))) 6. ==[ alpha ]==> ((a b)((^x.x)(a b))) 7. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 180088/20780193. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 180089/20780310. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 180090/20780337. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 180091/20780355. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))(^y.(a a)))) 5. ==[ beta ]==> (b ((a (a a))(^y.(a a)))) 6. ==[ alpha ]==> (b ((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 180092/20780364. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 180093/20780391. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.a)((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) a) REDUCED to normal form. ------ 180094/20780436. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 180095/20780472. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.(^y1.y1)))(^z1.z1))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.(^x1.x1)))(^y1.y1))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180096/20780517. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((a a)(^y.y)) c)) 3. ==[ beta ]==> (b (((a a)(^y.y)) c)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) c)) REDUCED to normal form. ------ 180097/20780526. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 180098/20780553. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 180099/20780580. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 180100/20780634. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 180101/20780661. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> ((b (^x.x))((^z.(a a))(^z.(a a)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 180102/20780697. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(c ((a a)(^y.y)))) 3. ==[ beta ]==> (((a a) b)(c ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a) b)(c ((a a)(^x.x)))) REDUCED to normal form. ------ 180103/20780724. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(b (b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(b (b a))) REDUCED to normal form. ------ 180104/20780751. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (b a))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (b a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 180105/20780778. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((b a)(a a))) REDUCED to normal form. ------ 180106/20780805. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((a a)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a a)(((a a)(^y.y))(a (^z.z)))) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 180107/20780832. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(a b))((a a)((^y.y) a))) 4. ==[ alpha ]==> ((((a a) a)(a b))((a a)((^x.x) a))) 5. ==[ beta ]==> ((((a a) a)(a b))((a a) a)) REDUCED to normal form. ------ 180108/20780859. ------ 1. ==[ start ]==> (((a b)((a a) a))((a b)(a (a a)))) REDUCED to normal form. ------ 180109/20780886. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x))(((a a) a)(^z.z))) 8. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 180110/20780913. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((^z.z)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.y)((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a) a)) REDUCED to normal form. ------ 180111/20780967. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a ((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a ((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (a a))) REDUCED to normal form. ------ 180112/20780994. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((b (a a))((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (a a))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 180113/20781021. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a a)(b a))) REDUCED to normal form. ------ 180114/20781057. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.y))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 180115/20781192. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (b ((^y.y)(^z.a))) 6. ==[ alpha ]==> (b ((^x.x)(^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 180116/20781417. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 180117/20781525. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 180118/20781552. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 180119/20781651. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(a a)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180120/20781750. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a (a a))((a a) a))) REDUCED to normal form. ------ 180121/20781777. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z) a)(a b))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z) a)(a b))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a)(a b))) 5. ==[ beta ]==> (((a (^x.x)) b)(a (a b))) REDUCED to normal form. ------ 180122/20781804. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a (^z.z))(a a))) REDUCED to normal form. ------ 180123/20781831. ------ 1. ==[ start ]==> (((a (a a))(b a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 180124/20782380. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(a a)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180125/20782551. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (^z.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 180126/20782650. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((a a) a)(^z.a))) 3. ==[ beta ]==> (b (((a a) a)(^z.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 180127/20782659. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 180128/20782686. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 180129/20782758. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a (^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180130/20782767. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 180131/20782794. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.a))((^z.z)(a a))) 6. ==[ alpha ]==> ((b (^x.a))((^y.y)(a a))) 7. ==[ beta ]==> ((b (^x.a))(a a)) REDUCED to normal form. ------ 180132/20782821. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 180133/20782992. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b (a b))) 3. ==[ beta ]==> (((^y.y)(b a))(b (a b))) 4. ==[ alpha ]==> (((^x.x)(b a))(b (a b))) 5. ==[ beta ]==> ((b a)(b (a b))) REDUCED to normal form. ------ 180134/20783019. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 180135/20783046. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a b)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b)(a a))) 3. ==[ beta ]==> (((a b)(a a))((a b)(a a))) REDUCED to normal form. ------ 180136/20783073. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((a a) a)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a b))(((a a) a)(a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a b))(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 180137/20783100. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z) a)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y) a)) 7. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 180138/20783154. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a (^z.z))) REDUCED to normal form. ------ 180139/20783181. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (^y.y))((a a) a))) 5. ==[ beta ]==> ((b a)((a (^y.y))((a a) a))) 6. ==[ alpha ]==> ((b a)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 180140/20783208. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a a)(a b))) REDUCED to normal form. ------ 180141/20783352. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 180142/20783433. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b) a)) 3. ==[ beta ]==> (b ((a b) a)) REDUCED to normal form. ------ 180143/20783676. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 7. ==[ beta ]==> ((^y.(^z.z)) c) 8. ==[ alpha ]==> ((^x.(^y.y)) c) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180144/20783766. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b (^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.a))) REDUCED to normal form. ------ 180145/20783793. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(a (^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(a (^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (^y1.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180146/20783838. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180147/20783847. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 180148/20783874. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(((^z.z) a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(a ((^z.z) a))) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(a ((^y.y) a))) 9. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 180149/20783901. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 180150/20783955. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a) a)) REDUCED to normal form. ------ 180151/20783982. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(^z.z))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 180152/20784009. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 180153/20784063. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(z z)))) 7. ==[ beta ]==> ((^y.a)(^z.(z z))) 8. ==[ alpha ]==> ((^x.a)(^y.(y y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 180154/20784099. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 180155/20784126. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a ((a a) a))) REDUCED to normal form. ------ 180156/20784153. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y)(^z.z))(a a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(^y.y))(a a))) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(a a))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(a a))) 7. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 180157/20784180. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (a a))(a (^y.y)))) 3. ==[ beta ]==> (((a (a a)) b)((a (a a))(a (^y.y)))) 4. ==[ alpha ]==> (((a (a a)) b)((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 180158/20784207. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a ((^x1.x1) a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z) a))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 180159/20784234. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 180160/20784261. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 180161/20784495. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 180162/20784900. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 180163/20784918. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z)) a)) 5. ==[ beta ]==> ((^y.y)((^z.(z z)) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(y y)) a)) 7. ==[ beta ]==> ((^y.(y y)) a) 8. ==[ alpha ]==> ((^x.(x x)) a) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180164/20784945. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a) b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a) b)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a) b)) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 180165/20785026. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x) a)(^y.y))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (^y.y))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.x))) REDUCED to normal form. ------ 180166/20785062. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180167/20785089. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((^y1.y1) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1) a)) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 180168/20785107. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y) a) a)) 3. ==[ beta ]==> (b (((^y.y) a) a)) 4. ==[ alpha ]==> (b (((^x.x) a) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 180169/20785170. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.a)) REDUCED to normal form. ------ 180170/20785215. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180171/20785251. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (^x1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (^x1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 180172/20785278. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 180173/20785332. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180174/20785350. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a) b)) 3. ==[ beta ]==> (((a a)(^y.y))((a a) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((a a) b)) REDUCED to normal form. ------ 180175/20785359. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 180176/20785377. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 180177/20785395. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a)(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(a a))) REDUCED to normal form. ------ 180178/20785422. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b a)) REDUCED to normal form. ------ 180179/20785449. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a b)) 3. ==[ beta ]==> ((a (b (^y.y)))(a b)) 4. ==[ alpha ]==> ((a (b (^x.x)))(a b)) REDUCED to normal form. ------ 180180/20785476. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 180181/20785503. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a a)) 5. ==[ beta ]==> (((^y.y) b)(a a)) 6. ==[ alpha ]==> (((^x.x) b)(a a)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 180182/20785650. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^z.(^x1.(^y1.(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180183/20793264. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180184/20796540. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180185/20796669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b)) b) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b)) b) 3. ==[ beta ]==> (((^y.y)((^z.z) b)) b) 4. ==[ alpha ]==> (((^x.x)((^y.y) b)) b) 5. ==[ beta ]==> (((^y.y) b) b) 6. ==[ alpha ]==> (((^x.x) b) b) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 180186/20796693. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180187/20796774. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180188/20796819. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^z.(^x1.(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 180189/20796822. ------ 1. ==[ start ]==> ((a (a (^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 180190/20797254. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((a (a a))(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((a (a a))(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 180191/20797278. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((^y.(y (^z.z)))(^x1.x1))(((^y.(y (^z.z)))(^x1.x1))((^y.(y (^z.z)))(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.(x1 (^y1.y1)))(^z1.z1))((^x2.(x2 (^y2.y2)))(^z2.z2)))) 5. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.(x1 (^y1.y1)))(^z1.z1))((^x2.(x2 (^y2.y2)))(^z2.z2)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(z (^x1.x1)))(^y1.y1))((^z1.(z1 (^x2.x2)))(^y2.y2)))) 7. ==[ beta ]==> ((^y.y)(((^z.(z (^x1.x1)))(^y1.y1))((^z1.(z1 (^x2.x2)))(^y2.y2)))) 8. ==[ alpha ]==> ((^x.x)(((^y.(y (^z.z)))(^x1.x1))((^y1.(y1 (^z1.z1)))(^x2.x2)))) 9. ==[ beta ]==> (((^y.(y (^z.z)))(^x1.x1))((^y1.(y1 (^z1.z1)))(^x2.x2))) 10. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 (^y1.y1)))(^z1.z1))) 11. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 (^y1.y1)))(^z1.z1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 13. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.y1))) 14. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 15. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 16. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 17. ==[ beta ]==> ((^z.z)(^y.y)) 18. ==[ alpha ]==> ((^x.x)(^y.y)) 19. ==[ beta ]==> (^y.y) 20. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180192/20798100. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)(^y1.((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (^y.((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> (^x.((^y.(^z.z)) a)) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180193/20798523. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^y.y))(^z.((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a (^x.x))(^y.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 180194/20798937. ------ 1. ==[ start ]==> (((^a.b)(a a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((^x.b)(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.b)(a a))(^y.(^z.z))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180195/20798961. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b (^z.z))(a a))) 3. ==[ beta ]==> (^y.(((b (^z.z))(a a))((b (^z.z))(a a)))) 4. ==[ alpha ]==> (^x.(((b (^y.y))(a a))((b (^z.z))(a a)))) REDUCED to normal form. ------ 180196/20799711. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 180197/20800098. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(b (^z.z)))) REDUCED to normal form. ------ 180198/20800599. ------ 1. ==[ start ]==> ((^a.(b a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ eta ]==> (b ((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180199/20801148. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b ((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b ((^y1.y1) b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180200/20801169. ------ 1. ==[ start ]==> (((a a)(b a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 180201/20801835. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 180202/20802168. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.z))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 180203/20803086. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 180204/20804433. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180205/20804436. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 180206/20805129. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 180207/20805354. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 180208/20805594. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.b)(a a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.b)(a a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180209/20806290. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.a))) REDUCED to normal form. ------ 180210/20806461. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 180211/20806758. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^x.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 180212/20806836. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^z.a)(^x1.a))(((^z.a)(^x1.a))(^y.y))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.a)(^x1.a))(^y1.y1))) 5. ==[ beta ]==> (a (((^z.a)(^x1.a))(^y1.y1))) 6. ==[ alpha ]==> (a (((^x.a)(^y.a))(^z.z))) 7. ==[ beta ]==> (a (a (^z.z))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 180213/20807235. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.d)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.d)) 3. ==[ beta ]==> (((^y.y) b)(^z.d)) 4. ==[ alpha ]==> (((^x.x) b)(^y.d)) 5. ==[ beta ]==> (b (^y.d)) 6. ==[ alpha ]==> (b (^x.d)) REDUCED to normal form. ------ 180214/20807253. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(z (z z)))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (y y)))) 7. ==[ beta ]==> (^y.(y (y y))) 8. ==[ alpha ]==> (^x.(x (x x))) REDUCED to normal form. ------ 180215/20807505. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 180216/20807586. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 180217/20807709. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180218/20807712. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(x1 (^y1.y1)))) REDUCED to normal form. ------ 180219/20807757. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 180220/20807784. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 180221/20807811. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 180222/20807838. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180223/20807868. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.x))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 180224/20807895. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 180225/20807922. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(a (b (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (b (^x.x)))) REDUCED to normal form. ------ 180226/20807949. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 180227/20807967. ------ 1. ==[ start ]==> (((a a)(a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 180228/20807994. ------ 1. ==[ start ]==> ((a (a (^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 180229/20808012. ------ 1. ==[ start ]==> (((a a) b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a) b)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 180230/20808039. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 180231/20808066. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 180232/20808093. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a))(^z.(z z)))) REDUCED to normal form. ------ 180233/20808129. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 180234/20808147. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 180235/20808156. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 180236/20808228. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 180237/20808282. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 180238/20808309. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 180239/20808372. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a a) a)((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(b (^y.y)))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 180240/20808399. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 180241/20808426. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a (a a))((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> ((a (a a))(a (a (^y.y)))) 6. ==[ alpha ]==> ((a (a a))(a (a (^x.x)))) REDUCED to normal form. ------ 180242/20808444. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x)) a)((a (a (^y.y))) a)) 3. ==[ beta ]==> ((a a)((a (a (^y.y))) a)) 4. ==[ alpha ]==> ((a a)((a (a (^x.x))) a)) REDUCED to normal form. ------ 180243/20808453. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a (a (a a)))((^z.z)(^y.y))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 180244/20808750. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 180245/20808813. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(c (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (b (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180246/20808840. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)(b ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180247/20808894. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(a a))) 5. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a)(a a))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a a))) 7. ==[ beta ]==> (((^y.(^z.z)) a)(a a)) 8. ==[ alpha ]==> (((^x.(^y.y)) a)(a a)) 9. ==[ beta ]==> ((^y.y)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180248/20808948. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 8. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 180249/20808957. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(a a)) d)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a)) d)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 180250/20808975. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (((^y.y) b)(a (a a))) 6. ==[ alpha ]==> (((^x.x) b)(a (a a))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 180251/20809029. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((b a)((a a) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((b a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a)((a a) a))) REDUCED to normal form. ------ 180252/20809272. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 180253/20809362. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(a a))(^y.a))) 5. ==[ beta ]==> (b (((a a)(a a))(^y.a))) 6. ==[ alpha ]==> (b (((a a)(a a))(^x.a))) REDUCED to normal form. ------ 180254/20809389. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a) a)(b (^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a) a)(b (^x.(x x)))) REDUCED to normal form. ------ 180255/20809443. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)(^x1.a))) REDUCED to normal form. ------ 180256/20809470. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 180257/20809497. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 180258/20809524. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180259/20809587. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 180260/20809614. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(((^x1.x1) b)((^x1.x1) b))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)((^x1.x1) b))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(b ((^x1.x1) b))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(b ((^z.z) b))) 9. ==[ beta ]==> (((a (^x.x))(^y.y))(b b)) REDUCED to normal form. ------ 180261/20809641. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (a (a a))) a) REDUCED to normal form. ------ 180262/20809668. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 180263/20809695. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a (^x.x))((^z.(^x1.x1)) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 180264/20809740. ------ 1. ==[ start ]==> (((^a.b) a)((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b) a)((b (^y.y)) b)) 3. ==[ beta ]==> (b ((b (^y.y)) b)) 4. ==[ alpha ]==> (b ((b (^x.x)) b)) REDUCED to normal form. ------ 180265/20810109. ------ 1. ==[ start ]==> (((^a.b)(a a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(a a))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (b (a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (b (a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 180266/20810136. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((b (^y.y))(a a))) REDUCED to normal form. ------ 180267/20810352. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.(a a))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.(a a))(((a a) a)((a a)(^y.y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180268/20810379. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b a)) 7. ==[ beta ]==> ((^y.y)(b a)) 8. ==[ alpha ]==> ((^x.x)(b a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180269/20810433. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1) b))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((^z1.z1) b))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) b))) 7. ==[ beta ]==> (((^y.y) a)((^z.z) b)) 8. ==[ alpha ]==> (((^x.x) a)((^y.y) b)) 9. ==[ beta ]==> (a ((^y.y) b)) 10. ==[ alpha ]==> (a ((^x.x) b)) 11. ==[ beta ]==> (a b) REDUCED to normal form. ------ 180270/20810523. ------ 1. ==[ start ]==> (((a b) b)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b) b)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 180271/20810550. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) a)(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 180272/20810577. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.a))) REDUCED to normal form. ------ 180273/20810604. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) REDUCED to normal form. ------ 180274/20810658. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 180275/20810685. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(a a))(^x1.b))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z)(a a))(^x1.b))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))(^z.b))) 7. ==[ beta ]==> ((((^y.y)(a a))(^z.b))(((^y.y)(a a))(^z.b))) 8. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(a a))(^x1.b))) 9. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(a a))(^x1.b))) 10. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a))(^z.b))) 11. ==[ beta ]==> (((a a)(^x.b))((a a)(^z.b))) 12. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.b))) REDUCED to normal form. ------ 180276/20810712. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a b)(^y.(a a)))) REDUCED to normal form. ------ 180277/20810739. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 180278/20810802. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 180279/20810829. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 180280/20810856. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 180281/20810883. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.y))) REDUCED to normal form. ------ 180282/20810955. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y) b) c)) 3. ==[ beta ]==> (b (((^y.y) b) c)) 4. ==[ alpha ]==> (b (((^x.x) b) c)) 5. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 180283/20810964. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.a)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.a)) REDUCED to normal form. ------ 180284/20810991. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 180285/20811270. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(a (b (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 180286/20811297. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a a))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 180287/20811306. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 180288/20811333. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.z) c)) 3. ==[ beta ]==> ((a (^y.b))((^z.z) c)) 4. ==[ alpha ]==> ((a (^x.b))((^y.y) c)) 5. ==[ beta ]==> ((a (^x.b)) c) REDUCED to normal form. ------ 180289/20811351. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 180290/20811432. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (b (((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> (b ((a a)((a a) a))) REDUCED to normal form. ------ 180291/20811585. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(c (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(c (^y.y))) 3. ==[ beta ]==> ((a (a b))(c (^y.y))) 4. ==[ alpha ]==> ((a (a b))(c (^x.x))) REDUCED to normal form. ------ 180292/20811612. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(b (^x.(a a)))) REDUCED to normal form. ------ 180293/20811693. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a b) a)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (((a b) a)(a (^y.y))) 6. ==[ alpha ]==> (((a b) a)(a (^x.x))) REDUCED to normal form. ------ 180294/20811720. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 180295/20811774. ------ 1. ==[ start ]==> ((a (b a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 180296/20812008. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a)(a a)) a)) REDUCED to normal form. ------ 180297/20812323. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b ((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b ((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 180298/20812341. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(b a))(^y.(a a))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(a a))) REDUCED to normal form. ------ 180299/20812620. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(b a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(b a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180300/20812899. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(a a))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(a a))) REDUCED to normal form. ------ 180301/20813007. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 180302/20813034. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1) b) a)) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1) b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) b) a)) 5. ==[ beta ]==> ((^y.b)(((^z.z) b) a)) 6. ==[ alpha ]==> ((^x.b)(((^y.y) b) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 180303/20813088. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a) c)) REDUCED to normal form. ------ 180304/20813232. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 180305/20813259. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 180306/20813313. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 180307/20813340. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 180308/20813538. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a b)) 7. ==[ beta ]==> ((^y.y)(a b)) 8. ==[ alpha ]==> ((^x.x)(a b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 180309/20813565. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (a a))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(a a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(a a))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 180310/20813817. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a) a)(^z.a))) REDUCED to normal form. ------ 180311/20813844. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.b))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.b))) 7. ==[ beta ]==> ((b a)(^y.b)) 8. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 180312/20813871. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 180313/20813979. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(a a))((a (^z.(^x1.x1))) a)) 6. ==[ alpha ]==> ((^x.(a a))((a (^y.(^z.z))) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180314/20814006. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((b a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((b a) b)) REDUCED to normal form. ------ 180315/20814033. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 180316/20814204. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 180317/20814258. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (b a))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (b a))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (b a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 180318/20814501. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(c (^y.(^z.z)))) 3. ==[ beta ]==> ((b (a a))(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 180319/20814843. ------ 1. ==[ start ]==> ((((^a.a) b) b)((b a) a)) 2. ==[ alpha ]==> ((((^x.x) b) b)((b a) a)) 3. ==[ beta ]==> ((b b)((b a) a)) REDUCED to normal form. ------ 180320/20814870. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((a a)(^x.x)) b)) REDUCED to normal form. ------ 180321/20815050. ------ 1. ==[ start ]==> (((^a.b)(a b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(c ((^y.y)(a a)))) 3. ==[ beta ]==> (b (c ((^y.y)(a a)))) 4. ==[ alpha ]==> (b (c ((^x.x)(a a)))) 5. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 180322/20815158. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1)(a a))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180323/20815167. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(a a)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 180324/20815338. ------ 1. ==[ start ]==> (((a (a a))(b a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 180325/20815419. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 180326/20815446. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.b)((^z.z) a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.b)((^z.z) a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.b)((^y.y) a))) 5. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 180327/20815527. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(z z))((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 180328/20815554. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(a b))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 180329/20815581. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 180330/20815608. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (b (^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 180331/20815887. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180332/20815923. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b) c)) 3. ==[ beta ]==> ((b c)((^y.b) c)) 4. ==[ alpha ]==> ((b c)((^x.b) c)) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 180333/20815950. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a) d)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a) d)) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 180334/20815995. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.x))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((b (^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 180335/20816022. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a) a))) 5. ==[ beta ]==> (((^y.y) a)((a a) a)) 6. ==[ alpha ]==> (((^x.x) a)((a a) a)) 7. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 180336/20816076. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(a a))) REDUCED to normal form. ------ 180337/20816166. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a) a)(^y.a))) REDUCED to normal form. ------ 180338/20816193. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> (((a a)(^x.b))(^z.(z z))) 8. ==[ alpha ]==> (((a a)(^x.b))(^y.(y y))) REDUCED to normal form. ------ 180339/20816274. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.x1))(^y1.b))) REDUCED to normal form. ------ 180340/20816301. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((b (^y.a))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((b (^x.a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 180341/20816328. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 180342/20816391. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 180343/20816418. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 180344/20816445. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((a b)(^y.y)) 10. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 180345/20816472. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 180346/20816499. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.b))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 180347/20816526. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.(a a))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(a a))) REDUCED to normal form. ------ 180348/20816688. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(c (^z.a))) 3. ==[ beta ]==> ((b ((^y.y) a))(c (^z.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(c (^y.a))) 5. ==[ beta ]==> ((b a)(c (^y.a))) 6. ==[ alpha ]==> ((b a)(c (^x.a))) REDUCED to normal form. ------ 180349/20816715. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(b (^y.b))) REDUCED to normal form. ------ 180350/20816769. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.b)(a a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.b)(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(a a))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 180351/20817183. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z))) 9. ==[ beta ]==> ((^y.y)(a (^z.z))) 10. ==[ alpha ]==> ((^x.x)(a (^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 180352/20817210. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) a))) 5. ==[ beta ]==> ((a (a a))((^y.y) a)) 6. ==[ alpha ]==> ((a (a a))((^x.x) a)) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 180353/20817264. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b b)((a (^y.y))((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((a (^x.x))((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b b)((a (^x.x))(^z.z))) 10. ==[ alpha ]==> ((b b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 180354/20817354. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 180355/20817381. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a))(^y.a))) REDUCED to normal form. ------ 180356/20817408. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.(z z)))) REDUCED to normal form. ------ 180357/20817462. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.a))) REDUCED to normal form. ------ 180358/20817489. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((a a) a) a)) 3. ==[ beta ]==> ((b (^y.(y y)))(((a a) a) a)) 4. ==[ alpha ]==> ((b (^x.(x x)))(((a a) a) a)) REDUCED to normal form. ------ 180359/20817516. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z) b)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y) b)) 5. ==[ beta ]==> ((((a a)(a a))(^x.a)) b) REDUCED to normal form. ------ 180360/20817606. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 180361/20817633. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.a)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.a)) REDUCED to normal form. ------ 180362/20817741. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(c (^x.(x x)))) REDUCED to normal form. ------ 180363/20817768. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 180364/20817822. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 180365/20817876. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a)((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 180366/20817903. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 180367/20817930. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 180368/20817984. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 180369/20818011. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 180370/20818425. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a (a (a a)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(a (a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a (a a)))) 5. ==[ beta ]==> ((^y.y)(a (a (a a)))) 6. ==[ alpha ]==> ((^x.x)(a (a (a a)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 180371/20818434. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(y y)) a)) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a a)) REDUCED to normal form. ------ 180372/20818452. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a)(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(a a))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (a a))) REDUCED to normal form. ------ 180373/20818461. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a) b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a) b)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 180374/20818479. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 180375/20818569. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 180376/20818596. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(^x1.a))) REDUCED to normal form. ------ 180377/20818677. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a) c)) REDUCED to normal form. ------ 180378/20818722. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (^x1.x1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180379/20818758. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z) c)) 5. ==[ beta ]==> ((b (^x.(^y.y))) c) REDUCED to normal form. ------ 180380/20818785. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 180381/20818839. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1)) a)) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180382/20818857. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b (a a))) 3. ==[ beta ]==> (((a a)(^y.y))(b (a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (a a))) REDUCED to normal form. ------ 180383/20818866. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a) b)) REDUCED to normal form. ------ 180384/20818884. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (a (^x1.x1)))) REDUCED to normal form. ------ 180385/20818902. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b (^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b (^y.y))) REDUCED to normal form. ------ 180386/20818929. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 180387/20818956. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z)(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 180388/20818983. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)(^y.y))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 180389/20819010. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a (^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (^z.z))) 5. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 6. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 180390/20826780. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180391/20830056. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180392/20830185. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b)) c) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b)) c) 3. ==[ beta ]==> (((^y.y)((^z.z) b)) c) 4. ==[ alpha ]==> (((^x.x)((^y.y) b)) c) 5. ==[ beta ]==> (((^y.y) b) c) 6. ==[ alpha ]==> (((^x.x) b) c) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 180393/20830356. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180394/20830461. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (^y.((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> (^x.((^y.(a a))(a (a a)))) 5. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 180395/20830533. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b a)(^z.b))) 3. ==[ eta ]==> ((^y.y)((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 180396/20830704. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 180397/20830803. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(x (x x)))((a (a (^y.y))) a)) 3. ==[ beta ]==> (((a (a (^y.y))) a)(((a (a (^y.y))) a)((a (a (^y.y))) a))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(((a (a (^y.y))) a)((a (a (^z.z))) a))) REDUCED to normal form. ------ 180398/20831028. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180399/20831919. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.a)(b a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 180400/20832099. ------ 1. ==[ start ]==> ((^a.(a b))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(x b))((b (^y.y)) b)) 3. ==[ beta ]==> (((b (^y.y)) b) b) 4. ==[ alpha ]==> (((b (^x.x)) b) b) REDUCED to normal form. ------ 180401/20832471. ------ 1. ==[ start ]==> (((a b)(^a.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 180402/20834124. ------ 1. ==[ start ]==> ((^a.(b a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ eta ]==> (b (((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 180403/20834673. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180404/20835054. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(^x1.(z z)))) 5. ==[ beta ]==> ((a a)(^z.(^x1.(z z)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(x x)))) REDUCED to normal form. ------ 180405/20835564. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180406/20836917. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 180407/20837466. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(b x1))) 3. ==[ eta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 180408/20837958. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180409/20837961. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 180410/20839119. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a b)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a b)(^x1.x1))) 3. ==[ eta ]==> ((^y.(^z.z))((a b)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180411/20839293. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.b)(^y.(^z.z))) a) 4. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180412/20839938. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 180413/20840778. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 7. ==[ beta ]==> (^y.(^z.(z z))) 8. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 180414/20840787. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(y (y y)))) REDUCED to normal form. ------ 180415/20840886. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 180416/20840967. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.((^z.z) a))) 3. ==[ beta ]==> (b (^y.((^z.z) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 180417/20841111. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 180418/20841234. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180419/20841237. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 180420/20841282. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.x1)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 180421/20841309. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 180422/20841363. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.a)) 5. ==[ beta ]==> (((^y.y) b)(^z.a)) 6. ==[ alpha ]==> (((^x.x) b)(^y.a)) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 180423/20841411. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (a (((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (a (((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> (a ((^y.y)((^z.z) b))) 6. ==[ alpha ]==> (a ((^x.x)((^y.y) b))) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 180424/20841438. ------ 1. ==[ start ]==> (((a a) a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 180425/20841465. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.x))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 180426/20841492. ------ 1. ==[ start ]==> (((^a.a) b)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x) b)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b ((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((a (^x.x))(^z.z))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 180427/20841519. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 180428/20841537. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180429/20841564. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 180430/20841645. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 180431/20841663. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 180432/20841717. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b a)(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x) a))((b a)(^y.b))) 3. ==[ beta ]==> ((a a)((b a)(^y.b))) 4. ==[ alpha ]==> ((a a)((b a)(^x.b))) REDUCED to normal form. ------ 180433/20841807. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)(b a))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)(b a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)(b a))) 5. ==[ beta ]==> (a ((^y.b)(b a))) 6. ==[ alpha ]==> (a ((^x.b)(b a))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 180434/20841888. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 180435/20841960. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((a (a a))((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a (a a))((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 180436/20841987. ------ 1. ==[ start ]==> ((a (a (a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (a (a a)))((a (a (^x.x))) a)) REDUCED to normal form. ------ 180437/20841996. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.(y y))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> (((^y.(y (^z.z)))(^x1.x1))((^y.(y (^z.z)))(^x1.x1))) 6. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 (^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 (^y1.y1)))(^z1.z1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 9. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.y1))) 10. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 11. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 12. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 13. ==[ beta ]==> ((^z.z)(^y.y)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180438/20842104. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 180439/20842212. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 180440/20842437. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(a a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(a a))) 5. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 180441/20842464. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> (a ((b (^y.y))(a (^z.z)))) 6. ==[ alpha ]==> (a ((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 180442/20842491. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 180443/20842518. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(b (a (a a)))) REDUCED to normal form. ------ 180444/20842545. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.a))((a (^y.(^z.z)))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 180445/20842572. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b a)((a a) a))) REDUCED to normal form. ------ 180446/20842599. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(a b))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(a b))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 7. ==[ beta ]==> (((a a)(^y.y))(a b)) 8. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 180447/20842941. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(a (a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(a (a a)))) 5. ==[ beta ]==> (((a a) a)(a (a a))) REDUCED to normal form. ------ 180448/20842968. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180449/20843103. ------ 1. ==[ start ]==> ((a (^a.b))((^c.a)(b a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.a)(b a))) 3. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 180450/20843121. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 180451/20843148. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.z))) REDUCED to normal form. ------ 180452/20843256. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y) a)) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.x) a)) 5. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 180453/20843283. ------ 1. ==[ start ]==> ((a (a b))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a (a b))((b (^x.x)) b)) REDUCED to normal form. ------ 180454/20843373. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) IRREDUCIBLE: cycle. ------ 180455/20843454. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 180456/20843481. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 180457/20843562. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(y y))(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x))(^y.y))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(^y.y))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 8. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 180458/20843598. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(c ((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(c ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(c ((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)(c ((a a)(a a)))) 6. ==[ alpha ]==> ((^x.a)(c ((a a)(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 180459/20843625. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b (b (^z.z)))) REDUCED to normal form. ------ 180460/20843652. ------ 1. ==[ start ]==> (((a b)(^a.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a b)(^x.x))(a (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 180461/20843841. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (b (((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a b))) 5. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 180462/20844129. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 180463/20844264. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 180464/20844336. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 180465/20844363. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(a (^y.y))) REDUCED to normal form. ------ 180466/20844444. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((b (^z.z)) a)) 3. ==[ beta ]==> (((^y.y)(a (a a)))((b (^z.z)) a)) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((b (^y.y)) a)) 5. ==[ beta ]==> ((a (a a))((b (^y.y)) a)) 6. ==[ alpha ]==> ((a (a a))((b (^x.x)) a)) REDUCED to normal form. ------ 180467/20844471. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a)(a a)) b)) 3. ==[ beta ]==> ((((a a) a) a)(((a a)(a a)) b)) REDUCED to normal form. ------ 180468/20844498. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) b) c)) 3. ==[ beta ]==> (((a b)(a (^x.x)))(b c)) REDUCED to normal form. ------ 180469/20844588. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180470/20844723. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180471/20844732. ------ 1. ==[ start ]==> (((a b) c)(d (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)(d (a (^x.(^y.y))))) REDUCED to normal form. ------ 180472/20844759. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(c ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(c ((^y.y) b))) 3. ==[ beta ]==> (((a a) b)(c ((^y.y) b))) 4. ==[ alpha ]==> (((a a) b)(c ((^x.x) b))) 5. ==[ beta ]==> (((a a) b)(c b)) REDUCED to normal form. ------ 180473/20844786. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(b ((a a)(a a)))) REDUCED to normal form. ------ 180474/20844840. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 180475/20844867. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.b))(b (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.b))(b (a (^y.y)))) REDUCED to normal form. ------ 180476/20844921. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((b a)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((b a)(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180477/20844948. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 180478/20844975. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.a))((a a)((a a) a))) REDUCED to normal form. ------ 180479/20845002. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a b)(a b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(a b))) REDUCED to normal form. ------ 180480/20845029. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(((a a) a)(a a))) REDUCED to normal form. ------ 180481/20845200. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 180482/20845227. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b) a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> (((a b) a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 180483/20845254. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 180484/20845281. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((b a)(^y.(y y)))) REDUCED to normal form. ------ 180485/20845308. ------ 1. ==[ start ]==> ((a (b a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 180486/20845398. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (b ((^z.a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (b ((^x.a)((^y.y)(a a)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180487/20845479. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180488/20845587. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 180489/20845614. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180490/20845668. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 180491/20845749. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180492/20845857. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 180493/20845929. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z) b)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z) b)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y) b)) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 180494/20845956. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.(^z.z))) c)) 3. ==[ beta ]==> (((a (a a))(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 180495/20846136. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a (a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180496/20846235. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(a (^z.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(a (^z.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(a (^z.(a a)))) 5. ==[ beta ]==> ((a a)(a (^z.(a a)))) 6. ==[ alpha ]==> ((a a)(a (^x.(a a)))) REDUCED to normal form. ------ 180497/20846451. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 180498/20846478. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(^y.y))) 7. ==[ beta ]==> (((a a)(^y.y))((a a)(^y.y))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 180499/20846532. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a (^z.(^x1.x1))))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 180500/20846613. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180501/20846721. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180502/20846748. ------ 1. ==[ start ]==> ((a (^b.b))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.b))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 180503/20846901. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.b) a)) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x) a)) 3. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 180504/20846928. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 180505/20847027. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180506/20847234. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180507/20847342. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180508/20847396. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a b))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a b))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180509/20847423. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(a a))) 7. ==[ beta ]==> (((^y.y)(a a))((^y.y)(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 180510/20847477. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 180511/20847819. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 180512/20847873. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y)) c)) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.x)) REDUCED to normal form. ------ 180513/20848098. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 180514/20848233. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180515/20848341. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180516/20848449. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((^y.(a a))(^z.a)) 6. ==[ alpha ]==> ((^x.(a a))(^y.a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180517/20848503. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 180518/20848584. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180519/20848593. ------ 1. ==[ start ]==> (((a b)(^a.b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(c ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))(c (a a))) REDUCED to normal form. ------ 180520/20848647. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(a (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (b a))) REDUCED to normal form. ------ 180521/20848701. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 180522/20848728. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a b)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a b)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a b)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a b) a)) REDUCED to normal form. ------ 180523/20848755. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 180524/20848926. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a)(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(a a))(((a a)(^y.y))(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 180525/20848953. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 180526/20848980. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a b)(^y.a))) 3. ==[ beta ]==> (((a a)((a a) a))((a b)(^y.a))) 4. ==[ alpha ]==> (((a a)((a a) a))((a b)(^x.a))) REDUCED to normal form. ------ 180527/20849007. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 180528/20849088. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> ((b (a (^x.x)))(a (^z.b))) 6. ==[ alpha ]==> ((b (a (^x.x)))(a (^y.b))) REDUCED to normal form. ------ 180529/20849115. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 180530/20849142. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 180531/20849232. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b)(^y2.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b)(^y2.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180532/20849313. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.a))) 5. ==[ beta ]==> (b ((^y.a)(^y.a))) 6. ==[ alpha ]==> (b ((^x.a)(^y.a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180533/20849457. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b)(a (^y.y)))) 3. ==[ beta ]==> ((b c)((a b)(a (^y.y)))) 4. ==[ alpha ]==> ((b c)((a b)(a (^x.x)))) REDUCED to normal form. ------ 180534/20849484. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((a a) a)((^x.x) a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(((a a) a) a)) REDUCED to normal form. ------ 180535/20849592. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(a b))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a b))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 180536/20849610. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(b (^x1.(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(b (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b (^y1.(a a)))) REDUCED to normal form. ------ 180537/20849619. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 180538/20849691. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 180539/20849799. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180540/20849925. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a) c)) REDUCED to normal form. ------ 180541/20850087. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a b)(a a))((^y.(a a)) a)) 4. ==[ alpha ]==> (((a b)(a a))((^x.(a a)) a)) 5. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 180542/20850114. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.b) b)) 3. ==[ beta ]==> (((a a)(a b))((^y.b) b)) 4. ==[ alpha ]==> (((a a)(a b))((^x.b) b)) 5. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 180543/20850303. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a b)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a b)(^z.z))) 3. ==[ beta ]==> ((a (^y.y))((a b)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 180544/20850393. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (a a)))) 7. ==[ beta ]==> ((^y.(y y))(a (a a))) 8. ==[ alpha ]==> ((^x.(x x))(a (a a))) 9. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 180545/20850474. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> (b ((^x1.x1)(a b))) 4. ==[ alpha ]==> (b ((^x.x)(a b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 180546/20850582. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(z1 z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180547/20850699. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((a a) a)(a a))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(a a))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(a a))) 5. ==[ beta ]==> (a (((a a) a)(a a))) REDUCED to normal form. ------ 180548/20850798. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(c (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(c (^y.(^z.z)))) 7. ==[ beta ]==> ((b b)(c (^y.(^z.z)))) 8. ==[ alpha ]==> ((b b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 180549/20850807. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 180550/20850834. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)((a a) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180551/20850879. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a)(a a))) 3. ==[ beta ]==> (b ((^z.a)(a a))) 4. ==[ alpha ]==> (b ((^x.a)(a a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180552/20850987. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))((^y2.y2)(^z2.z2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180553/20851122. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 180554/20851221. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z)) b)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y)) b)) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 180555/20851356. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 180556/20851410. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (^y1.a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.a))) REDUCED to normal form. ------ 180557/20851437. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((b (a (a a)))((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> ((b (a (a a)))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 180558/20851464. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 180559/20851518. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (a a)) b)) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a)) b)) 5. ==[ beta ]==> ((a a)((a (a a)) b)) REDUCED to normal form. ------ 180560/20851554. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((^z.a)(^x1.a))(^y.y)) 6. ==[ alpha ]==> (((^x.a)(^y.a))(^z.z)) 7. ==[ beta ]==> (a (^z.z)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 180561/20851941. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b ((^z.z) a))) 3. ==[ beta ]==> (((^y.y) b)(b ((^z.z) a))) 4. ==[ alpha ]==> (((^x.x) b)(b ((^y.y) a))) 5. ==[ beta ]==> (b (b ((^y.y) a))) 6. ==[ alpha ]==> (b (b ((^x.x) a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 180562/20851959. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((^y.y)(^z.(z z))) 8. ==[ alpha ]==> ((^x.x)(^y.(y y))) 9. ==[ beta ]==> (^y.(y y)) 10. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 180563/20851968. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a (a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a (a (a a)))) REDUCED to normal form. ------ 180564/20851995. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a)(a a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a (a a))) REDUCED to normal form. ------ 180565/20852067. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a (^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (^y.(y y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.(x x)))) REDUCED to normal form. ------ 180566/20852103. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(c b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c b)) 5. ==[ beta ]==> ((^y.y)(c b)) 6. ==[ alpha ]==> ((^x.x)(c b)) 7. ==[ beta ]==> (c b) REDUCED to normal form. ------ 180567/20852130. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b c)) REDUCED to normal form. ------ 180568/20852148. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180569/20852211. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (a (^z.z)))) REDUCED to normal form. ------ 180570/20852292. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(a (^z.z)))) REDUCED to normal form. ------ 180571/20852391. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 180572/20852400. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b (a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b (a a))) REDUCED to normal form. ------ 180573/20852418. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 180574/20852436. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 180575/20852463. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 180576/20852490. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a)(^z.z))) 3. ==[ beta ]==> ((a (b (^y.y)))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 180577/20852517. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a) a)) REDUCED to normal form. ------ 180578/20852544. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z) a)) 5. ==[ beta ]==> (((^y.y) b)((^z.z) a)) 6. ==[ alpha ]==> (((^x.x) b)((^y.y) a)) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180579/20852570. ------ 1. ==[ start ]==> (^a.(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(((x x) x)(x (^y.(^z.z))))) REDUCED to normal form. ------ 180580/20852571. ------ 1. ==[ start ]==> (a (((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (a (((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 180581/20863599. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180582/20863755. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a)))) a) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 180583/20863761. ------ 1. ==[ start ]==> ((^a.a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 180584/20863788. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^x1.x1) b))(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 5. ==[ beta ]==> (((^y.y)((^z.z) b))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 6. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) b))) 7. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))((^y1.y1) b))) 8. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))((^x1.x1) b))) 9. ==[ beta ]==> (b (((^y.y)(^z.z))((^x1.x1) b))) 10. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z) b))) 11. ==[ beta ]==> (b ((^y.y)((^z.z) b))) 12. ==[ alpha ]==> (b ((^x.x)((^y.y) b))) 13. ==[ beta ]==> (b ((^y.y) b)) 14. ==[ alpha ]==> (b ((^x.x) b)) 15. ==[ beta ]==> (b b) REDUCED to normal form. ------ 180585/20863815. ------ 1. ==[ start ]==> ((^a.b)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.b)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 180586/20863896. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> (((a a)(a (a (^z.z))))(^y.y)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 180587/20863917. ------ 1. ==[ start ]==> (((a a) b)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 180588/20864013. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> (^y.(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> (^x.(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 180589/20864349. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((a a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 180590/20865138. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((((^y.y) a)((a a)(a a)))(((^y.y) a)((a a)(a a))))(((^y.y) a)((a a)(a a)))) 4. ==[ alpha ]==> (((((^x.x) a)((a a)(a a)))(((^y.y) a)((a a)(a a))))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> (((a ((a a)(a a)))(((^y.y) a)((a a)(a a))))(((^z.z) a)((a a)(a a)))) 6. ==[ alpha ]==> (((a ((a a)(a a)))(((^x.x) a)((a a)(a a))))(((^y.y) a)((a a)(a a)))) 7. ==[ beta ]==> (((a ((a a)(a a)))(a ((a a)(a a))))(((^y.y) a)((a a)(a a)))) 8. ==[ alpha ]==> (((a ((a a)(a a)))(a ((a a)(a a))))(((^x.x) a)((a a)(a a)))) 9. ==[ beta ]==> (((a ((a a)(a a)))(a ((a a)(a a))))(a ((a a)(a a)))) REDUCED to normal form. ------ 180591/20866245. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a b)((^z.z)(a a)))((a b)((^z.z)(a a))))) 4. ==[ alpha ]==> ((^x.x)(((a b)((^y.y)(a a)))((a b)((^z.z)(a a))))) 5. ==[ beta ]==> (((a b)((^y.y)(a a)))((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b)((^y.y)(a a)))) 7. ==[ beta ]==> (((a b)(a a))((a b)((^y.y)(a a)))) 8. ==[ alpha ]==> (((a b)(a a))((a b)((^x.x)(a a)))) 9. ==[ beta ]==> (((a b)(a a))((a b)(a a))) REDUCED to normal form. ------ 180592/20867913. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.((a a)(a a)))) REDUCED to normal form. ------ 180593/20868273. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.((z z)(z z)))) REDUCED to normal form. ------ 180594/20868513. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x1.x1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 180595/20868939. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.b))(^y1.y1)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.x1)) 5. ==[ beta ]==> (((^y.y)(^z.b))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.b))(^z.z)) 7. ==[ beta ]==> ((^y.b)(^z.z)) 8. ==[ alpha ]==> ((^x.b)(^y.y)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 180596/20869272. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^x.b)) REDUCED to normal form. ------ 180597/20869431. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 180598/20869884. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(a a))(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180599/20870190. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 180600/20870430. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a (^y.y))((a a)(^z.z)))((a (^y.y))((a a)(^z.z))))(((a (^y.y))((a a)(^z.z)))((a (^y.y))((a a)(^z.z))))) 4. ==[ alpha ]==> ((((a (^x.x))((a a)(^y.y)))((a (^z.z))((a a)(^x1.x1))))(((a (^y1.y1))((a a)(^z1.z1)))((a (^x2.x2))((a a)(^y2.y2))))) REDUCED to normal form. ------ 180601/20870748. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.(y a))) 3. ==[ beta ]==> ((b b)(^y.(y a))) 4. ==[ alpha ]==> ((b b)(^x.(x a))) REDUCED to normal form. ------ 180602/20872233. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 180603/20872458. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a b)(a a))(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.((^y.y)(x x)))) 5. ==[ beta ]==> (((a b)(a a))(^x.(x x))) REDUCED to normal form. ------ 180604/20872845. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> (b (^x1.(^y1.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 180605/20873394. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((a a) a))) REDUCED to normal form. ------ 180606/20873565. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.((y y) y))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.((y y) y))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.((x x) x))) REDUCED to normal form. ------ 180607/20874339. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.(z z)))) REDUCED to normal form. ------ 180608/20874519. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.a))) 3. ==[ beta ]==> (b (^y.(^z.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 180609/20874690. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.y))) REDUCED to normal form. ------ 180610/20874744. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180611/20874786. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180612/20874789. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.b)) REDUCED to normal form. ------ 180613/20874807. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(y (^z.z)))) REDUCED to normal form. ------ 180614/20874888. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.b)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.b)) REDUCED to normal form. ------ 180615/20874915. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(x1 x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(z z))) 5. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 180616/20874942. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 180617/20874954. ------ 1. ==[ start ]==> ((a a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 180618/20874981. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a (a a))((^y.y)((^z.z) b))) 4. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y) b))) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 180619/20875008. ------ 1. ==[ start ]==> ((a b)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 180620/20875062. ------ 1. ==[ start ]==> (((a a)(a a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a a))((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(a a))((a (^x.x))(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 180621/20875080. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 180622/20875089. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 180623/20875107. ------ 1. ==[ start ]==> (((a a) b)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 180624/20875125. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 180625/20875134. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a (^x.x)) a)((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.y))) REDUCED to normal form. ------ 180626/20875152. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 180627/20875179. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 180628/20875206. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 180629/20875242. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180630/20875287. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b a)(^z.b))) 3. ==[ beta ]==> ((^y.a)((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.a)((b a)(^y.b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 180631/20875314. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 180632/20875323. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 180633/20875350. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 180634/20875377. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.b)(b a))) 3. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 180635/20875395. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 180636/20875431. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 180637/20875539. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a a)((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a a)((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 180638/20875557. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a (^z.z))) a)) 3. ==[ beta ]==> ((^y.(y y))((a (a (^z.z))) a)) 4. ==[ alpha ]==> ((^x.(x x))((a (a (^y.y))) a)) 5. ==[ beta ]==> (((a (a (^y.y))) a)((a (a (^y.y))) a)) 6. ==[ alpha ]==> (((a (a (^x.x))) a)((a (a (^y.y))) a)) REDUCED to normal form. ------ 180639/20875584. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((^y.(^z.z)) a) b) 6. ==[ alpha ]==> (((^x.(^y.y)) a) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 180640/20875674. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 180641/20875701. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 180642/20875863. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 180643/20875989. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 (^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 (^z1.z1))) a)) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 (^z1.z1))) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) a)) 7. ==[ beta ]==> ((^y.(y (^z.z))) a) 8. ==[ alpha ]==> ((^x.(x (^y.y))) a) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 180644/20876196. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 180645/20876223. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 180646/20876250. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a) a)(b a))) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a) a)(b a))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)(b a))) 5. ==[ beta ]==> ((a a)(((a a) a)(b a))) REDUCED to normal form. ------ 180647/20876277. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (a a))(a (^x.x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 180648/20876304. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a a)((a (a a))((^y.y) b))) 6. ==[ alpha ]==> ((a a)((a (a a))((^x.x) b))) 7. ==[ beta ]==> ((a a)((a (a a)) b)) REDUCED to normal form. ------ 180649/20876331. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))(a ((a a)(a a)))) REDUCED to normal form. ------ 180650/20876421. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.(^x1.x1)) a)(^y1.y1))) 5. ==[ beta ]==> (a (((^z.(^x1.x1)) a)(^y1.y1))) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a)(^z.z))) 7. ==[ beta ]==> (a ((^y.y)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 180651/20876502. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> (((a a) a)(b (^y.(y y)))) 6. ==[ alpha ]==> (((a a) a)(b (^x.(x x)))) REDUCED to normal form. ------ 180652/20876529. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 180653/20876538. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 180654/20876583. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(^y.y))(^z.b))) 7. ==[ beta ]==> ((a a)(((a a)(^y.y))(^z.b))) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 180655/20876592. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 180656/20876619. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180657/20876646. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 180658/20876853. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b (^z.z)) b)) 3. ==[ beta ]==> ((^y.b)((b (^z.z)) b)) 4. ==[ alpha ]==> ((^x.b)((b (^y.y)) b)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 180659/20876997. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 180660/20877024. ------ 1. ==[ start ]==> (((a b) a)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 180661/20877051. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 180662/20877105. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 180663/20877132. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 180664/20877159. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.a)(^z.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 180665/20877249. ------ 1. ==[ start ]==> (((a a)(a b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(a b))((b (^x.x))(a a))) REDUCED to normal form. ------ 180666/20877276. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 180667/20877303. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b)((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)((^z.z) a))) 7. ==[ beta ]==> ((a (^x.x))(b ((^z.z) a))) 8. ==[ alpha ]==> ((a (^x.x))(b ((^y.y) a))) 9. ==[ beta ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 180668/20877330. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 180669/20877357. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)((b a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)((b a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (a ((b a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> (a ((b a)((^x.x)(^y.y)))) 9. ==[ beta ]==> (a ((b a)(^y.y))) 10. ==[ alpha ]==> (a ((b a)(^x.x))) REDUCED to normal form. ------ 180670/20877384. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 180671/20877411. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x)(a a))(a b))) 3. ==[ beta ]==> (((a b)(a a))((a a)(a b))) REDUCED to normal form. ------ 180672/20877438. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a a))((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a (a a))((a b)((^x.x)(a a)))) 5. ==[ beta ]==> ((a (a a))((a b)(a a))) REDUCED to normal form. ------ 180673/20877663. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(((a a)(a a))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 180674/20877672. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 180675/20877690. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (((^y.y) b)(^z.a)) 6. ==[ alpha ]==> (((^x.x) b)(^y.a)) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 180676/20877699. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 180677/20877744. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((b a)(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)((b a)(^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 11. ==[ beta ]==> ((b a)(^y.(^z.z))) 12. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 180678/20877807. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 180679/20877825. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (b ((a b)(^z.(a a)))) 4. ==[ alpha ]==> (b ((a b)(^x.(a a)))) REDUCED to normal form. ------ 180680/20877834. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 180681/20878050. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 180682/20878293. ------ 1. ==[ start ]==> (((a b) c)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) c)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 180683/20878320. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a) b)((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a a) b)((^x.a)(^y.y))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 180684/20878446. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.y) c)) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y) c)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x) c)) 5. ==[ beta ]==> ((((a a) a)((a a) a)) c) REDUCED to normal form. ------ 180685/20878626. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 180686/20878653. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a (a a))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (a a))(b a))) REDUCED to normal form. ------ 180687/20878680. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a b))(a (a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a (a b))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 180688/20878707. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((a (^x.x))((^y.y) b))) 3. ==[ beta ]==> (((a (a a))((a a) a))((a (^x.x)) b)) REDUCED to normal form. ------ 180689/20878734. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a a)((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((a a)(a a)))) 7. ==[ beta ]==> ((^y.y)((a a)((a a)(a a)))) 8. ==[ alpha ]==> ((^x.x)((a a)((a a)(a a)))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 180690/20878959. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a) a)(^z.(a a)))) 5. ==[ beta ]==> (b (((a a) a)(^z.(a a)))) 6. ==[ alpha ]==> (b (((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 180691/20879040. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 180692/20879103. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)((a a)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((a a)(a a))) REDUCED to normal form. ------ 180693/20879148. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) b) b)) 3. ==[ beta ]==> ((b a)(((^y.y) b) b)) 4. ==[ alpha ]==> ((b a)(((^x.x) b) b)) 5. ==[ beta ]==> ((b a)(b b)) REDUCED to normal form. ------ 180694/20879238. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 180695/20879292. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 180696/20879319. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 180697/20879346. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 180698/20879436. ------ 1. ==[ start ]==> (((a a)(b a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(b a))(b ((^x.x) b))) 3. ==[ beta ]==> (((a a)(b a))(b b)) REDUCED to normal form. ------ 180699/20879463. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 180700/20879490. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z) b)(a a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) b)(a a))) 5. ==[ beta ]==> ((a (a a))(((^y.y) b)(a a))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) b)(a a))) 7. ==[ beta ]==> ((a (a a))(b (a a))) REDUCED to normal form. ------ 180701/20879517. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 180702/20879544. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((b a)((^z.z) a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((b a)((^y.y) a))) 5. ==[ beta ]==> (((a a) a)((b a)((^y.y) a))) 6. ==[ alpha ]==> (((a a) a)((b a)((^x.x) a))) 7. ==[ beta ]==> (((a a) a)((b a) a)) REDUCED to normal form. ------ 180703/20879571. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 180704/20879598. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x)(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a (a a)))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a b)(a (a a)))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a b)(a (a a)))((a a)(^y.y))) 6. ==[ alpha ]==> (((a b)(a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 180705/20879625. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a b)((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a b)((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a b)((a a) a))) 5. ==[ beta ]==> (((a a) a)((a b)((a a) a))) REDUCED to normal form. ------ 180706/20879652. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((a a) a)(a b))) REDUCED to normal form. ------ 180707/20879706. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (a a))((a a)(^z.z)))) REDUCED to normal form. ------ 180708/20879877. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> (b ((b a)(^x1.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 180709/20879985. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((a a) a)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180710/20880012. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(a a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 180711/20880021. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 180712/20880039. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 180713/20880093. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a a)(a a))((a (^y.y))(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 180714/20880102. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 180715/20880129. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> ((^y.b)((^z.z)((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.b)((^y.y)((^z.z) b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 180716/20880174. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 180717/20880183. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 180718/20880237. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 180719/20880291. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 180720/20880435. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a b))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(b (a (^y.(^z.z))))) 5. ==[ beta ]==> ((a b)(b (a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a b)(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 180721/20880462. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(a ((^x.x) b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(a b)) REDUCED to normal form. ------ 180722/20880489. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 180723/20880516. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((b a)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a (a a)))((b a)(a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((b a)(a (^x.x)))) REDUCED to normal form. ------ 180724/20880543. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a)(^y.y)) a)) REDUCED to normal form. ------ 180725/20880597. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a b)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a b)(^z.z))) REDUCED to normal form. ------ 180726/20880624. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((a b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 180727/20880795. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 180728/20880903. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180729/20880912. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) b) REDUCED to normal form. ------ 180730/20880939. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.a)((a a) a))) 3. ==[ beta ]==> ((b a)((^y.a)((a a) a))) 4. ==[ alpha ]==> ((b a)((^x.a)((a a) a))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 180731/20880957. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.b))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.b))) 7. ==[ beta ]==> (b ((^y.y)(^z.b))) 8. ==[ alpha ]==> (b ((^x.x)(^y.b))) 9. ==[ beta ]==> (b (^y.b)) 10. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 180732/20880966. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 180733/20880984. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a (a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.(a a))) 6. ==[ alpha ]==> ((a (a a))(^x.(a a))) REDUCED to normal form. ------ 180734/20880993. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^z1.z1)(a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))((^z1.z1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)((^z1.z1)(a a)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)((^y1.y1)(a a)))) 7. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(a a))) REDUCED to normal form. ------ 180735/20881074. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180736/20881101. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 180737/20881119. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((b a) b)) 2. ==[ alpha ]==> (((^x.b)((a a) a))((b a) b)) 3. ==[ beta ]==> (b ((b a) b)) REDUCED to normal form. ------ 180738/20881128. ------ 1. ==[ start ]==> (((a b)(^c.a))((^d.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 180739/20881155. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 180740/20881182. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 180741/20881263. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 180742/20881353. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(b (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(b (b a))) 3. ==[ beta ]==> ((a (b a))(b (b a))) REDUCED to normal form. ------ 180743/20881380. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 180744/20881407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((b a)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((b a)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b a)(a a))) 5. ==[ beta ]==> (((^y.y)(a a))((b a)(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))((b a)(a a))) 7. ==[ beta ]==> ((a a)((b a)(a a))) REDUCED to normal form. ------ 180745/20881434. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 180746/20881461. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(a a))((^y.y) a))) 3. ==[ beta ]==> (((a b)((a a) a))((a a)((^y.y) a))) 4. ==[ alpha ]==> (((a b)((a a) a))((a a)((^x.x) a))) 5. ==[ beta ]==> (((a b)((a a) a))((a a) a)) REDUCED to normal form. ------ 180747/20881488. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a b)(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a b)(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a b)(a (a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((a b)(a (a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a b)(a (a a)))) REDUCED to normal form. ------ 180748/20881515. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 180749/20881569. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a (a a))(a b))) REDUCED to normal form. ------ 180750/20881596. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b (a a))(((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x) a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b (a a))(a ((^y.y)(a a)))) 6. ==[ alpha ]==> ((b (a a))(a ((^x.x)(a a)))) 7. ==[ beta ]==> ((b (a a))(a (a a))) REDUCED to normal form. ------ 180751/20881623. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 180752/20881794. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 180753/20881902. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180754/20881938. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.y)(b a))) 3. ==[ beta ]==> ((b b)((^y.y)(b a))) 4. ==[ alpha ]==> ((b b)((^x.x)(b a))) 5. ==[ beta ]==> ((b b)(b a)) REDUCED to normal form. ------ 180755/20881983. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((a a)(^y.y)) b)) 3. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y)) b)) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 180756/20882010. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1)(a a)) c)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a)) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a)) c)) 5. ==[ beta ]==> (((^y.y)(a a)) c) 6. ==[ alpha ]==> (((^x.x)(a a)) c) 7. ==[ beta ]==> ((a a) c) REDUCED to normal form. ------ 180757/20882019. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 180758/20882046. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 180759/20882127. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.b)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.b)(^z.b))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 180760/20882154. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 180761/20882352. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)((a a)(a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a)((a a)(a a)))(^y.y)) 8. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 180762/20882379. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (a a))((a a) a))) REDUCED to normal form. ------ 180763/20882406. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)(a b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (a b))) REDUCED to normal form. ------ 180764/20882433. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(b a))((a (^x.x))(a a))) REDUCED to normal form. ------ 180765/20882460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a a)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^y.y))((a a)((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 180766/20882793. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a b) c)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b) c)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b) c)) 5. ==[ beta ]==> ((^y.(^z.z))((a b) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((a b) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180767/20883153. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c (^z.b))) 3. ==[ beta ]==> ((a (^y.y))(c (^z.b))) 4. ==[ alpha ]==> ((a (^x.x))(c (^y.b))) REDUCED to normal form. ------ 180768/20883180. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(b (^x1.(a a)))) REDUCED to normal form. ------ 180769/20883252. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 180770/20883261. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 180771/20883288. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 180772/20883369. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 180773/20883396. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 180774/20883423. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 180775/20883594. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(c ((a a) a))) 3. ==[ beta ]==> (((^y.y)(b a))(c ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(b a))(c ((a a) a))) 5. ==[ beta ]==> ((b a)(c ((a a) a))) REDUCED to normal form. ------ 180776/20883621. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b (a b))) REDUCED to normal form. ------ 180777/20883648. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a a))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(a ((^x.x)(a a)))) 5. ==[ beta ]==> (((a b)(a a))(a (a a))) REDUCED to normal form. ------ 180778/20883675. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a b)(a a))) 3. ==[ beta ]==> (((a a)(a b))((a b)(a a))) REDUCED to normal form. ------ 180779/20883702. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 180780/20883756. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 180781/20883783. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)(((^y.y) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a)(a ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b a)(a ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((b a)(a (^y.y))) 10. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 180782/20883810. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 180783/20883954. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(y y)))) 7. ==[ beta ]==> ((a (a a))(^y.(y y))) 8. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 180784/20884035. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.b))) 3. ==[ beta ]==> (b ((a a)(^x1.b))) 4. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 180785/20884305. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 5. ==[ beta ]==> ((^y.(^z.z)) c) 6. ==[ alpha ]==> ((^x.(^y.y)) c) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180786/20884368. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 180787/20884395. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(b (^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b (^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (^y1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180788/20884440. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((a a) a)(^z.z))) 3. ==[ beta ]==> (b (((a a) a)(^z.z))) 4. ==[ alpha ]==> (b (((a a) a)(^x.x))) REDUCED to normal form. ------ 180789/20884449. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 180790/20884476. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 180791/20884503. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(((^x1.x1) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a ((^x1.x1) a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a ((^z.z) a))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 180792/20884548. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180793/20884557. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 180794/20884584. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)((a a) a))) 5. ==[ beta ]==> ((b (^x.(x x)))((a a) a)) REDUCED to normal form. ------ 180795/20884611. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 180796/20884665. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.a))) 7. ==[ beta ]==> ((^y.(y y))(^z.a)) 8. ==[ alpha ]==> ((^x.(x x))(^y.a)) 9. ==[ beta ]==> ((^y.a)(^y.a)) 10. ==[ alpha ]==> ((^x.a)(^y.a)) 11. ==[ beta ]==> a REDUCED to normal form. ------ 180797/20884728. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 180798/20884755. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(a ((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a ((a a) a))) REDUCED to normal form. ------ 180799/20884782. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y)(^z.z))(a a))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y))(a a))) 5. ==[ beta ]==> (((a (a a)) b)((^y.y)(a a))) 6. ==[ alpha ]==> (((a (a a)) b)((^x.x)(a a))) 7. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 180800/20884809. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(a (^z.z)))) REDUCED to normal form. ------ 180801/20884836. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(b a))(a ((^y.y) a))) 4. ==[ alpha ]==> ((((a a) a)(b a))(a ((^x.x) a))) 5. ==[ beta ]==> ((((a a) a)(b a))(a a)) REDUCED to normal form. ------ 180802/20884863. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 180803/20884890. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a a)(a a))((a a)(^y.y))) 8. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 180804/20884998. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c d)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c d)) 3. ==[ beta ]==> ((b (a (a a)))(c d)) REDUCED to normal form. ------ 180805/20885097. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 180806/20885502. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180807/20885529. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.(z z))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(y y))) REDUCED to normal form. ------ 180808/20885547. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(z z)) a)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z)) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y)) a)) 5. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 180809/20885574. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a) b)) 3. ==[ beta ]==> ((^y.y)((^y1.a) b)) 4. ==[ alpha ]==> ((^x.x)((^y.a) b)) 5. ==[ beta ]==> ((^y.a) b) 6. ==[ alpha ]==> ((^x.a) b) 7. ==[ beta ]==> a REDUCED to normal form. ------ 180810/20885664. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a a))) 5. ==[ beta ]==> ((^y.y)((^z.a)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a a))) 7. ==[ beta ]==> ((^y.a)(a a)) 8. ==[ alpha ]==> ((^x.a)(a a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 180811/20885691. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 180812/20885709. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a a)(^y.a))) 3. ==[ beta ]==> (b ((a a)(^y.a))) 4. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 180813/20885772. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 180814/20885817. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.a) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180815/20885853. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 180816/20885880. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.a))) REDUCED to normal form. ------ 180817/20885934. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180818/20885952. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (^z.z)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 180819/20885961. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 180820/20885979. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a) b)) REDUCED to normal form. ------ 180821/20885997. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (a (^y.y)))) REDUCED to normal form. ------ 180822/20886024. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 180823/20886051. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b a)) 3. ==[ beta ]==> ((a (b (^y.y)))(b a)) 4. ==[ alpha ]==> ((a (b (^x.x)))(b a)) REDUCED to normal form. ------ 180824/20886078. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a b)) REDUCED to normal form. ------ 180825/20886105. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a (a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a (a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (a a))) 5. ==[ beta ]==> (((^y.y) b)(a (a a))) 6. ==[ alpha ]==> (((^x.x) b)(a (a a))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 180826/20886132. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 180827/20886738. ------ 1. ==[ start ]==> ((^a.(a (a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((^y.(a (a (^z.z))))((^y.(a (a (^z.z))))(^y.(a (a (^z.z)))))) 4. ==[ alpha ]==> ((^x.(a (a (^y.y))))((^z.(a (a (^x1.x1))))(^y1.(a (a (^z1.z1)))))) 5. ==[ beta ]==> (a (a (^y.y))) 6. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 180828/20888421. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((^x.(^y.(x x)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180829/20895054. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(^y1.(x1 x1)))) 3. ==[ eta ]==> ((^y.(^z.z))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180830/20897325. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a)))) b) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 180831/20897349. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180832/20897430. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180833/20897475. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((b (^z.(z (^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((b (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 180834/20897664. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180835/20897934. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((^y.y)(a (a (^z.z))))(((^y.y)(a (a (^z.z))))((^y.y)(a (a (^z.z)))))) 4. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z)(a (a (^x1.x1))))((^y1.y1)(a (a (^z1.z1)))))) 5. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(a (a (^x1.x1))))((^y1.y1)(a (a (^z1.z1)))))) 6. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(a (a (^z.z))))((^x1.x1)(a (a (^y1.y1)))))) 7. ==[ beta ]==> ((a (a (^x.x)))((a (a (^z.z)))((^x1.x1)(a (a (^y1.y1)))))) 8. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))((^z.z)(a (a (^x1.x1)))))) 9. ==[ beta ]==> ((a (a (^x.x)))((a (a (^y.y)))(a (a (^x1.x1))))) 10. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))(a (a (^z.z))))) REDUCED to normal form. ------ 180836/20897937. ------ 1. ==[ start ]==> ((a (a (a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 180837/20898378. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(y1 (y1 (^z1.z1))))) 5. ==[ beta ]==> ((^y.y)(^y1.(y1 (y1 (^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 7. ==[ beta ]==> (^y.(y (y (^z.z)))) 8. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 180838/20899206. ------ 1. ==[ start ]==> ((((a a) a)(a a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(a a))(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a)(a a))(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 180839/20899617. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.((a ((^z.(^x1.x1)) a))(a ((^z.(^x1.x1)) a)))) 4. ==[ alpha ]==> (^x.((a ((^y.(^z.z)) a))(a ((^x1.(^y1.y1)) a)))) 5. ==[ beta ]==> (^x.((a (^z.z))(a ((^x1.(^y1.y1)) a)))) 6. ==[ alpha ]==> (^x.((a (^y.y))(a ((^z.(^x1.x1)) a)))) 7. ==[ beta ]==> (^x.((a (^y.y))(a (^x1.x1)))) 8. ==[ alpha ]==> (^x.((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 180840/20899620. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 180841/20899998. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> (b (^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 180842/20900394. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(y (^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a (a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 180843/20900499. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2))))(^z2.z2)) 5. ==[ beta ]==> (((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2))))(^z2.z2)) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1))))(^x2.x2)) 7. ==[ beta ]==> ((^y.y)(^x2.x2)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180844/20900781. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 180845/20901492. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.(a a)))) REDUCED to normal form. ------ 180846/20901852. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 180847/20902185. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.((^x1.x1) b))) 5. ==[ beta ]==> ((a a)(^z.((^x1.x1) b))) 6. ==[ alpha ]==> ((a a)(^x.((^y.y) b))) 7. ==[ beta ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 180848/20902518. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^c.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 180849/20902851. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 180850/20903463. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180851/20903769. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 180852/20904048. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^c.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(b a))) 3. ==[ beta ]==> ((^y.y)(^x1.(b a))) 4. ==[ alpha ]==> ((^x.x)(^y.(b a))) 5. ==[ beta ]==> (^y.(b a)) 6. ==[ alpha ]==> (^x.(b a)) REDUCED to normal form. ------ 180853/20904327. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.(^z.a))) 3. ==[ beta ]==> ((b b)(^y.(^z.a))) 4. ==[ alpha ]==> ((b b)(^x.(^y.a))) REDUCED to normal form. ------ 180854/20905089. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 180855/20905371. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.((y1 y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((y1 y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180856/20906037. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 180857/20906250. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(a (^x1.(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))(a (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180858/20906253. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(y y)))) REDUCED to normal form. ------ 180859/20906973. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.a))) REDUCED to normal form. ------ 180860/20907144. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.(^z.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.a))) REDUCED to normal form. ------ 180861/20907306. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.y))) REDUCED to normal form. ------ 180862/20907492. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.(z z))(^x1.(^y1.y1)))(((^z.(z z))(^x1.(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.(x1 x1))(^y1.(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.(x1 x1))(^y1.(^z1.z1)))(^x2.x2))) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(y1 y1))(^z1.(^x2.x2)))(^y2.y2))) 7. ==[ beta ]==> ((^y.y)(((^y1.(y1 y1))(^z1.(^x2.x2)))(^y2.y2))) 8. ==[ alpha ]==> ((^x.x)(((^y.(y y))(^z.(^x1.x1)))(^y1.y1))) 9. ==[ beta ]==> (((^y.(y y))(^z.(^x1.x1)))(^y1.y1)) 10. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.x1)) 11. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.x1)) 12. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 13. ==[ beta ]==> ((^y.y)(^y1.y1)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180863/20907936. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.(z (z z)))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(z (z z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y (y y)))) REDUCED to normal form. ------ 180864/20908206. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))((a a) a))(^y1.y1)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180865/20908269. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.c)) REDUCED to normal form. ------ 180866/20908365. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 180867/20908386. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 180868/20908440. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 180869/20908467. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(a a))) REDUCED to normal form. ------ 180870/20908494. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180871/20908521. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 180872/20908551. ------ 1. ==[ start ]==> ((a (^a.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 180873/20908578. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 180874/20908605. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 180875/20908632. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 180876/20908677. ------ 1. ==[ start ]==> ((a (a (^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 180877/20908686. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (a (^z.z))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180878/20908722. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 180879/20908749. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 180880/20908776. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 180881/20908830. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 180882/20908839. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 180883/20908866. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 180884/20908911. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 180885/20908992. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 180886/20909019. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 180887/20909055. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 180888/20909082. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 180889/20909109. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 180890/20909127. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((a a)((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a a)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 180891/20909136. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> ((a (a (a a)))(a (a (^y.y)))) 4. ==[ alpha ]==> ((a (a (a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 180892/20909208. ------ 1. ==[ start ]==> ((((^a.a) a) b)((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a) b)((b (^y.y)) c)) 3. ==[ beta ]==> ((a b)((b (^y.y)) c)) 4. ==[ alpha ]==> ((a b)((b (^x.x)) c)) REDUCED to normal form. ------ 180893/20909379. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 180894/20909460. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 180895/20909577. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(a (a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(a (a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (a (a (^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(a (a (a (^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)(a (a (a (^y.y))))) 7. ==[ beta ]==> (a (a (a (^y.y)))) 8. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 180896/20909586. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(x (^y.y))) a)) 3. ==[ beta ]==> (((a (a a)) b)(a (^y.y))) 4. ==[ alpha ]==> (((a (a a)) b)(a (^x.x))) REDUCED to normal form. ------ 180897/20909631. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((b (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((b (^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 180898/20909658. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 180899/20909712. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 180900/20909955. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 180901/20910045. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((b (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 180902/20910072. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a) a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 180903/20910126. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) REDUCED to normal form. ------ 180904/20910153. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b a)(^z.a))) 3. ==[ beta ]==> ((a (^y.(y y)))((b a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((b a)(^y.a))) REDUCED to normal form. ------ 180905/20910180. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 180906/20910207. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180907/20910234. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 180908/20910297. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 180909/20910324. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> ((a (a (a a)))(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> ((a (a (a a)))(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> ((a (a (a a)))(b ((^y.y) b))) 8. ==[ alpha ]==> ((a (a (a a)))(b ((^x.x) b))) 9. ==[ beta ]==> ((a (a (a a)))(b b)) REDUCED to normal form. ------ 180910/20910351. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.a)((a a)(a a)))) 5. ==[ beta ]==> (((a (a a)) a) a) REDUCED to normal form. ------ 180911/20910378. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(b (^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 180912/20910405. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y)) a)) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 180913/20910423. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.b) a)(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (b (((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 180914/20910792. ------ 1. ==[ start ]==> (((^a.b)(a a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(b (b (^y.y)))) 3. ==[ beta ]==> (b (b (b (^y.y)))) 4. ==[ alpha ]==> (b (b (b (^x.x)))) REDUCED to normal form. ------ 180915/20910819. ------ 1. ==[ start ]==> ((a (^b.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (^x.(a a)))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 180916/20911035. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.(a a))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((a b)((^y.y)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180917/20911062. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 180918/20911116. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a a))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a (a a))(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 180919/20911197. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> (b ((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((a a)(b (^x.x)))) REDUCED to normal form. ------ 180920/20911233. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((b (^y.y))(^z.z))) 3. ==[ beta ]==> (((a a) a)((b (^y.y))(^z.z))) 4. ==[ alpha ]==> (((a a) a)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 180921/20911260. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 180922/20911287. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(b (^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (^z.a))) REDUCED to normal form. ------ 180923/20911341. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 180924/20911395. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a a)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((a a)(^y.b))) REDUCED to normal form. ------ 180925/20911422. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.(a a)))) REDUCED to normal form. ------ 180926/20911485. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(b a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 180927/20911512. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 180928/20911539. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a ((a a) a))((^y.a)((^z.z) b))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.a)((^y.y) b))) 5. ==[ beta ]==> ((a ((a a) a)) a) REDUCED to normal form. ------ 180929/20911566. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 180930/20911593. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(b (^z.z)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(b (^y.y)))) 7. ==[ beta ]==> ((a (a a))(b (^y.y))) 8. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 180931/20911638. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b) c)(((a a)(a a)) b)) 3. ==[ beta ]==> (b (((a a)(a a)) b)) REDUCED to normal form. ------ 180932/20911647. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 180933/20911674. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.a)) 6. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 180934/20911701. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 180935/20911953. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b ((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((a a)(a a)))) REDUCED to normal form. ------ 180936/20911980. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(a (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(a (b (^y.y)))) 5. ==[ beta ]==> (a (b (^y.y))) 6. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 180937/20912016. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a)) b)) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a)) b)) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a)) b)) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 180938/20912034. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(b (a (^y.y)))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(b (a (^x.x)))) REDUCED to normal form. ------ 180939/20912115. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 180940/20912322. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b (^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b (^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b (^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(a a)))) 7. ==[ beta ]==> ((^y.y)(b (^z.(a a)))) 8. ==[ alpha ]==> ((^x.x)(b (^y.(a a)))) 9. ==[ beta ]==> (b (^y.(a a))) 10. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 180941/20912376. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))(a a))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))(a a))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 180942/20912403. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 180943/20912430. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 180944/20912691. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a a)(^y.(a a)))) REDUCED to normal form. ------ 180945/20913024. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 180946/20913303. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 180947/20913384. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a a)((^z.z) b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a a)((^z.z) b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a a)((^z.z) b))) 5. ==[ beta ]==> ((a a)((a a)((^z.z) b))) 6. ==[ alpha ]==> ((a a)((a a)((^x.x) b))) 7. ==[ beta ]==> ((a a)((a a) b)) REDUCED to normal form. ------ 180948/20913582. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a) a)(^z.b))) REDUCED to normal form. ------ 180949/20913609. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((^y1.y1)(^z1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.(a a))) 6. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(a a))) REDUCED to normal form. ------ 180950/20913690. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 180951/20913717. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a a)(^z.z))) 5. ==[ beta ]==> ((^y.b)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.b)((a a)(^y.y))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 180952/20913771. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 180953/20913798. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((b a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((b a) c)) 3. ==[ beta ]==> (((a a)(^y.(y y)))((b a) c)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((b a) c)) REDUCED to normal form. ------ 180954/20913942. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 180955/20914023. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 180956/20914050. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(^y.y))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 180957/20914221. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((a a) a))) 5. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 180958/20914248. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(a b))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(^x2.x2))(a b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a b)) 7. ==[ beta ]==> ((^y.y)(a b)) 8. ==[ alpha ]==> ((^x.x)(a b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 180959/20914500. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 180960/20914527. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((a a) a)(^y.a))) 3. ==[ beta ]==> ((b a)(((a a) a)(^y.a))) 4. ==[ alpha ]==> ((b a)(((a a) a)(^x.a))) REDUCED to normal form. ------ 180961/20914554. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 180962/20914581. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (a a))(^y1.(a a)))) REDUCED to normal form. ------ 180963/20914662. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 180964/20914689. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 180965/20914716. ------ 1. ==[ start ]==> (((a b)(^c.a))((b a) b)) 2. ==[ alpha ]==> (((a b)(^x.a))((b a) b)) REDUCED to normal form. ------ 180966/20914743. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a)(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z)) c)) REDUCED to normal form. ------ 180967/20914887. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (((a a) b)((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 180968/20914914. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) a) REDUCED to normal form. ------ 180969/20914968. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 180970/20915247. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(b a))) 3. ==[ beta ]==> ((^y.y)((a a)(b a))) 4. ==[ alpha ]==> ((^x.x)((a a)(b a))) 5. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 180971/20915553. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((b a) a)) REDUCED to normal form. ------ 180972/20915607. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a) c)) REDUCED to normal form. ------ 180973/20915841. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((a a)(^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180974/20915850. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 180975/20915877. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(a a)) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(a a)) c)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 180976/20916021. ------ 1. ==[ start ]==> (((a (a a))(b a))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(c (^x.(a a)))) REDUCED to normal form. ------ 180977/20916048. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 180978/20916102. ------ 1. ==[ start ]==> (((a b)(a b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 180979/20916129. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 180980/20916156. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 180981/20916210. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 180982/20916237. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(y y))((a a) a))) 5. ==[ beta ]==> ((b (a (^x.x)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 180983/20916264. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.a)(a b))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 180984/20916291. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 180985/20916570. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(a ((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 180986/20916606. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(a a)) b)) 3. ==[ beta ]==> ((b c)((^y.(a a)) b)) 4. ==[ alpha ]==> ((b c)((^x.(a a)) b)) 5. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 180987/20916633. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b) c)) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 180988/20916678. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b (^x.x))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((b (^x.x))(a (a a))) REDUCED to normal form. ------ 180989/20916705. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 180990/20916759. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(a b))) REDUCED to normal form. ------ 180991/20916849. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 180992/20916876. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a) a)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a)(^y.a))) REDUCED to normal form. ------ 180993/20916984. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 180994/20917011. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 180995/20917074. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 180996/20917128. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 180997/20917155. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 180998/20917182. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.a))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.a))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 180999/20917209. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 181000/20917236. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a b)(a a))(^y.(a a))) 6. ==[ alpha ]==> (((a b)(a a))(^x.(a a))) REDUCED to normal form. ------ 181001/20917452. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(a (^z.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 181002/20917848. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.b) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.b) a)) 3. ==[ beta ]==> (((^y.y) a)((^z.b) a)) 4. ==[ alpha ]==> (((^x.x) a)((^y.b) a)) 5. ==[ beta ]==> (a ((^y.b) a)) 6. ==[ alpha ]==> (a ((^x.b) a)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 181003/20917866. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((a a) a)(a a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((a a) a)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a) a)(a a))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(a a))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 181004/20917893. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 181005/20917947. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)(a (a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)(a (a a)))) 7. ==[ beta ]==> ((b b)(((^y.y) a)(a (a a)))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)(a (a a)))) 9. ==[ beta ]==> ((b b)(a (a (a a)))) REDUCED to normal form. ------ 181006/20918037. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 181007/20918064. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 181008/20918091. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (a a))(^z.a))) REDUCED to normal form. ------ 181009/20918145. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) REDUCED to normal form. ------ 181010/20918172. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)(^z.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)(^z.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)(^y.a))) REDUCED to normal form. ------ 181011/20918199. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((a a) a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((a a) a) a)) REDUCED to normal form. ------ 181012/20918289. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 181013/20918316. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 181014/20918451. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c (^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (^y.(y y)))) REDUCED to normal form. ------ 181015/20918478. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 181016/20918505. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a (^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.a))) REDUCED to normal form. ------ 181017/20918559. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(y1 y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))(a (^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a (^y1.y1))(a (^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 181018/20918586. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 181019/20918613. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 181020/20918667. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 181021/20918685. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (a a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (a a)) b)) 3. ==[ beta ]==> ((a (^y.y))((a (a a)) b)) 4. ==[ alpha ]==> ((a (^x.x))((a (a a)) b)) REDUCED to normal form. ------ 181022/20918694. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 6. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 181023/20919090. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z)) c)) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z)) c)) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y)) c)) 5. ==[ beta ]==> (b ((a (^y.y)) c)) 6. ==[ alpha ]==> (b ((a (^x.x)) c)) REDUCED to normal form. ------ 181024/20919108. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b ((^x1.x1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b ((^z.z) a))) 5. ==[ beta ]==> ((^y.y)(b ((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)(b ((^y.y) a))) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181025/20919135. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(a (a (a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))(a (a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (a (a a)))) REDUCED to normal form. ------ 181026/20919144. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(z z)) a)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 181027/20919162. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1) a)(a a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a))) 5. ==[ beta ]==> (((^y.y) a)(a a)) 6. ==[ alpha ]==> (((^x.x) a)(a a)) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 181028/20919216. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)((^y.y) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)((^x.x) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a) a)) REDUCED to normal form. ------ 181029/20919252. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 7. ==[ beta ]==> (((^y.y) a)(^z.z)) 8. ==[ alpha ]==> (((^x.x) a)(^y.y)) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 181030/20919279. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 181031/20919297. ------ 1. ==[ start ]==> (((^a.b)(b a))(b c)) 2. ==[ alpha ]==> (((^x.b)(b a))(b c)) 3. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 181032/20919360. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z)) b)) REDUCED to normal form. ------ 181033/20919405. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181034/20919441. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181035/20919522. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181036/20919549. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (^z.z)) a)) REDUCED to normal form. ------ 181037/20919567. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (a a))) REDUCED to normal form. ------ 181038/20919585. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 181039/20919612. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b (^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b (^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.z))) REDUCED to normal form. ------ 181040/20919639. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 181041/20919666. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)(a a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 181042/20919693. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181043/20919720. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (^z.z))) REDUCED to normal form. ------ 181044/20931102. ------ 1. ==[ start ]==> (((a a) b)(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 181045/20931120. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 181046/20931441. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 181047/20931540. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a)(^y.(y (^z.z))))(((a a)(^y.(y (^z.z))))((a a)(^y.(y (^z.z)))))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((a a)(^z.(z (^x1.x1))))((a a)(^y1.(y1 (^z1.z1)))))) REDUCED to normal form. ------ 181048/20931552. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.(y y))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(a (a (^z.z))))) 5. ==[ beta ]==> ((^y.(a (a (^z.z))))(^y.(a (a (^z.z))))) 6. ==[ alpha ]==> ((^x.(a (a (^y.y))))(^z.(a (a (^x1.x1))))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 181049/20931765. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181050/20931984. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 5. ==[ beta ]==> ((^y.y)(^y1.(^z1.(z1 (^x2.x2))))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 7. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 8. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 181051/20931993. ------ 1. ==[ start ]==> (((a (a a)) b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 181052/20932416. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (a (^z.(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> (a (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 181053/20932656. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 181054/20932836. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.(x b))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((((^y.(^z.z)) a) a) b) 4. ==[ alpha ]==> ((((^x.(^y.y)) a) a) b) 5. ==[ beta ]==> (((^y.y) a) b) 6. ==[ alpha ]==> (((^x.x) a) b) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 181055/20933613. ------ 1. ==[ start ]==> (((a b) b)(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 181056/20934396. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 181057/20934861. ------ 1. ==[ start ]==> ((^a.(b a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((b a)(^y.(y y)))) 3. ==[ eta ]==> (b ((b a)(^y.(y y)))) 4. ==[ alpha ]==> (b ((b a)(^x.(x x)))) REDUCED to normal form. ------ 181058/20935410. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181059/20936301. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181060/20936790. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.x1))) 3. ==[ beta ]==> (b (^z.(^x1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 181061/20938695. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181062/20938977. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181063/20940255. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.(a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(z b))) 3. ==[ beta ]==> (((^y.y) a)(^z.(z b))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(y b))) 5. ==[ beta ]==> (a (^y.(y b))) 6. ==[ alpha ]==> (a (^x.(x b))) REDUCED to normal form. ------ 181064/20940435. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.b))) 3. ==[ beta ]==> (b (^z.(^x1.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 181065/20940675. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 181066/20941098. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a)) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a)) b)) 3. ==[ beta ]==> (((a (a a)) b)(((a (a a)) b)(^y.y))) 4. ==[ alpha ]==> (((a (a a)) b)(((a (a a)) b)(^x.x))) REDUCED to normal form. ------ 181067/20941542. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 181068/20941551. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(z (z z)))) REDUCED to normal form. ------ 181069/20941812. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181070/20941947. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (^z.z)))) REDUCED to normal form. ------ 181071/20941971. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181072/20942046. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.z)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 181073/20942100. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.a)) 5. ==[ beta ]==> (((^y.y) b)(^z.a)) 6. ==[ alpha ]==> (((^x.x) b)(^y.a)) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 181074/20942127. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.a)) REDUCED to normal form. ------ 181075/20942175. ------ 1. ==[ start ]==> (((^a.a) a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (a (((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> (a (((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 181076/20942202. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a) a)((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y) b))) 5. ==[ beta ]==> (((a a) a)((^y.y) b)) 6. ==[ alpha ]==> (((a a) a)((^x.x) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 181077/20942229. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 181078/20942256. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (b (((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> (b (((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> (b (a (b (^y.y)))) 6. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 181079/20942283. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 181080/20942301. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181081/20942310. ------ 1. ==[ start ]==> (((a a) b)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 181082/20942328. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 181083/20942355. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 181084/20942427. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 181085/20942454. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 181086/20942490. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 181087/20942571. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (a ((^y.(a a))((a a)(^z.z)))) 6. ==[ alpha ]==> (a ((^x.(a a))((a a)(^y.y)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 181088/20942598. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 181089/20942652. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 181090/20942751. ------ 1. ==[ start ]==> ((a (a (a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 181091/20942760. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.(y y))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(x x))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> (((^y.y)(a (a (^z.z))))((^y.y)(a (a (^z.z))))) 6. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.z)(a (a (^x1.x1))))) 7. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(a (a (^x1.x1))))) 8. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a (a (^z.z))))) 9. ==[ beta ]==> ((a (a (^x.x)))(a (a (^z.z)))) 10. ==[ alpha ]==> ((a (a (^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 181092/20942787. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 7. ==[ beta ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181093/20942895. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181094/20942976. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181095/20943111. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181096/20943192. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(z1 (^x2.x2))))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(z1 (^x2.x2))))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z (^x1.x1))))) 7. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 9. ==[ beta ]==> (^y.(y (^z.z))) 10. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 181097/20943201. ------ 1. ==[ start ]==> (((a (a a)) b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)(a (a (a (^x.x))))) REDUCED to normal form. ------ 181098/20943228. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((^y.y) a)(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (a (((^y.(^z.z)) a)(a a))) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a)(a a))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 181099/20943255. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 181100/20943282. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 181101/20943309. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> ((a (^x.a))(b (a (a a)))) REDUCED to normal form. ------ 181102/20943336. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1)))(^z1.z1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 181103/20943363. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b a)((a a) a))) 5. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 7. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 181104/20943570. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(c (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(^z.z)))) 5. ==[ beta ]==> (c (^y.(^z.z))) 6. ==[ alpha ]==> (c (^x.(^y.y))) REDUCED to normal form. ------ 181105/20943624. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(a (^z.(z (^x1.x1))))) 5. ==[ beta ]==> (a (a (^z.(z (^x1.x1))))) 6. ==[ alpha ]==> (a (a (^x.(x (^y.y))))) REDUCED to normal form. ------ 181106/20943732. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(a (a a))) 6. ==[ alpha ]==> ((^x.x)(a (a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 181107/20943867. ------ 1. ==[ start ]==> ((a (^a.b))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 181108/20943912. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 181109/20943939. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a (a a))(^y.y))) 3. ==[ beta ]==> ((a (a (a a)))((a (a a))(^y.y))) 4. ==[ alpha ]==> ((a (a (a a)))((a (a a))(^x.x))) REDUCED to normal form. ------ 181110/20944047. ------ 1. ==[ start ]==> ((a (a b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a (a b))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> ((a (a b))((^y.y) a)) 4. ==[ alpha ]==> ((a (a b))((^x.x) a)) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 181111/20944137. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 181112/20944218. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181113/20944245. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 181114/20944272. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 181115/20944326. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 181116/20944416. ------ 1. ==[ start ]==> (((a b)(^a.a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(b (b (^y.y)))) REDUCED to normal form. ------ 181117/20944605. ------ 1. ==[ start ]==> (((^a.b) b)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) b)(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> (b (((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 181118/20944821. ------ 1. ==[ start ]==> (((a b) b)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b) b)((a a)(b (^x.x)))) REDUCED to normal form. ------ 181119/20944893. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 181120/20944947. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))(a (a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a (a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 11. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 12. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 13. ==[ beta ]==> (^y.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181121/20945028. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(a a))(a b))) 3. ==[ beta ]==> (b ((^z.(a a))(a b))) 4. ==[ alpha ]==> (b ((^x.(a a))(a b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 181122/20945127. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181123/20945154. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) a)(^y.y))) 5. ==[ beta ]==> ((a ((a a) a))(a (^y.y))) 6. ==[ alpha ]==> ((a ((a a) a))(a (^x.x))) REDUCED to normal form. ------ 181124/20945235. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((b (^y.y)) a)) 3. ==[ beta ]==> ((((a a) a) a)((b (^y.y)) a)) 4. ==[ alpha ]==> ((((a a) a) a)((b (^x.x)) a)) REDUCED to normal form. ------ 181125/20945262. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(a a)) b)) REDUCED to normal form. ------ 181126/20945289. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y) b) c)) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) b) c)) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b) c)) 5. ==[ beta ]==> (((a a)(a a))(b c)) REDUCED to normal form. ------ 181127/20945604. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a (b (^z.z)))) REDUCED to normal form. ------ 181128/20945631. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((a (^y.b))(((a a)(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(a a))(a a))) REDUCED to normal form. ------ 181129/20945685. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))((^y1.y1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181130/20945712. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((b a)(a (a a)))) REDUCED to normal form. ------ 181131/20945739. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 181132/20945766. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 181133/20945793. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)(a b))) REDUCED to normal form. ------ 181134/20945991. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a)(a a))(^y.y))) 3. ==[ beta ]==> (((a b) a)(((a a)(a a))(^y.y))) 4. ==[ alpha ]==> (((a b) a)(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 181135/20946018. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 181136/20946045. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 181137/20946072. ------ 1. ==[ start ]==> ((a (b a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (b a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 181138/20946162. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.b)(a b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.b)(a b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b)(a b))) 5. ==[ beta ]==> (b ((^z.b)(a b))) 6. ==[ alpha ]==> (b ((^x.b)(a b))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 181139/20946243. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(z z))(b a))) 3. ==[ beta ]==> (b ((^z.(z z))(b a))) 4. ==[ alpha ]==> (b ((^x.(x x))(b a))) 5. ==[ beta ]==> (b ((b a)(b a))) REDUCED to normal form. ------ 181140/20946351. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((b a)((^y.(a a))(^z.z))) 4. ==[ alpha ]==> ((b a)((^x.(a a))(^y.y))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 181141/20946378. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181142/20946513. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.b)(^z.b))) 3. ==[ beta ]==> (b ((^y.b)(^z.b))) 4. ==[ alpha ]==> (b ((^x.b)(^y.b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 181143/20946621. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 181144/20946720. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.b) b)) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x) b)) 3. ==[ beta ]==> (((a (a a))(a b)) b) REDUCED to normal form. ------ 181145/20946900. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181146/20946999. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(b (^z.z))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(b (^z.z))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(b (^z.z))) 5. ==[ beta ]==> ((a a)(b (^z.z))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 181147/20947080. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 181148/20947188. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.b)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181149/20947242. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181150/20947296. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.a)(b a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.a)(b a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)(b a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(b a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(b a))) 7. ==[ beta ]==> (((a a)(a a))((^y.a)(b a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.a)(b a))) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 181151/20947377. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.x)(^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181152/20947485. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181153/20947512. ------ 1. ==[ start ]==> ((a (^b.b))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.a))) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 181154/20947692. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.z) a)) 3. ==[ beta ]==> (((a b)(^y.y))((^z.z) a)) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y) a)) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 181155/20947719. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 181156/20947791. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181157/20947998. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(a (^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(a (^z.z))) 3. ==[ beta ]==> (b (a (^z.z))) 4. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 181158/20948106. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181159/20948160. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)((a a) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)((a a) a))) 5. ==[ beta ]==> (b ((^y.a)((a a) a))) 6. ==[ alpha ]==> (b ((^x.a)((a a) a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181160/20948187. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))(a b)) 6. ==[ alpha ]==> ((^x.(^y.y))(a b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181161/20948241. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 181162/20948322. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 181163/20948430. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181164/20948610. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1))) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1))) a)) 7. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1))) a)) 8. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) a)) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 181165/20948664. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y)) c)) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 181166/20948997. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b)(a (a a)))) 3. ==[ beta ]==> (b ((^z.b)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.b)(a (a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 181167/20949105. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181168/20949213. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181169/20949267. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (((b a)(b a))((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.b)(^y.(y y)))) 5. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 181170/20949348. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.b))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.b))) 5. ==[ beta ]==> (b ((^y.b)(^y.b))) 6. ==[ alpha ]==> (b ((^x.b)(^y.b))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 181171/20949411. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b ((a a)(^x1.x1)))) REDUCED to normal form. ------ 181172/20949465. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a)(^x1.x1))(a a))) REDUCED to normal form. ------ 181173/20949492. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(a (^z.z)))) REDUCED to normal form. ------ 181174/20949519. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a b)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a b) a)) REDUCED to normal form. ------ 181175/20949717. ------ 1. ==[ start ]==> (((a b)(a b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 181176/20949744. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)((a a) a))((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)((a a) a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 181177/20949771. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)(^z.a))) REDUCED to normal form. ------ 181178/20949825. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 181179/20949852. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (a a))(^z.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (a a))(^y.a))) REDUCED to normal form. ------ 181180/20949879. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x) a)(^y.b))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a (^y.b))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(a (^x.b))) REDUCED to normal form. ------ 181181/20949906. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 181182/20949996. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(a a))(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(a a))(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181183/20950077. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181184/20950221. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(a a))(a a))) 3. ==[ beta ]==> ((b c)(((^y.y)(a a))(a a))) 4. ==[ alpha ]==> ((b c)(((^x.x)(a a))(a a))) 5. ==[ beta ]==> ((b c)((a a)(a a))) REDUCED to normal form. ------ 181185/20950248. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a b)(a (^x.x)))) REDUCED to normal form. ------ 181186/20950356. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(a ((a a) a))) REDUCED to normal form. ------ 181187/20950383. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(a b))) REDUCED to normal form. ------ 181188/20950455. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(a a))(a a))) 3. ==[ beta ]==> (b ((^z.(a a))(a a))) 4. ==[ alpha ]==> (b ((^x.(a a))(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 181189/20950563. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181190/20950689. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a b) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a b) b)) REDUCED to normal form. ------ 181191/20950878. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(a a)) a)) 3. ==[ beta ]==> (((a a)(a b))((^y.(a a)) a)) 4. ==[ alpha ]==> (((a a)(a b))((^x.(a a)) a)) 5. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 181192/20950905. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.b) b)) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 181193/20951157. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181194/20951238. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181195/20951346. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181196/20951463. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(a (a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(a (a b))) 3. ==[ beta ]==> (((^y.y) a)(a (a b))) 4. ==[ alpha ]==> (((^x.x) a)(a (a b))) 5. ==[ beta ]==> (a (a (a b))) REDUCED to normal form. ------ 181197/20951571. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (a (a a)))) REDUCED to normal form. ------ 181198/20951598. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181199/20951643. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(a (^z.b))) 3. ==[ beta ]==> (b (a (^z.b))) 4. ==[ alpha ]==> (b (a (^x.b))) REDUCED to normal form. ------ 181200/20951751. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181201/20951886. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 181202/20951985. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^c.a) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a) a)) 3. ==[ beta ]==> (((a (a a)) b)((^y.a) a)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a) a)) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 181203/20952012. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1)) b)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1)) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) b)) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181204/20952039. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x)) c)) 3. ==[ beta ]==> ((((a a) a)(b a))(c c)) REDUCED to normal form. ------ 181205/20952174. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 181206/20952201. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((b (a (a a)))(a (^y.a))) 6. ==[ alpha ]==> ((b (a (a a)))(a (^x.a))) REDUCED to normal form. ------ 181207/20952228. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 181208/20952282. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z)) a)) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y)) a)) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 181209/20952309. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (a a)) b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (a a)) b)) REDUCED to normal form. ------ 181210/20952318. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^z.(z z))(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.x1)) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 9. ==[ beta ]==> ((^y.y)(^y1.y1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181211/20952705. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c (a (^z.z)))) 3. ==[ beta ]==> (((^y.y) b)(c (a (^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)(c (a (^y.y)))) 5. ==[ beta ]==> (b (c (a (^y.y)))) 6. ==[ alpha ]==> (b (c (a (^x.x)))) REDUCED to normal form. ------ 181212/20952723. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181213/20952732. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b ((^y.y) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(b a)) REDUCED to normal form. ------ 181214/20952750. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(z z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 181215/20952759. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(a (a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a (a (a a)))) REDUCED to normal form. ------ 181216/20952831. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (^y.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (^y.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b (^x.a))) REDUCED to normal form. ------ 181217/20952912. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181218/20952975. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c (a a))) REDUCED to normal form. ------ 181219/20953020. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181220/20953056. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 181221/20953083. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 181222/20953137. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b b)) 5. ==[ beta ]==> ((^y.(^z.z))(b b)) 6. ==[ alpha ]==> ((^x.(^y.y))(b b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181223/20953155. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 181224/20953182. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 181225/20953200. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a) b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a) b)) REDUCED to normal form. ------ 181226/20953227. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 181227/20953254. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z) b)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z) b)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y) b)) 5. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 181228/20953281. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a a)(^x.x))) REDUCED to normal form. ------ 181229/20953308. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a) a)) 5. ==[ beta ]==> (((^y.y) b)((a a) a)) 6. ==[ alpha ]==> (((^x.x) b)((a a) a)) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 181230/20953335. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z) a)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 181231/20953361. ------ 1. ==[ start ]==> (^a.((a b)(b a))) 2. ==[ alpha ]==> (^x.((x b)(b x))) REDUCED to normal form. ------ 181232/20953362. ------ 1. ==[ start ]==> (a ((a b)(b a))) REDUCED to normal form. ------ 181233/20964573. ------ 1. ==[ start ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 181234/20964579. ------ 1. ==[ start ]==> ((^a.a)((a b)(b a))) 2. ==[ alpha ]==> ((^x.x)((a b)(b a))) 3. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 181235/20964606. ------ 1. ==[ start ]==> ((^a.(a a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((((a a) a)(a (^y.(^z.z))))(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(((a a) a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 181236/20964633. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 181237/20964714. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^z.z))((^x1.(^y1.y1)) a))(^y.y)) 4. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.x1)) 5. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 181238/20964762. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 181239/20964831. ------ 1. ==[ start ]==> ((^a.(^b.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.x))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> (^y.((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> (^x.((b (^y.y))(^z.a))) REDUCED to normal form. ------ 181240/20965074. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 181241/20965626. ------ 1. ==[ start ]==> (((a (a a)) b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 181242/20965956. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((((a (a a))((^y.y) b))((a (a a))((^y.y) b)))((a (a a))((^y.y) b))) 4. ==[ alpha ]==> ((((a (a a))((^x.x) b))((a (a a))((^y.y) b)))((a (a a))((^z.z) b))) 5. ==[ beta ]==> ((((a (a a)) b)((a (a a))((^y.y) b)))((a (a a))((^z.z) b))) 6. ==[ alpha ]==> ((((a (a a)) b)((a (a a))((^x.x) b)))((a (a a))((^y.y) b))) 7. ==[ beta ]==> ((((a (a a)) b)((a (a a)) b))((a (a a))((^y.y) b))) 8. ==[ alpha ]==> ((((a (a a)) b)((a (a a)) b))((a (a a))((^x.x) b))) 9. ==[ beta ]==> ((((a (a a)) b)((a (a a)) b))((a (a a)) b)) REDUCED to normal form. ------ 181243/20966289. ------ 1. ==[ start ]==> ((^a.(^a.b))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 181244/20966463. ------ 1. ==[ start ]==> (((^a.b) a)(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) a)(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b (^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b (^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 181245/20966877. ------ 1. ==[ start ]==> (((a a)(a b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a b))(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> (((a a)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 181246/20967063. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((^y.y)((((^z.z)(a a))(a b))(((^z.z)(a a))(a b)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y)(a a))(a b))(((^z.z)(a a))(a b)))) 5. ==[ beta ]==> ((((^y.y)(a a))(a b))(((^z.z)(a a))(a b))) 6. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(a a))(a b))) 7. ==[ beta ]==> (((a a)(a b))(((^y.y)(a a))(a b))) 8. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a))(a b))) 9. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 181247/20969118. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.((z z)(z z)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.((z z)(z z)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.((y y)(y y)))) 5. ==[ beta ]==> ((a (a a))(^y.((y y)(y y)))) 6. ==[ alpha ]==> ((a (a a))(^x.((x x)(x x)))) REDUCED to normal form. ------ 181248/20969331. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((((^x1.x1)(^y1.y1))((^z1.z1)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 181249/20970117. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.((^z.z) b))) 5. ==[ beta ]==> (((a b)(^x.x))(^y.b)) REDUCED to normal form. ------ 181250/20970249. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 181251/20970729. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 181252/20971035. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(z (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(y (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.(y (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 181253/20971248. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((((^y.y) a)((^z.z)(a a)))(((^y.y) a)((^z.z)(a a))))((((^y.y) a)((^z.z)(a a)))(((^y.y) a)((^z.z)(a a))))) 4. ==[ alpha ]==> (((((^x.x) a)((^y.y)(a a)))(((^z.z) a)((^x1.x1)(a a))))((((^y1.y1) a)((^z1.z1)(a a)))(((^x2.x2) a)((^y2.y2)(a a))))) 5. ==[ beta ]==> (((a ((^y.y)(a a)))(((^z.z) a)((^x1.x1)(a a))))((((^y1.y1) a)((^z1.z1)(a a)))(((^x2.x2) a)((^y2.y2)(a a))))) 6. ==[ alpha ]==> (((a ((^x.x)(a a)))(((^y.y) a)((^z.z)(a a))))((((^x1.x1) a)((^y1.y1)(a a)))(((^z1.z1) a)((^x2.x2)(a a))))) 7. ==[ beta ]==> (((a (a a))(((^y.y) a)((^z.z)(a a))))((((^x1.x1) a)((^y1.y1)(a a)))(((^z1.z1) a)((^x2.x2)(a a))))) 8. ==[ alpha ]==> (((a (a a))(((^x.x) a)((^y.y)(a a))))((((^z.z) a)((^x1.x1)(a a)))(((^y1.y1) a)((^z1.z1)(a a))))) 9. ==[ beta ]==> (((a (a a))(a ((^y.y)(a a))))((((^z.z) a)((^x1.x1)(a a)))(((^y1.y1) a)((^z1.z1)(a a))))) 10. ==[ alpha ]==> (((a (a a))(a ((^x.x)(a a))))((((^y.y) a)((^z.z)(a a)))(((^x1.x1) a)((^y1.y1)(a a))))) 11. ==[ beta ]==> (((a (a a))(a (a a)))((((^y.y) a)((^z.z)(a a)))(((^x1.x1) a)((^y1.y1)(a a))))) 12. ==[ alpha ]==> (((a (a a))(a (a a)))((((^x.x) a)((^y.y)(a a)))(((^z.z) a)((^x1.x1)(a a))))) 13. ==[ beta ]==> (((a (a a))(a (a a)))((a ((^y.y)(a a)))(((^z.z) a)((^x1.x1)(a a))))) 14. ==[ alpha ]==> (((a (a a))(a (a a)))((a ((^x.x)(a a)))(((^y.y) a)((^z.z)(a a))))) 15. ==[ beta ]==> (((a (a a))(a (a a)))((a (a a))(((^y.y) a)((^z.z)(a a))))) 16. ==[ alpha ]==> (((a (a a))(a (a a)))((a (a a))(((^x.x) a)((^y.y)(a a))))) 17. ==[ beta ]==> (((a (a a))(a (a a)))((a (a a))(a ((^y.y)(a a))))) 18. ==[ alpha ]==> (((a (a a))(a (a a)))((a (a a))(a ((^x.x)(a a))))) 19. ==[ beta ]==> (((a (a a))(a (a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 181254/20971593. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(^b.(b a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(x a))) REDUCED to normal form. ------ 181255/20973303. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a a)(a b))(^y.((^z.z)(y y)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.((^y.y)(x x)))) 5. ==[ beta ]==> (((a a)(a b))(^x.(x x))) REDUCED to normal form. ------ 181256/20973489. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a a)(a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a a)(a b))) 3. ==[ eta ]==> ((^y.(^z.z))((a a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181257/20973888. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.z))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.y))) 5. ==[ beta ]==> (a (^y.(^z.y))) 6. ==[ alpha ]==> (a (^x.(^y.x))) REDUCED to normal form. ------ 181258/20974077. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 181259/20974239. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((a a) a))) REDUCED to normal form. ------ 181260/20974410. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.((y y) y))) 3. ==[ beta ]==> (((a (a a)) b)(^y.((y y) y))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.((x x) x))) REDUCED to normal form. ------ 181261/20974545. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 181262/20975184. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 181263/20975292. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 7. ==[ beta ]==> (^y.(^z.(z z))) 8. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 181264/20975589. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 181265/20975604. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1)) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181266/20975652. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 181267/20975679. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 181268/20975733. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.b)) 5. ==[ beta ]==> (((^y.y) b)(^z.b)) 6. ==[ alpha ]==> (((^x.x) b)(^y.b)) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 181269/20975760. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(z z))) REDUCED to normal form. ------ 181270/20975787. ------ 1. ==[ start ]==> (((a b)(b a))(^a.a)) 2. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 181271/20975799. ------ 1. ==[ start ]==> ((a a)((a b)(b a))) REDUCED to normal form. ------ 181272/20975826. ------ 1. ==[ start ]==> ((a (a a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 181273/20975853. ------ 1. ==[ start ]==> ((a b)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a b)((^y.y)((^z.z) b))) 4. ==[ alpha ]==> ((a b)((^x.x)((^y.y) b))) 5. ==[ beta ]==> ((a b)((^y.y) b)) 6. ==[ alpha ]==> ((a b)((^x.x) b)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 181274/20975907. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(a (b (^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(a (b (^x.x)))) REDUCED to normal form. ------ 181275/20975934. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a (^x.x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 181276/20975952. ------ 1. ==[ start ]==> (((a a) b)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 181277/20975979. ------ 1. ==[ start ]==> (((a (^a.a)) a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181278/20975997. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 181279/20976006. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 181280/20976024. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181281/20976051. ------ 1. ==[ start ]==> ((a (^b.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.a))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 181282/20976087. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))(a (a a))) 6. ==[ alpha ]==> ((^x.(a a))(a (a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 181283/20976132. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 181284/20976159. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 181285/20976222. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 181286/20976249. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.b)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 181287/20976294. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 181288/20976384. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 181289/20976402. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.(y y))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(x x))((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> (((a a)(^y.(y (^z.z))))((a a)(^y.(y (^z.z))))) 6. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 181290/20976429. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 5. ==[ beta ]==> ((a (a (^y.y))) a) 6. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 181291/20976483. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((b (^z.z)) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))((b (^z.z)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z)) c)) 5. ==[ beta ]==> ((^y.y)((b (^z.z)) c)) 6. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 7. ==[ beta ]==> ((b (^y.y)) c) 8. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 181292/20976546. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 181293/20976708. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 181294/20976843. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 181295/20977041. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 181296/20977068. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 181297/20977095. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)((a b)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a a)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 181298/20977122. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((a a) a)(b a))) REDUCED to normal form. ------ 181299/20977149. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)((^y.y)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 9. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 10. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 181300/20977176. ------ 1. ==[ start ]==> ((a ((a a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((a a) a))((a (a a))((^x.x) b))) 3. ==[ beta ]==> ((a ((a a) a))((a (a a)) b)) REDUCED to normal form. ------ 181301/20977347. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> (((a a) a)(((a a)(a a))(^y.a))) 4. ==[ alpha ]==> (((a a) a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 181302/20977374. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 181303/20977383. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (a a))) REDUCED to normal form. ------ 181304/20977410. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 181305/20977428. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((b a)(^z.a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((b a)(^z.a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b a)(^z.a))) 5. ==[ beta ]==> ((a ((^y.y) a))((b a)(^z.a))) 6. ==[ alpha ]==> ((a ((^x.x) a))((b a)(^y.a))) 7. ==[ beta ]==> ((a a)((b a)(^y.a))) 8. ==[ alpha ]==> ((a a)((b a)(^x.a))) REDUCED to normal form. ------ 181306/20977491. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 181307/20977509. ------ 1. ==[ start ]==> ((a (^a.b))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 181308/20977680. ------ 1. ==[ start ]==> (((^a.b) a)((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b ((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181309/20977698. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((^y.b)(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> ((^x.b)(((^y.(^z.z)) a) a)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 181310/20977869. ------ 1. ==[ start ]==> (((a b) a)((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 181311/20977896. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 181312/20977950. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 181313/20977977. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 181314/20978004. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((^y.a)((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((^y.(y y))(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 181315/20978031. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 181316/20978094. ------ 1. ==[ start ]==> (((a a)(a b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a b))(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a a)(a b))(a (^y.y))) 4. ==[ alpha ]==> (((a a)(a b))(a (^x.x))) REDUCED to normal form. ------ 181317/20978121. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((b (^y.y))(a a))) REDUCED to normal form. ------ 181318/20978148. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 181319/20978175. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) b)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(b ((^y.y) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(b ((^x.x) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(b a)) REDUCED to normal form. ------ 181320/20978202. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> (((^y.y) a)((a (^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> (((^x.x) a)((a (^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> (a ((a (^y.(^z.z)))(a (a a)))) 8. ==[ alpha ]==> (a ((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 181321/20978229. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((b a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((b a)(^y.y))) REDUCED to normal form. ------ 181322/20978256. ------ 1. ==[ start ]==> (((a b)(a a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a a))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 181323/20978283. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))(a b))) 5. ==[ beta ]==> ((a (a a))((a a)(a b))) REDUCED to normal form. ------ 181324/20978508. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((a a)((b (^y.y))(^z.z))) 6. ==[ alpha ]==> ((a a)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 181325/20978535. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 181326/20978544. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 181327/20978589. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 9. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 10. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(x1 x1)))) 11. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 x1))) 12. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 181328/20978598. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 181329/20978652. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 181330/20978670. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (b ((a a)(^y.b))) 6. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 181331/20978679. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 181332/20978706. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 181333/20978895. ------ 1. ==[ start ]==> (((^a.b) c)((^d.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181334/20979138. ------ 1. ==[ start ]==> (((a b) c)((^b.(^a.a))(^d.a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 181335/20979165. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) b)((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) b)((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 181336/20979192. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 181337/20979471. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(((a a) a)(a a))) REDUCED to normal form. ------ 181338/20979498. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((a a)(^z.z)))) 7. ==[ beta ]==> (((a (^x.x))(a a))((a a)(^z.z))) 8. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.y))) REDUCED to normal form. ------ 181339/20979525. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (a a))(b a))) 3. ==[ beta ]==> ((a (a b))((a (a a))(b a))) REDUCED to normal form. ------ 181340/20979552. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a (a a))((a a) a))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 181341/20979579. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.x1) b))) 7. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1) b))) 8. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z) b))) 9. ==[ beta ]==> ((a (^y.y))((^z.z) b)) 10. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 11. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 181342/20979606. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 181343/20979804. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a b)(^z.b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a b)(^z.b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a b)(^z.b))) 5. ==[ beta ]==> (b ((a b)(^z.b))) 6. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 181344/20979948. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 181345/20979993. ------ 1. ==[ start ]==> (((^a.a)(b a))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(b a))(((a a)(a a)) a)) 3. ==[ beta ]==> ((b a)(((a a)(a a)) a)) REDUCED to normal form. ------ 181346/20980020. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) b) b)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) b)) 5. ==[ beta ]==> (((^y.y) b) b) 6. ==[ alpha ]==> (((^x.x) b) b) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 181347/20980056. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 181348/20980137. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 181349/20980164. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.b)(^z.b))) 3. ==[ beta ]==> (((a b)(^x.(x x))) b) REDUCED to normal form. ------ 181350/20980191. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 181351/20980218. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 181352/20980281. ------ 1. ==[ start ]==> (((a a)(b a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 181353/20980308. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(b ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(b b)) REDUCED to normal form. ------ 181354/20980335. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(a ((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(a ((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(a ((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))(a ((a a)(a a)))) REDUCED to normal form. ------ 181355/20980362. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x) b)(a a))) 3. ==[ beta ]==> (((a (a a))(a b))(b (a a))) REDUCED to normal form. ------ 181356/20980389. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 181357/20980416. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((b a)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((b a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((b a)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((b a) a)) REDUCED to normal form. ------ 181358/20980443. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 181359/20980470. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(((^y.y)(a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a) a)((a a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> (((a a) a)((a a)((^x.x)(^y.y)))) 9. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 10. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 181360/20980497. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a b)((a a) a))) REDUCED to normal form. ------ 181361/20980551. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(a a))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 181362/20980722. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 181363/20980830. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a b)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181364/20980839. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 181365/20980857. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a) a)(^x1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.b))) REDUCED to normal form. ------ 181366/20980884. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a a))) 7. ==[ beta ]==> ((^y.y)(^z.(a a))) 8. ==[ alpha ]==> ((^x.x)(^y.(a a))) 9. ==[ beta ]==> (^y.(a a)) 10. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 181367/20980947. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)(b a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 181368/20980974. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 181369/20981019. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1) b) a)) 3. ==[ beta ]==> (b (((^x1.x1) b) a)) 4. ==[ alpha ]==> (b (((^x.x) b) a)) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 181370/20981028. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181371/20981055. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 181372/20981136. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 181373/20981280. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(c (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(c (b a))) 3. ==[ beta ]==> (((^y.y)(a b))(c (b a))) 4. ==[ alpha ]==> (((^x.x)(a b))(c (b a))) 5. ==[ beta ]==> ((a b)(c (b a))) REDUCED to normal form. ------ 181374/20981307. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 181375/20981334. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(a ((^z.z) b))) 3. ==[ beta ]==> (((a b)(^y.y))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a b)(^x.x))(a ((^y.y) b))) 5. ==[ beta ]==> (((a b)(^x.x))(a b)) REDUCED to normal form. ------ 181376/20981361. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 181377/20981388. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((b a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((b a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((b a)(a (^y.y)))) REDUCED to normal form. ------ 181378/20981442. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a)(a (a a)))) REDUCED to normal form. ------ 181379/20981469. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a b)((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a b)((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a b)((a b)(^y.y))) 6. ==[ alpha ]==> ((a b)((a b)(^x.x))) REDUCED to normal form. ------ 181380/20981748. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(a a))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(a a))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181381/20981757. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a a)) REDUCED to normal form. ------ 181382/20981784. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 181383/20981802. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((a a) a)(^z.a))) 3. ==[ beta ]==> (((^y.y) b)(((a a) a)(^z.a))) 4. ==[ alpha ]==> (((^x.x) b)(((a a) a)(^y.a))) 5. ==[ beta ]==> (b (((a a) a)(^y.a))) 6. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 181384/20981811. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 181385/20981829. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.b)) 7. ==[ beta ]==> ((^y.y)(^z.b)) 8. ==[ alpha ]==> ((^x.x)(^y.b)) 9. ==[ beta ]==> (^y.b) 10. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 181386/20981838. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 181387/20981919. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 181388/20981946. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 181389/20981964. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a (^y.(^z.z))) a)) 3. ==[ beta ]==> (b ((a (^y.(^z.z))) a)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 181390/20981973. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 181391/20982081. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 181392/20982108. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 181393/20982198. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(c ((a a)(^y.y)))) 3. ==[ beta ]==> ((a (b a))(c ((a a)(^y.y)))) 4. ==[ alpha ]==> ((a (b a))(c ((a a)(^x.x)))) REDUCED to normal form. ------ 181394/20982225. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(b (b a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(b (b a))) REDUCED to normal form. ------ 181395/20982252. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(a (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((^y.y)(a a))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((^x.x)(a a))(a (a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)(a (a (^y.(^z.z))))) 8. ==[ alpha ]==> ((a a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 181396/20982279. ------ 1. ==[ start ]==> ((((a a) a)(a b))((b a)(a a))) REDUCED to normal form. ------ 181397/20982306. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 181398/20982333. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)((^z.z) a))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y) a))) 9. ==[ beta ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 181399/20982360. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a b)(a (a a)))) REDUCED to normal form. ------ 181400/20982414. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((^y1.y1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.x1)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a) a)) REDUCED to normal form. ------ 181401/20982441. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a (a a))(a b))) 3. ==[ beta ]==> ((b (a a))((a (a a))(a b))) REDUCED to normal form. ------ 181402/20982468. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(a ((^x.x)(a a)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 181403/20982639. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a b)(^z.(z z)))) 3. ==[ beta ]==> (b ((a b)(^z.(z z)))) 4. ==[ alpha ]==> (b ((a b)(^x.(x x)))) REDUCED to normal form. ------ 181404/20982747. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1) a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181405/20982783. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 181406/20982810. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(b a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b a)) REDUCED to normal form. ------ 181407/20982828. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((b a) a)) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((b a) a)) 3. ==[ beta ]==> (((a a)(a a))((b a) a)) REDUCED to normal form. ------ 181408/20982855. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((a a)(^x1.x1)) b)) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y)) b)) 5. ==[ beta ]==> (((a a)(^y.y)) b) 6. ==[ alpha ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 181409/20982864. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 181410/20982891. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))(^y1.a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 181411/20982972. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 181412/20982999. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.b)(^z.b))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 181413/20983053. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 181414/20983197. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 181415/20983224. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.z))) 9. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 10. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 181416/20983251. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a (a a))((a a) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (a a))((a a) a))) REDUCED to normal form. ------ 181417/20983278. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x) a)(a b))) 3. ==[ beta ]==> (((a (a a))(b a))(a (a b))) REDUCED to normal form. ------ 181418/20983305. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 181419/20983332. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a a)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 181420/20983638. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a)) b)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a)) b)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(a a)) b)) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(a a)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181421/20983935. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.a) d)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a) d)) 3. ==[ beta ]==> ((b (^y.y))((^z.a) d)) 4. ==[ alpha ]==> ((b (^x.x))((^y.a) d)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 181422/20984097. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 181423/20984106. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 181424/20984133. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 181425/20984205. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181426/20984214. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^y1.y1)(^z1.z1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)(^z1.z1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(^y1.y1))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 181427/20984241. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)((a a) a))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)((a a) a))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 181428/20984268. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181429/20984493. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b (a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(b (a b))) 3. ==[ beta ]==> (((a b)(a a))(b (a b))) REDUCED to normal form. ------ 181430/20984520. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a b))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(a ((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)(a b))(a (a a))) REDUCED to normal form. ------ 181431/20984547. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a b)(a a))) REDUCED to normal form. ------ 181432/20984601. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1) a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z) a)) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 181433/20984628. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((b a)((a (a a))(a (a a)))) REDUCED to normal form. ------ 181434/20984655. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 181435/20984709. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a a)(a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a a)(a b))) 3. ==[ beta ]==> ((a (^y.y))((a a)(a b))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(a b))) REDUCED to normal form. ------ 181436/20984799. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 9. ==[ beta ]==> ((^y.y)(^z.a)) 10. ==[ alpha ]==> ((^x.x)(^y.a)) 11. ==[ beta ]==> (^y.a) 12. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 181437/20984880. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 181438/20984988. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2)) c)) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181439/20985105. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.z)(^x1.b))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.b))) 5. ==[ beta ]==> (a ((^y.y)(^z.b))) 6. ==[ alpha ]==> (a ((^x.x)(^y.b))) 7. ==[ beta ]==> (a (^y.b)) 8. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 181440/20985123. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.b) a)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.b) a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.b) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.b) a)) 5. ==[ beta ]==> ((^y.y)((^z.b) a)) 6. ==[ alpha ]==> ((^x.x)((^y.b) a)) 7. ==[ beta ]==> ((^y.b) a) 8. ==[ alpha ]==> ((^x.b) a) 9. ==[ beta ]==> b REDUCED to normal form. ------ 181441/20985150. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a) b)) 3. ==[ beta ]==> ((^y.y)((^x1.a) b)) 4. ==[ alpha ]==> ((^x.x)((^y.a) b)) 5. ==[ beta ]==> ((^y.a) b) 6. ==[ alpha ]==> ((^x.a) b) 7. ==[ beta ]==> a REDUCED to normal form. ------ 181442/20985294. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.b))) REDUCED to normal form. ------ 181443/20985321. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^c.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(a a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(a a))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 181444/20985348. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 181445/20985393. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1) a)(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181446/20985402. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 181447/20985429. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 181448/20985456. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a a) a)) REDUCED to normal form. ------ 181449/20985510. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181450/20985573. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (a (a a)))) REDUCED to normal form. ------ 181451/20985600. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(b (^y.y))) 6. ==[ alpha ]==> ((a ((a a)(a a)))(b (^x.x))) REDUCED to normal form. ------ 181452/20985627. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a ((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a ((a a) a))) 3. ==[ beta ]==> (((a (a a)) b)(a ((a a) a))) REDUCED to normal form. ------ 181453/20985654. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(a a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 181454/20985681. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 181455/20985708. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a ((^y.y) a))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 181456/20985735. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))((a (^y.y))(a (a a)))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 181457/20985762. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)(^y.y))) REDUCED to normal form. ------ 181458/20985942. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 181459/20985960. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (a a)) b)) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (a a)) b)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a)) b)) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 181460/20986347. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181461/20986374. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 181462/20986401. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(z z))) REDUCED to normal form. ------ 181463/20986419. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(y1 y1)) a)) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1)) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(y y)) a)) 5. ==[ beta ]==> ((^y.(y y)) a) 6. ==[ alpha ]==> ((^x.(x x)) a) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 181464/20986509. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(a (^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(y y)))) 7. ==[ beta ]==> (a (^y.(y y))) 8. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 181465/20986536. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 181466/20986554. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 181467/20986617. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 181468/20986698. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (^x1.x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (^z.z))) REDUCED to normal form. ------ 181469/20986725. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 181470/20986779. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181471/20986797. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 181472/20986806. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 181473/20986824. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1)) a)) REDUCED to normal form. ------ 181474/20986842. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b (a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b (a a))) REDUCED to normal form. ------ 181475/20986869. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a (a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a (^z.z)))) REDUCED to normal form. ------ 181476/20986896. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a)(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))((a a)(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 181477/20986923. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b a)) REDUCED to normal form. ------ 181478/20986950. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a b)) 5. ==[ beta ]==> (((^y.y) b)(a b)) 6. ==[ alpha ]==> (((^x.x) b)(a b)) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 181479/20986977. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 181480/20987004. ------ 1. ==[ start ]==> (((a b)(b a))(a a)) REDUCED to normal form. ------ 181481/20988906. ------ 1. ==[ start ]==> ((^a.(a b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.((^z.(^x1.x1)) a)) b) 4. ==[ alpha ]==> ((^x.((^y.(^z.z)) a)) b) 5. ==[ beta ]==> ((^y.(^z.z)) a) 6. ==[ alpha ]==> ((^x.(^y.y)) a) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181482/20998041. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181483/20998224. ------ 1. ==[ start ]==> (((a b)(b a)) b) REDUCED to normal form. ------ 181484/20998248. ------ 1. ==[ start ]==> ((^a.(^a.a))((a b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a b)(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181485/20998329. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181486/20998563. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ eta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181487/20998833. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.(^z.z))((^x1.(^y1.y1)) a))(((^y.(^z.z))((^x1.(^y1.y1)) a))((^y.(^z.z))((^x1.(^y1.y1)) a)))) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.(^z1.z1))((^x2.(^y2.y2)) a))((^z2.(^x3.x3))((^y3.(^z3.z3)) a)))) 5. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1))((^x2.(^y2.y2)) a))((^z2.(^x3.x3))((^y3.(^z3.z3)) a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((^x1.(^y1.y1)) a))((^z1.(^x2.x2))((^y2.(^z2.z2)) a)))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.(^y1.y1)) a))((^z1.(^x2.x2))((^y2.(^z2.z2)) a))) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 9. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 11. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 12. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181488/20999184. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181489/20999709. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (a (^z.((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> (a (^x.((^y.(^z.z)) a))) 7. ==[ beta ]==> (a (^x.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 181490/21000129. ------ 1. ==[ start ]==> ((^a.(a b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y)((^z.(^x1.x1)) a)) b) 4. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a)) b) 5. ==[ beta ]==> (((^y.(^z.z)) a) b) 6. ==[ alpha ]==> (((^x.(^y.y)) a) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 181491/21000132. ------ 1. ==[ start ]==> ((a (a b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a b))(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a b))(^x.(^z.z))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 181492/21000516. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(b (b (^z.z)))) 3. ==[ beta ]==> (^y.((b (b (^z.z)))(b (b (^z.z))))) 4. ==[ alpha ]==> (^x.((b (b (^y.y)))(b (b (^z.z))))) REDUCED to normal form. ------ 181493/21001320. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(^y.(y (^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 181494/21001398. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((^z.z)(^x1.a))((^z.z)(^x1.a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.x)(^y.a))((^z.z)(^x1.a)))(^y1.y1)) 5. ==[ beta ]==> (((^y.a)((^z.z)(^x1.a)))(^y1.y1)) 6. ==[ alpha ]==> (((^x.a)((^y.y)(^z.a)))(^x1.x1)) 7. ==[ beta ]==> (a (^x1.x1)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 181495/21002154. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ eta ]==> (b ((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 181496/21002778. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(^z.(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.(a a)))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 181497/21003777. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 181498/21004083. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 181499/21004389. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 181500/21004695. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181501/21005541. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^y1.(b y1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))((^x1.x1) a)) b) 4. ==[ beta ]==> ((^y.(^z.z)) b) 5. ==[ alpha ]==> ((^x.(^y.y)) b) 6. ==[ beta ]==> (^y.y) 7. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181502/21005988. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181503/21006963. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 181504/21007149. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(b (^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(b (^x1.b))) 3. ==[ eta ]==> ((^y.(^z.z))(b (^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181505/21007566. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(x1 b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(x1 b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(z b))) 5. ==[ beta ]==> ((^y.y)(^z.(z b))) 6. ==[ alpha ]==> ((^x.x)(^y.(y b))) 7. ==[ beta ]==> (^y.(y b)) 8. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 181506/21007728. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((a a) a))) 3. ==[ beta ]==> (b (^z.((a a) a))) 4. ==[ alpha ]==> (b (^x.((a a) a))) REDUCED to normal form. ------ 181507/21007899. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.a))) REDUCED to normal form. ------ 181508/21008070. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.a))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.a))) REDUCED to normal form. ------ 181509/21008367. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a a)(^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)(^x.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 181510/21008391. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y1.y1))(((^z.(^x1.x1))(^y1.y1))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.(^y1.y1))(^z1.z1))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.z1))(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.x1))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.x1)) 9. ==[ beta ]==> ((^y.y)(^x1.x1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181511/21008862. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.(y1 (y1 y1)))) 3. ==[ beta ]==> ((^y.y)(^y1.(y1 (y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (y y)))) 5. ==[ beta ]==> (^y.(y (y y))) 6. ==[ alpha ]==> (^x.(x (x x))) REDUCED to normal form. ------ 181512/21009264. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181513/21009267. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.c)) REDUCED to normal form. ------ 181514/21009312. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 181515/21009366. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 181516/21009393. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(a a))) 5. ==[ beta ]==> (((^y.y) b)(^z.(a a))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(a a))) 7. ==[ beta ]==> (b (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 181517/21009420. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 181518/21009447. ------ 1. ==[ start ]==> (((a b)(b a))(^a.(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 181519/21009477. ------ 1. ==[ start ]==> ((a (^a.a))((a b)(b a))) 2. ==[ alpha ]==> ((a (^x.x))((a b)(b a))) REDUCED to normal form. ------ 181520/21009504. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 181521/21009531. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a a)((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a a)((^y.y) b)) 8. ==[ alpha ]==> ((a a)((^x.x) b)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 181522/21009558. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 181523/21009612. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181524/21009639. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 181525/21009675. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 181526/21009702. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 181527/21009756. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 181528/21009792. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 181529/21009837. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b a)(^y.b))) REDUCED to normal form. ------ 181530/21009864. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 181531/21009891. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 181532/21009945. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181533/21009981. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 181534/21010008. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 181535/21010035. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((a (a a))((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 181536/21010062. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a (a a)))(^y.y)) 4. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 181537/21010134. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a b)(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> ((a b)((^y.y) b)) 6. ==[ alpha ]==> ((a b)((^x.x) b)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 181538/21010161. ------ 1. ==[ start ]==> (((a (a a)) a)((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (a a)) a)((b (^x.x)) c)) REDUCED to normal form. ------ 181539/21010332. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 181540/21010413. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 181541/21010503. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b ((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.y)(b ((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.x)(b ((^y.(^z.z)) a))) 7. ==[ beta ]==> (b ((^y.(^z.z)) a)) 8. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181542/21010539. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y) a)((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> (a ((^y.(y (^z.z))) a)) 6. ==[ alpha ]==> (a ((^x.(x (^y.y))) a)) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 181543/21010557. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(^y1.y1)) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(a a))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a a))) 7. ==[ beta ]==> (((^y.(^z.z)) a)(a a)) 8. ==[ alpha ]==> (((^x.(^y.y)) a)(a a)) 9. ==[ beta ]==> ((^y.y)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 181544/21010584. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 181545/21010620. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a)) d)) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a)) d)) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a)) d)) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 181546/21010638. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (a (a a)))) REDUCED to normal form. ------ 181547/21010881. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((a a)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((a a)(a a))) 7. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 181548/21010935. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (a ((a a)((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> (a ((a a)((^x.(^y.y)) a))) 7. ==[ beta ]==> (a ((a a)(^y.y))) 8. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 181549/21010971. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y) b)(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> (b (((^y.(^z.z)) a)(^x1.x1))) 6. ==[ alpha ]==> (b (((^x.(^y.y)) a)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181550/21010998. ------ 1. ==[ start ]==> ((((a a) a) a)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 181551/21011052. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.(x1 x1)))) REDUCED to normal form. ------ 181552/21011079. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 181553/21011106. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((b a)(^y.a))) REDUCED to normal form. ------ 181554/21011133. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181555/21011160. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 181556/21011196. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 181557/21011250. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 181558/21011277. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> (((a (a a)) a)(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> (((a (a a)) a)(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> (((a (a a)) a)(b ((^y.y) b))) 8. ==[ alpha ]==> (((a (a a)) a)(b ((^x.x) b))) 9. ==[ beta ]==> (((a (a a)) a)(b b)) REDUCED to normal form. ------ 181559/21011304. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a)(a a)))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 181560/21011331. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 181561/21011358. ------ 1. ==[ start ]==> ((a (a b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a b))((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y)) a)) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 181562/21011718. ------ 1. ==[ start ]==> (((^a.b)(a a))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(c ((a a)(a a)))) 3. ==[ beta ]==> (b (c ((a a)(a a)))) REDUCED to normal form. ------ 181563/21011745. ------ 1. ==[ start ]==> ((a (^b.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(b (b (^y.y)))) REDUCED to normal form. ------ 181564/21011961. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a))(a b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 181565/21011988. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)((^y.y)(a a))) 6. ==[ alpha ]==> ((a b)((^x.x)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 181566/21012042. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(b a))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(b a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(b a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b a)) 9. ==[ beta ]==> ((^y.y)(b a)) 10. ==[ alpha ]==> ((^x.x)(b a)) 11. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181567/21012123. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (b ((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 181568/21012186. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 181569/21012213. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 181570/21012267. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) REDUCED to normal form. ------ 181571/21012294. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))((b a)(^y.(^z.z)))) 7. ==[ beta ]==> (((b a)(^y.(^z.z)))((b a)(^y.(^z.z)))) 8. ==[ alpha ]==> (((b a)(^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 181572/21012321. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 181573/21012348. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(^x1.b))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 181574/21012375. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a b)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.(a a)))) REDUCED to normal form. ------ 181575/21012438. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 181576/21012465. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a ((a a) a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 181577/21012492. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)((^z.z) b))) 5. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 181578/21012519. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))((a a)(a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((a a)(a a)))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 181579/21012546. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)(b (^y.y)))) 5. ==[ beta ]==> ((((a a) a) a)(b (^y.y))) 6. ==[ alpha ]==> ((((a a) a) a)(b (^x.x))) REDUCED to normal form. ------ 181580/21012564. ------ 1. ==[ start ]==> (((^a.b) c)((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b) c)((b (^y.y)) a)) 3. ==[ beta ]==> (b ((b (^y.y)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 181581/21012627. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.a)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 181582/21012906. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(b ((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(b ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(b ((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 181583/21012960. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 181584/21012996. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1) c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1) c)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181585/21013041. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 181586/21013275. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(b (^x.(a a)))) REDUCED to normal form. ------ 181587/21013356. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 181588/21013383. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 181589/21013617. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.y))(^z.z))) REDUCED to normal form. ------ 181590/21013725. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.(^x1.x1))) c)) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 181591/21013950. ------ 1. ==[ start ]==> (((a a)(b a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 181592/21013977. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 181593/21014229. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181594/21014310. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((a (^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 181595/21014508. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a b)(^z.a))) REDUCED to normal form. ------ 181596/21014535. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((a a) a)(^x1.b))) REDUCED to normal form. ------ 181597/21014643. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.b)((a (^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.b)((a (^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 181598/21014697. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 181599/21014724. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 181600/21014751. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((b a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((b a) c)) REDUCED to normal form. ------ 181601/21014841. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 181602/21014868. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 181603/21014895. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 181604/21014976. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 181605/21015003. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 181606/21015102. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1)) d)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) d)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) d)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181607/21015147. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 181608/21015174. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((a a) a))) 5. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 181609/21015309. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 181610/21015426. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)(^z.(z z)))) REDUCED to normal form. ------ 181611/21015453. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((b a)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 181612/21015480. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 181613/21015507. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^z1.z1)(^x2.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.b))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.b)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.b)) REDUCED to normal form. ------ 181614/21015615. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181615/21015642. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 181616/21015669. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((b a) b)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b a) b)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a) b)) REDUCED to normal form. ------ 181617/21015813. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 181618/21015840. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(a a))(^y1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a a)) REDUCED to normal form. ------ 181619/21015867. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 181620/21015921. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 10. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 181621/21016173. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 181622/21016452. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 181623/21016533. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z)) b)) REDUCED to normal form. ------ 181624/21016767. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(a (b a))) 3. ==[ beta ]==> ((^y.(^z.z))(a (b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181625/21016803. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181626/21016830. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(a a)) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 181627/21017001. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 181628/21017082. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 181629/21017163. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 181630/21017190. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(x x))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 181631/21017217. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(a b))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 181632/21017496. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(b ((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181633/21017532. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z)) a)) 3. ==[ beta ]==> ((b c)((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((b c)((^x.(^y.y)) a)) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 181634/21017559. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a)) b)(a a)) REDUCED to normal form. ------ 181635/21017604. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((b (^y.y))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((b (^x.x))(((a a) a) a)) REDUCED to normal form. ------ 181636/21017631. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (a a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (a a))) 7. ==[ beta ]==> ((^y.y)(a (a a))) 8. ==[ alpha ]==> ((^x.x)(a (a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 181637/21017685. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1) a)((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a ((a a) a))) REDUCED to normal form. ------ 181638/21017775. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 181639/21017802. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 181640/21017883. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (a a))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 181641/21017910. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((b (^x.a))(a (^z.a))) 6. ==[ alpha ]==> ((b (^x.a))(a (^y.a))) REDUCED to normal form. ------ 181642/21017937. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 181643/21018000. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 181644/21018027. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 181645/21018054. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.a))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 181646/21018081. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 181647/21018108. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> ((b a)((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((b a)(^y.y)) 10. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 181648/21018135. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) a) REDUCED to normal form. ------ 181649/21018162. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 181650/21018189. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a b))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a b))(^y.(a a))) 6. ==[ alpha ]==> (((a a)(a b))(^x.(a a))) REDUCED to normal form. ------ 181651/21018378. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(b (^a.b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(b (^z.b))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.b))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.b))) REDUCED to normal form. ------ 181652/21018792. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(a (a b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(a (a b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a (a b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a (a b))) 5. ==[ beta ]==> ((^y.y)(a (a b))) 6. ==[ alpha ]==> ((^x.x)(a (a b))) 7. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 181653/21018819. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((a a) a)(a a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a a))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 181654/21018873. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (a a))((^z.z) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (a a))((^z.z) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (a a))((^z.z) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (a a))((^y.y) a))) 7. ==[ beta ]==> ((b b)((a (a a))((^y.y) a))) 8. ==[ alpha ]==> ((b b)((a (a a))((^x.x) a))) 9. ==[ beta ]==> ((b b)((a (a a)) a)) REDUCED to normal form. ------ 181655/21018954. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a)((a a) a))) 3. ==[ beta ]==> (b ((a a)((a a) a))) REDUCED to normal form. ------ 181656/21018990. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((a a) a)(^z.z))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 181657/21019017. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 181658/21019071. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.(y1 y1)))) REDUCED to normal form. ------ 181659/21019098. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 181660/21019125. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 181661/21019179. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1)(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1)) b)) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1)) b)) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) b)) 7. ==[ beta ]==> (((^y.y)(^z.z)) b) 8. ==[ alpha ]==> (((^x.x)(^y.y)) b) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 181662/21019215. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.a)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 181663/21019242. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 181664/21019269. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 181665/21019296. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.a))) 5. ==[ beta ]==> (((a (a a)) b)(^y.a)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.a)) REDUCED to normal form. ------ 181666/21019431. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (^y.(^z.z)))) REDUCED to normal form. ------ 181667/21019485. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 181668/21019512. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> ((b (a (a a)))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> ((b (a (a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 181669/21019539. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 181670/21019593. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 181671/21019611. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> ((a (^x.x))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 181672/21019620. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 181673/21020016. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a) b)) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a) b)) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a) b)) 5. ==[ beta ]==> (b (((^y.y) a) b)) 6. ==[ alpha ]==> (b (((^x.x) a) b)) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 181674/21020061. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b ((^z.z) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(b ((^z.z) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b ((^y.y) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(b a)) REDUCED to normal form. ------ 181675/21020088. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(a (a (a a)))) 3. ==[ beta ]==> ((^y.y)(a (a (a a)))) 4. ==[ alpha ]==> ((^x.x)(a (a (a a)))) 5. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 181676/21020142. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 181677/21020205. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 181678/21020223. ------ 1. ==[ start ]==> (((^a.b)(b a))(c b)) 2. ==[ alpha ]==> (((^x.b)(b a))(c b)) 3. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 181679/21020286. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z) a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 181680/21020331. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b (a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181681/21020367. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a) a)) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 181682/21020394. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 181683/21020448. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181684/21020466. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b b)) 3. ==[ beta ]==> (((a a)(^y.y))(b b)) 4. ==[ alpha ]==> (((a a)(^x.x))(b b)) REDUCED to normal form. ------ 181685/21020475. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 181686/21020493. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a c)) REDUCED to normal form. ------ 181687/21020511. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 181688/21020538. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 181689/21020565. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b (^z.z))) 3. ==[ beta ]==> ((a (b (^y.y)))(b (^z.z))) 4. ==[ alpha ]==> ((a (b (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 181690/21020592. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 181691/21020619. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(a a))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(a a))) 7. ==[ beta ]==> (b ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 181692/21020646. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 181693/21020673. ------ 1. ==[ start ]==> (((a b)(b a))(a (^a.a))) 2. ==[ alpha ]==> (((a b)(b a))(a (^x.x))) REDUCED to normal form. ------ 181694/21031719. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181695/21031902. ------ 1. ==[ start ]==> (((a b)(b a)) c) REDUCED to normal form. ------ 181696/21032127. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 181697/21032250. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^y.y)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 181698/21032559. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 181699/21033000. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(y (y (^z.z))))) 5. ==[ beta ]==> (a (^y.(y (y (^z.z))))) 6. ==[ alpha ]==> (a (^x.(x (x (^y.y))))) REDUCED to normal form. ------ 181700/21033636. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 181701/21033828. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.b)(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.b)(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 181702/21035085. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) b) c)) 3. ==[ beta ]==> (((((^z.z) b) c)(((^z.z) b) c))(^y.y)) 4. ==[ alpha ]==> (((((^x.x) b) c)(((^y.y) b) c))(^z.z)) 5. ==[ beta ]==> (((b c)(((^y.y) b) c))(^z.z)) 6. ==[ alpha ]==> (((b c)(((^x.x) b) c))(^y.y)) 7. ==[ beta ]==> (((b c)(b c))(^y.y)) 8. ==[ alpha ]==> (((b c)(b c))(^x.x)) REDUCED to normal form. ------ 181703/21035403. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(b (^z.z)))) REDUCED to normal form. ------ 181704/21035841. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.(^z.z)))(^x1.a))) 3. ==[ eta ]==> (b ((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 181705/21036123. ------ 1. ==[ start ]==> (((^a.a)(b a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.((a a)(a a)))) 3. ==[ beta ]==> ((b a)(^y.((a a)(a a)))) 4. ==[ alpha ]==> ((b a)(^x.((a a)(a a)))) REDUCED to normal form. ------ 181706/21037149. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.b)((^y.y)(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (b (^x1.x1)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181707/21037281. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181708/21037770. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^d.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181709/21038094. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 181710/21038958. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^b.(b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(^y.(y a))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y a))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x a))) REDUCED to normal form. ------ 181711/21039237. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(b x1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 181712/21039675. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181713/21039993. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((y y)(^z.z)))) 3. ==[ beta ]==> ((b c)(^y.((y y)(^z.z)))) 4. ==[ alpha ]==> ((b c)(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 181714/21040227. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 181715/21041253. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.z))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 7. ==[ beta ]==> (^y.(^z.y)) 8. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 181716/21041424. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((a a) a))) REDUCED to normal form. ------ 181717/21041655. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 181718/21042078. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((((^z.z)(^x1.x1)) a)((((^z.z)(^x1.x1)) a)(^y.y))) 4. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((((^z.z)(^x1.x1)) a)(^y1.y1))) 5. ==[ beta ]==> (((^y.y) a)((((^z.z)(^x1.x1)) a)(^y1.y1))) 6. ==[ alpha ]==> (((^x.x) a)((((^y.y)(^z.z)) a)(^x1.x1))) 7. ==[ beta ]==> (a ((((^y.y)(^z.z)) a)(^x1.x1))) 8. ==[ alpha ]==> (a ((((^x.x)(^y.y)) a)(^z.z))) 9. ==[ beta ]==> (a (((^y.y) a)(^z.z))) 10. ==[ alpha ]==> (a (((^x.x) a)(^y.y))) 11. ==[ beta ]==> (a (a (^y.y))) 12. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 181719/21042549. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 5. ==[ beta ]==> (^y.(^z.(z z))) 6. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 181720/21042639. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a))) 7. ==[ beta ]==> (^y.((^z.z) a)) 8. ==[ alpha ]==> (^x.((^y.y) a)) 9. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 181721/21042828. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((^x.x) b)(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181722/21042951. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181723/21042954. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(a (^y1.y1)))) REDUCED to normal form. ------ 181724/21043053. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.b)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 181725/21043080. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 181726/21043134. ------ 1. ==[ start ]==> (((a b)(b a))(^b.a)) 2. ==[ alpha ]==> (((a b)(b a))(^x.a)) REDUCED to normal form. ------ 181727/21043182. ------ 1. ==[ start ]==> (((^a.a) a)((a b)(b a))) 2. ==[ alpha ]==> (((^x.x) a)((a b)(b a))) 3. ==[ beta ]==> (a ((a b)(b a))) REDUCED to normal form. ------ 181728/21043209. ------ 1. ==[ start ]==> (((a a) a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 181729/21043236. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 181730/21043263. ------ 1. ==[ start ]==> (((^a.a) b)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x) b)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (b ((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 181731/21043290. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 181732/21043317. ------ 1. ==[ start ]==> (((a a) b)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a) b)((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a) b)((a (^x.x))(^z.z))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 181733/21043335. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(b (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 181734/21043344. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 181735/21043362. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181736/21043389. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 181737/21043434. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 181738/21043461. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 181739/21043488. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 181740/21043497. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 181741/21043524. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181742/21043605. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 181743/21043677. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 181744/21043767. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((^y.(^z.z))((^x1.(^y1.y1)) a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 7. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 9. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181745/21043794. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 181746/21044118. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181747/21044208. ------ 1. ==[ start ]==> (((a (a a)) b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a)) b)(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a (a a)) b)(b (^y.y))) 4. ==[ alpha ]==> (((a (a a)) b)(b (^x.x))) REDUCED to normal form. ------ 181748/21044235. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(a (a (a (^z.z))))) 3. ==[ beta ]==> (((^y.y) a)(a (a (a (^z.z))))) 4. ==[ alpha ]==> (((^x.x) a)(a (a (a (^y.y))))) 5. ==[ beta ]==> (a (a (a (a (^y.y))))) 6. ==[ alpha ]==> (a (a (a (a (^x.x))))) REDUCED to normal form. ------ 181749/21044262. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 181750/21044289. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 181751/21044316. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^y.a))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a (^x.a))(((a a)(a a)) a)) REDUCED to normal form. ------ 181752/21044343. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(b (a (a a)))) REDUCED to normal form. ------ 181753/21044370. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181754/21044793. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 181755/21044874. ------ 1. ==[ start ]==> ((a (^a.b))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 181756/21044892. ------ 1. ==[ start ]==> (((a a)((a a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 181757/21044946. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (a (a a)))((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (a (a a)))(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 181758/21044973. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a (a a))(^y.y))) 3. ==[ beta ]==> (((a (a a)) a)((a (a a))(^y.y))) 4. ==[ alpha ]==> (((a (a a)) a)((a (a a))(^x.x))) REDUCED to normal form. ------ 181759/21045063. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.b)((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.b)((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 181760/21045252. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 181761/21045279. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(a a))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 181762/21045414. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181763/21045423. ------ 1. ==[ start ]==> (((a b)(^a.a))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(c ((a a)(a a)))) REDUCED to normal form. ------ 181764/21045612. ------ 1. ==[ start ]==> (((^a.b) b)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (b ((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (b ((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((b a)(^y.y))) 6. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 181765/21045819. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (^x1.(a a)))) 3. ==[ beta ]==> (b (c (^x1.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 181766/21045828. ------ 1. ==[ start ]==> (((a b) b)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b) b)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 181767/21045855. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a a)(b (^y.y)))) 3. ==[ beta ]==> (((a a) a)((a a)(b (^y.y)))) 4. ==[ alpha ]==> (((a a) a)((a a)(b (^x.x)))) REDUCED to normal form. ------ 181768/21045954. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)((^z1.z1) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)((^z1.z1) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)((^y1.y1) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.y1) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1) a))) 9. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) a))) 10. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 11. ==[ beta ]==> ((^y.y)((^z.z) a)) 12. ==[ alpha ]==> ((^x.x)((^y.y) a)) 13. ==[ beta ]==> ((^y.y) a) 14. ==[ alpha ]==> ((^x.x) a) 15. ==[ beta ]==> a REDUCED to normal form. ------ 181769/21046035. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181770/21046161. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a (a a))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a) a))((a (a a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((a a) a))((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 181771/21046188. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.y))) REDUCED to normal form. ------ 181772/21046269. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((b (^y.y)) a)) REDUCED to normal form. ------ 181773/21046296. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a)(a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 181774/21046323. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) b) c)) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(b c)) REDUCED to normal form. ------ 181775/21046359. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181776/21046494. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181777/21046575. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 181778/21046611. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(b ((a a)(a a)))) REDUCED to normal form. ------ 181779/21046638. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(a (b (^z.z)))) 3. ==[ beta ]==> ((a (^y.b))(a (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.b))(a (b (^y.y)))) REDUCED to normal form. ------ 181780/21046692. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181781/21046719. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 181782/21046746. ------ 1. ==[ start ]==> (((a b)(^b.a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)(a (a a)))) REDUCED to normal form. ------ 181783/21046773. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 181784/21046800. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)((a a) a))) REDUCED to normal form. ------ 181785/21047025. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 181786/21047052. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 181787/21047079. ------ 1. ==[ start ]==> ((a (b a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((a (b a))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 181788/21047169. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))((a a) a))) 5. ==[ beta ]==> (b ((^z.(a a))((a a) a))) 6. ==[ alpha ]==> (b ((^x.(a a))((a a) a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 181789/21047250. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181790/21047358. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> ((b a)((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> ((b a)((^x.x)((a a)(a a)))) 5. ==[ beta ]==> ((b a)((a a)(a a))) REDUCED to normal form. ------ 181791/21047439. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 181792/21047520. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 181793/21047727. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 181794/21047754. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z) b)) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.z) b)) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y) b)) 5. ==[ beta ]==> (((a a) a)((^y.y) b)) 6. ==[ alpha ]==> (((a a) a)((^x.x) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 181795/21047907. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((a a) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181796/21048006. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(c (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)(c (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 181797/21048087. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> (b ((^x1.x1)(a a))) 4. ==[ alpha ]==> (b ((^x.x)(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 181798/21048195. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181799/21048222. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.b)((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 181800/21048249. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.a)(a b))) 3. ==[ beta ]==> ((^y.y)((^z.a)(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a b))) 5. ==[ beta ]==> ((^y.a)(a b)) 6. ==[ alpha ]==> ((^x.a)(a b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 181801/21048303. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))((a a)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(y y))((a a)(^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(x x))((a a)(^y.y)))) 9. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))((a a)(^y.y)))) 10. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 181802/21048384. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> (b ((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) b))) 5. ==[ beta ]==> (b ((^y.y) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 181803/21048519. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 181804/21048726. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.y) a)) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y) a)) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x) a)) 5. ==[ beta ]==> (((a a)(a (a a))) a) REDUCED to normal form. ------ 181805/21048753. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 181806/21048798. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((a a)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181807/21049005. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 181808/21049167. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.b)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.b)((^y.y)(^z.z)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 181809/21049248. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^x1.x1)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)((^x1.x1)(a a)))) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)((^z.z)(a a)))) 9. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 181810/21049329. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 181811/21049437. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181812/21049644. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 181813/21049869. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(^z.z)))) 5. ==[ beta ]==> (c (^y.(^z.z))) 6. ==[ alpha ]==> (c (^x.(^y.y))) REDUCED to normal form. ------ 181814/21050004. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 181815/21050112. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(y1 y1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181816/21050193. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.y)(b a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(b a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(b a))) 5. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 181817/21050274. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 181818/21050355. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181819/21050418. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(c ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(c (a a))) REDUCED to normal form. ------ 181820/21050472. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(a (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a (b a))) REDUCED to normal form. ------ 181821/21050499. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 181822/21050526. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a a)(a (^y.y)))) REDUCED to normal form. ------ 181823/21050751. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((a a)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a)((a a) a))(((a a)(^y.y))(^z.z))) 4. ==[ alpha ]==> (((a a)((a a) a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 181824/21050778. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 181825/21050832. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a) a)(^z.(z z)))) REDUCED to normal form. ------ 181826/21050859. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b (a (^x.x)))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 181827/21050913. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> ((a (b (^x.x)))(a (^z.b))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.b))) REDUCED to normal form. ------ 181828/21051084. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181829/21051192. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181830/21051228. ------ 1. ==[ start ]==> ((((^a.a) b) c)(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(a ((a a)(^y.y)))) 3. ==[ beta ]==> ((b c)(a ((a a)(^y.y)))) 4. ==[ alpha ]==> ((b c)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 181831/21051255. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a)(a a))) REDUCED to normal form. ------ 181832/21051363. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 181833/21051390. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1) a)((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a ((a a) a))) REDUCED to normal form. ------ 181834/21051462. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 181835/21051570. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181836/21051696. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a a) a)) REDUCED to normal form. ------ 181837/21051723. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a b) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a b) b)) REDUCED to normal form. ------ 181838/21051750. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((a a) a) c)) 3. ==[ beta ]==> ((a ((^y.y) b))(((a a) a) c)) 4. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a) c)) 5. ==[ beta ]==> ((a b)(((a a) a) c)) REDUCED to normal form. ------ 181839/21051912. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 181840/21052164. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z)))) 7. ==[ beta ]==> ((^y.a)(a (^z.z))) 8. ==[ alpha ]==> ((^x.a)(a (^y.y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 181841/21052245. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181842/21052353. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181843/21052470. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(b ((a a) a))) 3. ==[ beta ]==> (((^y.y) a)(b ((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)(b ((a a) a))) 5. ==[ beta ]==> (a (b ((a a) a))) REDUCED to normal form. ------ 181844/21052488. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.b))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.b))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.b))) 7. ==[ beta ]==> ((^y.y)(^z.b)) 8. ==[ alpha ]==> ((^x.x)(^y.b)) 9. ==[ beta ]==> (^y.b) 10. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 181845/21052578. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a (a a)) a)) REDUCED to normal form. ------ 181846/21052605. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(a (a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 181847/21052650. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(b (^z.a))) 3. ==[ beta ]==> (b (b (^z.a))) 4. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 181848/21052659. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 181849/21052758. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(z1 z1))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181850/21052893. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 181851/21053046. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y)) b)) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 181852/21053073. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a)) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y)) c)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(c c)) REDUCED to normal form. ------ 181853/21053181. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1)(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 181854/21053208. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 181855/21053235. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a (^y.a))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.a))) REDUCED to normal form. ------ 181856/21053289. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 181857/21053316. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.z) a)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y) a)) 5. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 181858/21053325. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((^z.(^x1.x1))(^y1.y1))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.x1)) 7. ==[ beta ]==> ((^y.y)(^x1.x1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181859/21053730. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 181860/21053757. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 181861/21053766. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b ((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(b a)) REDUCED to normal form. ------ 181862/21053784. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.y1)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(z z))) 6. ==[ alpha ]==> ((^x.x)(^y.(y y))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 181863/21053874. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.y) a))) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 181864/21053919. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a)(a a))) 3. ==[ beta ]==> (b ((^y.a)(a a))) 4. ==[ alpha ]==> (b ((^x.a)(a a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 181865/21054027. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181866/21054063. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a ((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 181867/21054090. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 181868/21054162. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 181869/21054171. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b b)) REDUCED to normal form. ------ 181870/21054189. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 181871/21054207. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (^y.y)) a)) REDUCED to normal form. ------ 181872/21054234. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a) b)) REDUCED to normal form. ------ 181873/21054261. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 181874/21054288. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a) b)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x) b)) 3. ==[ beta ]==> (((a (a a))((a a)(a a))) b) REDUCED to normal form. ------ 181875/21054315. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(^z.z))) 5. ==[ beta ]==> (((^y.y) b)((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x) b)((a a)(^y.y))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 181876/21054342. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a) a)) REDUCED to normal form. ------ 181877/21054369. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a) a)) 2. ==[ alpha ]==> (((a b)(b a))((^x.x) a)) 3. ==[ beta ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 181878/21054395. ------ 1. ==[ start ]==> (^a.(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (^x.(((^y.y)(x x))((x x)(^z.z)))) 3. ==[ beta ]==> (^x.((x x)((x x)(^z.z)))) 4. ==[ alpha ]==> (^x.((x x)((x x)(^y.y)))) REDUCED to normal form. ------ 181879/21054396. ------ 1. ==[ start ]==> (a (((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (a (((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (a ((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> (a ((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 181880/21065424. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181881/21065634. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a))) a) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y))) a) 3. ==[ beta ]==> (((a a)((a a)(^y.y))) a) 4. ==[ alpha ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 181882/21065640. ------ 1. ==[ start ]==> ((^a.a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 5. ==[ beta ]==> ((a a)((a a)(^y.y))) 6. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 181883/21065667. ------ 1. ==[ start ]==> ((^a.(a a))((a b)(b a))) 2. ==[ alpha ]==> ((^x.(x x))((a b)(b a))) 3. ==[ beta ]==> (((a b)(b a))((a b)(b a))) REDUCED to normal form. ------ 181884/21065694. ------ 1. ==[ start ]==> ((^a.b)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 181885/21065775. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((((^z.z) a)(b (^x1.x1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.z)) 5. ==[ beta ]==> ((a (b (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 181886/21065850. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 181887/21065892. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^x.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181888/21066135. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 181889/21066273. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 181890/21066714. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> (a (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 181891/21067017. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((((^y.y)(^z.z))(a (^x1.(^y1.y1))))(((^y.y)(^z.z))(a (^x1.(^y1.y1)))))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2)))))(((^z2.z2)(^x3.x3))(a (^y3.(^z3.z3))))) 5. ==[ beta ]==> ((((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2)))))(((^z2.z2)(^x3.x3))(a (^y3.(^z3.z3))))) 6. ==[ alpha ]==> ((((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2)))))(((^y2.y2)(^z2.z2))(a (^x3.(^y3.y3))))) 7. ==[ beta ]==> (((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2)))))(((^y2.y2)(^z2.z2))(a (^x3.(^y3.y3))))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1)))))(((^x2.x2)(^y2.y2))(a (^z2.(^x3.x3))))) 9. ==[ beta ]==> (((a (^x.(^y.y)))((^x1.x1)(a (^y1.(^z1.z1)))))(((^x2.x2)(^y2.y2))(a (^z2.(^x3.x3))))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1)))))(((^z1.z1)(^x2.x2))(a (^y2.(^z2.z2))))) 11. ==[ beta ]==> (((a (^x.(^y.y)))(a (^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(a (^y2.(^z2.z2))))) 12. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 13. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(a (^x2.(^y2.y2))))) 14. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(a (^z1.(^x2.x2))))) 15. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^z1.(^x2.x2)))) 16. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.(^z1.z1)))) REDUCED to normal form. ------ 181892/21067146. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> (b (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 181893/21067350. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 181894/21067965. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a (^x.x))((a a) a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(^z.z))) REDUCED to normal form. ------ 181895/21068124. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> ((^y.y)((((a a)(^z.z))((a a) a))(((a a)(^z.z))((a a) a)))) 4. ==[ alpha ]==> ((^x.x)((((a a)(^y.y))((a a) a))(((a a)(^z.z))((a a) a)))) 5. ==[ beta ]==> ((((a a)(^y.y))((a a) a))(((a a)(^z.z))((a a) a))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 181896/21068739. ------ 1. ==[ start ]==> (((^a.b) c)(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(y (^z.z)))) 3. ==[ beta ]==> (b (^y.(y (^z.z)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 181897/21069477. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.((a a)(a a)))) 3. ==[ beta ]==> (((a b) a)(^y.((a a)(a a)))) 4. ==[ alpha ]==> (((a b) a)(^x.((a a)(a a)))) REDUCED to normal form. ------ 181898/21069837. ------ 1. ==[ start ]==> (((^a.a)(b a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(a a)))) 3. ==[ beta ]==> ((b a)(^y.(^z.(a a)))) 4. ==[ alpha ]==> ((b a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 181899/21070206. ------ 1. ==[ start ]==> (((a (a a))(a b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.((x x)(x x)))) REDUCED to normal form. ------ 181900/21070392. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((a a) a)(a b))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 181901/21070863. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (b (^x1.(^y1.y1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 181902/21070872. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181903/21071205. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.((^z.z) b))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.((^y.y) b))) 5. ==[ beta ]==> (((a a)(a (a a)))(^x.b)) REDUCED to normal form. ------ 181904/21071310. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 181905/21071808. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181906/21071817. ------ 1. ==[ start ]==> (((a b)(^c.a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 181907/21072123. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 181908/21072309. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a (a a))(a b))) 3. ==[ beta ]==> ((((a (a a))(a b))((a (a a))(a b)))(((a (a a))(a b))((a (a a))(a b)))) REDUCED to normal form. ------ 181909/21073203. ------ 1. ==[ start ]==> (((a b)(a b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 181910/21073707. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 181911/21073950. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 181912/21074391. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^y.(y y))) REDUCED to normal form. ------ 181913/21074550. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (^x1.x1))((a a) a))) 3. ==[ eta ]==> ((^y.(^z.z))((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181914/21075138. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 181915/21075165. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.b))) REDUCED to normal form. ------ 181916/21075369. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1)(^y1.y1)) b)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 181917/21075498. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.((y1 y1) y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.((y1 y1) y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.((x1 x1) x1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((x1 x1) x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((z z) z))) REDUCED to normal form. ------ 181918/21075786. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 181919/21076380. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.(y1 y1)))) REDUCED to normal form. ------ 181920/21076461. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^z.a)) REDUCED to normal form. ------ 181921/21076542. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 181922/21076623. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181923/21076665. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 181924/21076668. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 181925/21076740. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 181926/21076821. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.b)) REDUCED to normal form. ------ 181927/21076848. ------ 1. ==[ start ]==> (((a b)(b a))(^a.(a a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(x x))) REDUCED to normal form. ------ 181928/21076875. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.z)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.z)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 181929/21076887. ------ 1. ==[ start ]==> ((a a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a a)(((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> ((a a)((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((a a)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 181930/21076914. ------ 1. ==[ start ]==> ((a (a a))((a b)(b a))) REDUCED to normal form. ------ 181931/21076941. ------ 1. ==[ start ]==> ((a b)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 181932/21076995. ------ 1. ==[ start ]==> (((a a)(a a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 181933/21077022. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a (a (^x.x)))(a (b (^z.z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 181934/21077067. ------ 1. ==[ start ]==> (((a (^a.a)) a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 181935/21077094. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 181936/21077112. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 181937/21077121. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 181938/21077139. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 181939/21077220. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 181940/21077256. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 181941/21077301. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (a (((a a)(^y.y))(^z.(a a)))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 181942/21077310. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 181943/21077337. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 181944/21077364. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b)(b a))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(b a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(b a))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 181945/21077382. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 181946/21077472. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 181947/21077517. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 181948/21077553. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a b)((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a b)((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a b)((^z.z)(^y.y))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 181949/21077571. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a) b)) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a) b)) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 7. ==[ beta ]==> (((^y.(^z.z)) a) b) 8. ==[ alpha ]==> (((^x.(^y.y)) a) b) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 181950/21077598. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((b (^y.y)) c)) 3. ==[ beta ]==> ((a (a a))((b (^y.y)) c)) 4. ==[ alpha ]==> ((a (a a))((b (^x.x)) c)) REDUCED to normal form. ------ 181951/21077634. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 181952/21077661. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 181953/21077958. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(y (^z.z))))) 7. ==[ beta ]==> (a (^y.(y (^z.z)))) 8. ==[ alpha ]==> (a (^x.(x (^y.y)))) REDUCED to normal form. ------ 181954/21077976. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 (^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1))) a)) 5. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1))) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) a)) 7. ==[ beta ]==> ((^y.(y (^z.z))) a) 8. ==[ alpha ]==> ((^x.(x (^y.y))) a) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 181955/21078129. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)((a a) a))) REDUCED to normal form. ------ 181956/21078156. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 181957/21078183. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a a)(((^y.y)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((a a)((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> ((a a)((a a)((^x.x)(a a)))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 181958/21078210. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 181959/21078237. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a) a)(b a))) 5. ==[ beta ]==> ((a a)(((a a) a)(b a))) REDUCED to normal form. ------ 181960/21078264. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a ((a a) a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a ((a a) a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 181961/21078390. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) b)(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) b)(a (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (a (^y.(y (^z.z))))) 6. ==[ alpha ]==> (b (a (^x.(x (^y.y))))) REDUCED to normal form. ------ 181962/21078435. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 181963/21078462. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((a a)(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.a)) 6. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 181964/21078471. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 181965/21078498. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))(a (a a))) REDUCED to normal form. ------ 181966/21078516. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 181967/21078525. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 181968/21078597. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.b))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 181969/21078768. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 181970/21078930. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 181971/21078984. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 181972/21079038. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 181973/21079092. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 181974/21079119. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181975/21079146. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 181976/21079182. ------ 1. ==[ start ]==> (((a a)(a b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))(b (b (^x.x)))) REDUCED to normal form. ------ 181977/21079209. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(a (^y.y))) REDUCED to normal form. ------ 181978/21079236. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((b (^x1.x1))(a a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b (^z.z))(a a))) 5. ==[ beta ]==> ((a (^y.y))((b (^z.z))(a a))) 6. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(a a))) REDUCED to normal form. ------ 181979/21079263. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 181980/21079290. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z) b)((^x1.x1) a))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)((^z.z) a))) 7. ==[ beta ]==> (a (((^y.y) b)((^z.z) a))) 8. ==[ alpha ]==> (a (((^x.x) b)((^y.y) a))) 9. ==[ beta ]==> (a (b ((^y.y) a))) 10. ==[ alpha ]==> (a (b ((^x.x) a))) 11. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 181981/21079317. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 181982/21079344. ------ 1. ==[ start ]==> (((a b)(a a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a b)(a a))((b a)(^y.y))) 4. ==[ alpha ]==> (((a b)(a a))((b a)(^x.x))) REDUCED to normal form. ------ 181983/21079371. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> ((a (a a))(((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 181984/21079551. ------ 1. ==[ start ]==> (((a b) b)(c (^c.(a a)))) 2. ==[ alpha ]==> (((a b) b)(c (^x.(a a)))) REDUCED to normal form. ------ 181985/21079623. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 181986/21079677. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)(^z1.a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b)(^z1.a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)(^y1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(^y1.a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(^x1.a))) 9. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.a))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.a))) 11. ==[ beta ]==> (((^y.y) b)(^z.a)) 12. ==[ alpha ]==> (((^x.x) b)(^y.a)) 13. ==[ beta ]==> (b (^y.a)) 14. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 181987/21079686. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z) a)) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 181988/21079713. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.(^y1.y1)))(a (a a)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1)))(a (a a)))) 7. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(a (a a)))((^y.(^z.(^x1.x1)))(a (a a)))) 8. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 9. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a (a a)))) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 181989/21079758. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 181990/21079767. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 181991/21079794. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(a a))(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(a b))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 181992/21079983. ------ 1. ==[ start ]==> (((^a.b) c)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (b ((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> (b ((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 181993/21080226. ------ 1. ==[ start ]==> (((a b) c)((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 181994/21080280. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 181995/21080334. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 181996/21080559. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a b)(a b))) REDUCED to normal form. ------ 181997/21080586. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(((a a) a)(a a))) REDUCED to normal form. ------ 181998/21080613. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (a b))((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (a b))((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> ((a (a b))((a a)(^y.y))) 8. ==[ alpha ]==> ((a (a b))((a a)(^x.x))) REDUCED to normal form. ------ 181999/21080640. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (a a))(b a))) REDUCED to normal form. ------ 182000/21080667. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (^z.(^x1.x1))))) 9. ==[ beta ]==> (((^y.y) a)(a (^z.(^x1.x1)))) 10. ==[ alpha ]==> (((^x.x) a)(a (^y.(^z.z)))) 11. ==[ beta ]==> (a (a (^y.(^z.z)))) 12. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 182001/21080694. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((a (^x.x))((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((a (^x.x)) b)) REDUCED to normal form. ------ 182002/21080721. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((a b) a)((a a)((a a)(a a)))) REDUCED to normal form. ------ 182003/21080892. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> (b (((^z.z)(a a))(^x1.a))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(^y.a))) 7. ==[ beta ]==> (b ((a a)(^y.a))) 8. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 182004/21080973. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 182005/21081036. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 182006/21081081. ------ 1. ==[ start ]==> (((^a.a)(b a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((a a)(^y.(a a)))) 3. ==[ beta ]==> ((b a)((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((b a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 182007/21081108. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((a a)(a a)) a)) 3. ==[ beta ]==> ((^y.y)(((a a)(a a)) a)) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a)) a)) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 182008/21081144. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 182009/21081162. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.(^z.z))) c)) 3. ==[ beta ]==> (((a b)(a b))((a (^y.(^z.z))) c)) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 182010/21081171. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 182011/21081225. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 182012/21081252. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 182013/21081279. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.b)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 182014/21081423. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(b ((^z.z) b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(b ((^z.z) b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(b ((^y.y) b))) 5. ==[ beta ]==> ((a (a a))(b ((^y.y) b))) 6. ==[ alpha ]==> ((a (a a))(b ((^x.x) b))) 7. ==[ beta ]==> ((a (a a))(b b)) REDUCED to normal form. ------ 182015/21081450. ------ 1. ==[ start ]==> (((a (a a))(a b))(a ((a a)(a a)))) REDUCED to normal form. ------ 182016/21081477. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) b)(a a))) 5. ==[ beta ]==> (((a a) a)(((^y.y) b)(a a))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b)(a a))) 7. ==[ beta ]==> (((a a) a)(b (a a))) REDUCED to normal form. ------ 182017/21081504. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 182018/21081531. ------ 1. ==[ start ]==> (((a b)(a (a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((b a)((^x.x) a))) 3. ==[ beta ]==> (((a b)(a (a a)))((b a) a)) REDUCED to normal form. ------ 182019/21081558. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(a (a a)))) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 182020/21081585. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 182021/21081639. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a) a)(a b))) REDUCED to normal form. ------ 182022/21081810. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> (b (((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.y))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 182023/21081918. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182024/21081927. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 182025/21081945. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a b)(^x1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 182026/21081954. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.b)((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 182027/21081972. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((a a) a)(^z.b))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.b))) 5. ==[ beta ]==> (((a a) a)(^y.b)) 6. ==[ alpha ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 182028/21082035. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(((a a)(^z.z))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 182029/21082062. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(b a))) 5. ==[ beta ]==> ((^y.b)((^z.a)(b a))) 6. ==[ alpha ]==> ((^x.b)((^y.a)(b a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 182030/21082107. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a a)(^x1.x1))) 3. ==[ beta ]==> (b ((a a)(^x1.x1))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 182031/21082116. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 182032/21082143. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 182033/21082170. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 182034/21082422. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^y.y))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(^x.x))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 182035/21082449. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(a ((^y.y) b))) 3. ==[ beta ]==> (((a a)(a (a a)))(a ((^y.y) b))) 4. ==[ alpha ]==> (((a a)(a (a a)))(a ((^x.x) b))) 5. ==[ beta ]==> (((a a)(a (a a)))(a b)) REDUCED to normal form. ------ 182036/21082476. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 182037/21082530. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 182038/21082557. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> ((a b)((a a)(a (a a)))) REDUCED to normal form. ------ 182039/21082836. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a)(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182040/21082845. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 182041/21082872. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((b a)((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> ((b a)((^x.(a a))(a (a a)))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 182042/21082890. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 182043/21082899. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 182044/21082971. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 182045/21083007. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)((a a)(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182046/21083034. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 182047/21083052. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 182048/21083061. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^x.a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 182049/21083088. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 182050/21083169. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 182051/21083196. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 182052/21083340. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(b (b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(b (b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b (b a))) 5. ==[ beta ]==> (((^y.y)(a a))(b (b a))) 6. ==[ alpha ]==> (((^x.x)(a a))(b (b a))) 7. ==[ beta ]==> ((a a)(b (b a))) REDUCED to normal form. ------ 182053/21083367. ------ 1. ==[ start ]==> ((((a a) a)(a b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 182054/21083394. ------ 1. ==[ start ]==> (((a b)((a a) a))((b a)(a a))) REDUCED to normal form. ------ 182055/21083421. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((a a)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 182056/21083448. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)((^y.y) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a) a)) REDUCED to normal form. ------ 182057/21083502. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 182058/21083529. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> ((b (a a))((^y.y)((a a) a))) 6. ==[ alpha ]==> ((b (a a))((^x.x)((a a) a))) 7. ==[ beta ]==> ((b (a a))((a a) a)) REDUCED to normal form. ------ 182059/21083556. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a (a a))(a b))) REDUCED to normal form. ------ 182060/21083727. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (b ((a a)(^y.a))) 6. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 182061/21083835. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a (a a))(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182062/21083871. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b b)((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b b)((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 182063/21083898. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 182064/21083943. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((b a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((b a) a)) 3. ==[ beta ]==> ((^y.y)((b a) a)) 4. ==[ alpha ]==> ((^x.x)((b a) a)) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 182065/21083997. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(a a)) c)) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a)) c)) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a)) c)) 5. ==[ beta ]==> (((b a)(b a))((a a) c)) REDUCED to normal form. ------ 182066/21084060. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 182067/21084087. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 182068/21084141. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 182069/21084285. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a b)((^x.x) a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a b) a)) REDUCED to normal form. ------ 182070/21084312. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a) a)(a (a a)))) REDUCED to normal form. ------ 182071/21084339. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 10. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 182072/21084366. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (a a))((a a) a))) REDUCED to normal form. ------ 182073/21084393. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)(a b))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(a b))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(a b))) 7. ==[ beta ]==> (((a a)(^x.x))(a (a b))) REDUCED to normal form. ------ 182074/21084420. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a (^x.x))(a a))) REDUCED to normal form. ------ 182075/21084447. ------ 1. ==[ start ]==> (((a b)(a b))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 182076/21084726. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1)) a)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a)(^x2.x2)) a)) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x2.x2)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182077/21084951. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((b c)(^y.(^z.z))) 6. ==[ alpha ]==> ((b c)(^x.(^y.y))) REDUCED to normal form. ------ 182078/21085023. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.b) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.b) c)) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 182079/21085194. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 182080/21085221. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(a a))(a a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(a a))(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(a a))) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 182081/21085293. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182082/21085302. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 182083/21085329. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.a))((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((b (^x.a))((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((b (^x.a))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.z))) 11. ==[ beta ]==> ((b (^x.a))(^z.z)) 12. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 182084/21085356. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 182085/21085581. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c ((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c ((a a) a))) 3. ==[ beta ]==> (((a b)(a a))(c ((a a) a))) REDUCED to normal form. ------ 182086/21085608. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(b (a b))) 3. ==[ beta ]==> (((a a)(a b))(b (a b))) REDUCED to normal form. ------ 182087/21085635. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a (a a))) REDUCED to normal form. ------ 182088/21085689. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((a a) a)(a (^z.z)))) REDUCED to normal form. ------ 182089/21085716. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))((^z.z) a))) 7. ==[ beta ]==> ((b a)((^y.y)((^z.z) a))) 8. ==[ alpha ]==> ((b a)((^x.x)((^y.y) a))) 9. ==[ beta ]==> ((b a)((^y.y) a)) 10. ==[ alpha ]==> ((b a)((^x.x) a)) 11. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 182090/21085743. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 182091/21085797. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 182092/21085887. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 182093/21085968. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 182094/21086076. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a) a) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182095/21086238. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.b) a)) 3. ==[ beta ]==> ((^y.y)((^x1.b) a)) 4. ==[ alpha ]==> ((^x.x)((^y.b) a)) 5. ==[ beta ]==> ((^y.b) a) 6. ==[ alpha ]==> ((^x.b) a) 7. ==[ beta ]==> b REDUCED to normal form. ------ 182096/21086292. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z)) c)) 7. ==[ beta ]==> ((b b)((^y.(^z.z)) c)) 8. ==[ alpha ]==> ((b b)((^x.(^y.y)) c)) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 182097/21086382. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 182098/21086409. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(a (^z.b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(a (^z.b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.b))) REDUCED to normal form. ------ 182099/21086436. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^c.a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 182100/21086481. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (a a))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182101/21086490. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^z1.z1) a)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^z1.z1) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^y1.y1) a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 182102/21086517. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 182103/21086544. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 182104/21086616. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.x1) b)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z) b)) 5. ==[ beta ]==> ((a (^x.(x (^y.y)))) b) REDUCED to normal form. ------ 182105/21086715. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a)) b)(b (^y.y))) 6. ==[ alpha ]==> (((a (a a)) b)(b (^x.x))) REDUCED to normal form. ------ 182106/21086742. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(a ((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(a ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(a ((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a ((a a) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((a a) a))) REDUCED to normal form. ------ 182107/21086769. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x)(^y.y))(a a))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y)(a a))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(a a))) 5. ==[ beta ]==> ((((a a) a)(b a))(a a)) REDUCED to normal form. ------ 182108/21086796. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 182109/21086823. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a))(a ((^y.y) a))) 8. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) a))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 182110/21086850. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 182111/21087030. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 182112/21087048. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1)(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1)(^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> ((((^z.z)(^x1.x1)) a)(^y.y)) 6. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(^z.z)) 7. ==[ beta ]==> (((^y.y) a)(^z.z)) 8. ==[ alpha ]==> (((^x.x) a)(^y.y)) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 182113/21087435. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.z))) 5. ==[ beta ]==> (b ((^y.(y y))(^z.z))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 7. ==[ beta ]==> (b ((^y.y)(^y.y))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182114/21087453. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a) b)) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a) b)) 5. ==[ beta ]==> ((^y.y)(((^z.z) a) b)) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a) b)) 7. ==[ beta ]==> (((^y.y) a) b) 8. ==[ alpha ]==> (((^x.x) a) b) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 182115/21087462. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 182116/21087489. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 182117/21087561. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a) b)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a) b)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 182118/21087597. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.a))) 5. ==[ beta ]==> ((^y.y)(b (^z.a))) 6. ==[ alpha ]==> ((^x.x)(b (^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 182119/21087624. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.(x1 x1)))) REDUCED to normal form. ------ 182120/21087642. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 182121/21087705. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))((^x1.x1) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 182122/21087750. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (^x1.x1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182123/21087786. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.a)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 182124/21087867. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182125/21087885. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 182126/21087894. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 182127/21087912. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 182128/21087957. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b (a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b (a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (a a))) REDUCED to normal form. ------ 182129/21087984. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a (a (^z.z)))) 3. ==[ beta ]==> ((a (b (^y.y)))(a (a (^z.z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 182130/21088011. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 182131/21088038. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b a)) 5. ==[ beta ]==> (((^y.y) b)(b a)) 6. ==[ alpha ]==> (((^x.x) b)(b a)) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 182132/21088065. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 182133/21088092. ------ 1. ==[ start ]==> (((a b)(b a))(a (a a))) REDUCED to normal form. ------ 182134/21088119. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 182135/21098283. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^z.((^x1.x1)(^y1.y1)))((^z.((^x1.x1)(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.((^y1.y1)(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182136/21099366. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a))) b) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y))) b) 3. ==[ beta ]==> (((a a)((a a)(^y.y))) b) 4. ==[ alpha ]==> (((a a)((a a)(^x.x))) b) REDUCED to normal form. ------ 182137/21099390. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182138/21099471. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182139/21099975. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((^y.a)(b (^z.z)))(((^y.a)(b (^z.z)))((^y.a)(b (^z.z))))) 4. ==[ alpha ]==> (((^x.a)(b (^y.y)))(((^z.a)(b (^x1.x1)))((^y1.a)(b (^z1.z1))))) 5. ==[ beta ]==> (a (((^z.a)(b (^x1.x1)))((^y1.a)(b (^z1.z1))))) 6. ==[ alpha ]==> (a (((^x.a)(b (^y.y)))((^z.a)(b (^x1.x1))))) 7. ==[ beta ]==> (a (a ((^z.a)(b (^x1.x1))))) 8. ==[ alpha ]==> (a (a ((^x.a)(b (^y.y))))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 182140/21100473. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 (x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(z (z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 7. ==[ beta ]==> (^y.(y (y (^z.z)))) 8. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 182141/21101271. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(b (^x1.x1))) b) 4. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z))) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 182142/21101658. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(c ((a a)(a a)))) 3. ==[ beta ]==> (^y.((c ((a a)(a a)))(c ((a a)(a a))))) 4. ==[ alpha ]==> (^x.((c ((a a)(a a)))(c ((a a)(a a))))) REDUCED to normal form. ------ 182143/21102480. ------ 1. ==[ start ]==> (((^a.b) c)(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 182144/21102489. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 182145/21102876. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(b (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 182146/21103296. ------ 1. ==[ start ]==> ((^a.(b a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)(a (^z.z)))) 3. ==[ eta ]==> (b ((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 182147/21103947. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 182148/21104613. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 182149/21104946. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(^y.(^z.z))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 182150/21105558. ------ 1. ==[ start ]==> (((a b)(^c.a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 182151/21105864. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 182152/21107130. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182153/21107682. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 5. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 182154/21107916. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 182155/21108132. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 182156/21108735. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(x1 b))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 b))) 4. ==[ alpha ]==> ((^x.x)(^y.(y b))) 5. ==[ beta ]==> (^y.(y b)) 6. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 182157/21109239. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.(^z1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 182158/21109533. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)((^x1.x1)(^y1.y1)))(((^z.z)((^x1.x1)(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)((^y1.y1)(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)((^y1.y1)(^z1.z1)))(^x2.x2))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)((^x1.x1)(^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> ((^y.y)(((^z.z)((^x1.x1)(^y1.y1)))(^z1.z1))) 8. ==[ alpha ]==> ((^x.x)(((^y.y)((^z.z)(^x1.x1)))(^y1.y1))) 9. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.y1)) 10. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.x1)) 11. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 12. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 13. ==[ beta ]==> ((^y.y)(^z.z)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182159/21109536. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 182160/21110202. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.a))) REDUCED to normal form. ------ 182161/21110283. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.x1)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 182162/21110364. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.c)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.c)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182163/21110406. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 182164/21110427. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(a (^z.z)))) REDUCED to normal form. ------ 182165/21110481. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 182166/21110535. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 182167/21110562. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 182168/21110589. ------ 1. ==[ start ]==> (((a b)(b a))(^b.(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 182169/21110616. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 182170/21110646. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 182171/21110673. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 182172/21110700. ------ 1. ==[ start ]==> (((^a.a)(a a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a a)(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a a)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 182173/21110727. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 182174/21110781. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(b (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182175/21110808. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 182176/21110835. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((a (^y.y))((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 182177/21110871. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 182178/21110925. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 182179/21111006. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 182180/21111033. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a) a)((b a)(^y.b))) 3. ==[ beta ]==> ((a a)((b a)(^y.b))) 4. ==[ alpha ]==> ((a a)((b a)(^x.b))) REDUCED to normal form. ------ 182181/21111060. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 182182/21111177. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 182183/21111204. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 182184/21111231. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.a)(b (^y.y)))) 3. ==[ beta ]==> ((a (a (a a))) a) REDUCED to normal form. ------ 182185/21111303. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a) b)((a (a (^y.y))) a)) 3. ==[ beta ]==> ((a b)((a (a (^y.y))) a)) 4. ==[ alpha ]==> ((a b)((a (a (^x.x))) a)) REDUCED to normal form. ------ 182186/21111330. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> (((a (a a)) a)((^y.y) b)) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x) b)) 5. ==[ beta ]==> (((a (a a)) a) b) REDUCED to normal form. ------ 182187/21111357. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((b (^y.y)) c)) REDUCED to normal form. ------ 182188/21111528. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 182189/21111726. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a (a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)(a (a (a (^z.z))))) 6. ==[ alpha ]==> ((^x.x)(a (a (a (^y.y))))) 7. ==[ beta ]==> (a (a (a (^y.y)))) 8. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 182190/21111735. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 182191/21111753. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a a)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a a)) 7. ==[ beta ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182192/21111807. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 182193/21112050. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a a))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 182194/21112104. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (a ((a (^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> (a ((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 182195/21112167. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.(^y.y)) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a) a) a)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 182196/21112221. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(a a))(^x1.a))) REDUCED to normal form. ------ 182197/21112248. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.(x x)))(b (^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.(y y)))) REDUCED to normal form. ------ 182198/21112275. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 182199/21112302. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182200/21112329. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 182201/21112365. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 182202/21112392. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 182203/21112446. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (a a)) a)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 182204/21112473. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x))(((^z.z) b)((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)((^z.z) b))) 9. ==[ beta ]==> ((a (^x.x))(b ((^z.z) b))) 10. ==[ alpha ]==> ((a (^x.x))(b ((^y.y) b))) 11. ==[ beta ]==> ((a (^x.x))(b b)) REDUCED to normal form. ------ 182205/21112500. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 182206/21112527. ------ 1. ==[ start ]==> ((a (a b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 182207/21112914. ------ 1. ==[ start ]==> ((a (^b.(a a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(c ((a a)(a a)))) REDUCED to normal form. ------ 182208/21113130. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))((a a) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182209/21113157. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a b))) 5. ==[ beta ]==> (((^y.y)(a a))(a b)) 6. ==[ alpha ]==> (((^x.x)(a a))(a b)) 7. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 182210/21113211. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)((a a)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)((a a)(^y.y)))) 7. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 8. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 182211/21113292. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> (b (((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (b (a ((^y.y) b))) 6. ==[ alpha ]==> (b (a ((^x.x) b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 182212/21113346. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a a)(b (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)(b (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)((a a)(b (^y.y)))) 6. ==[ alpha ]==> ((a a)((a a)(b (^x.x)))) REDUCED to normal form. ------ 182213/21113382. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 182214/21113436. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(b (^x1.a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 182215/21113463. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(y y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z)))(^x1.(x1 x1)))) 7. ==[ beta ]==> (((a (^y.(^z.z)))(^x1.(x1 x1)))((a (^y.(^z.z)))(^x1.(x1 x1)))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) REDUCED to normal form. ------ 182216/21113490. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 182217/21113517. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 182218/21113544. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.b))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 182219/21113580. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 182220/21113607. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 182221/21113634. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 182222/21113661. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (a a))(^x.x))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 182223/21113688. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.a)((^z.z) b))) 5. ==[ beta ]==> ((a (a a))((^y.a)((^z.z) b))) 6. ==[ alpha ]==> ((a (a a))((^x.a)((^y.y) b))) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 182224/21113715. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((((a a) a) a)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 182225/21113733. ------ 1. ==[ start ]==> (((^a.b) c)((a a)(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((a a)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 182226/21113742. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(b (^z.z))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 182227/21114129. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(a (b (^y.y)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(a (b (^y.y)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(a (b (^x.x)))) REDUCED to normal form. ------ 182228/21114165. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182229/21114192. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) c) REDUCED to normal form. ------ 182230/21114210. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 182231/21114471. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(b (^y.(a a)))) 3. ==[ beta ]==> (((a b) a)(b (^y.(a a)))) 4. ==[ alpha ]==> (((a b) a)(b (^x.(a a)))) REDUCED to normal form. ------ 182232/21114552. ------ 1. ==[ start ]==> ((a (b a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> ((a (b a))(a (^y.y))) 4. ==[ alpha ]==> ((a (b a))(a (^x.x))) REDUCED to normal form. ------ 182233/21114786. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 182234/21114894. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) b) b)) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) b) b)) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b) b)) 5. ==[ beta ]==> ((a (^x.(a a)))(b b)) REDUCED to normal form. ------ 182235/21114921. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 182236/21115146. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 182237/21115173. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 182238/21115200. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(^y.(a a)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.(a a))) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.(a a))) REDUCED to normal form. ------ 182239/21115398. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(a b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182240/21115479. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z) a)(b a))) 5. ==[ beta ]==> ((a a)(((^z.z) a)(b a))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(b a))) 7. ==[ beta ]==> ((a a)(a (b a))) REDUCED to normal form. ------ 182241/21115677. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 182242/21115704. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a b)(^x1.a))) REDUCED to normal form. ------ 182243/21115785. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 182244/21115866. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 182245/21115893. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z) b) a)) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z) b) a)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) b) a)) 5. ==[ beta ]==> (((a a)(^x.(x x)))(b a)) REDUCED to normal form. ------ 182246/21115920. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 182247/21116010. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 182248/21116037. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(b a)) b) REDUCED to normal form. ------ 182249/21116091. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 182250/21116118. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((a b)(^y.y)) 10. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 182251/21116172. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 182252/21116199. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 182253/21116316. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(a (a a))) 6. ==[ alpha ]==> (((^x.x)(a a))(a (a a))) 7. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 182254/21116343. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a b)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 182255/21116478. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.z))(b a))) 3. ==[ beta ]==> (b ((a (^z.z))(b a))) 4. ==[ alpha ]==> (b ((a (^x.x))(b a))) REDUCED to normal form. ------ 182256/21116595. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 182257/21116622. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((b a)(((^y.y)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b a)(((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> ((b a)((a a)(^y.(y y)))) 6. ==[ alpha ]==> ((b a)((a a)(^x.(x x)))) REDUCED to normal form. ------ 182258/21116649. ------ 1. ==[ start ]==> (((a a)(^b.b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 182259/21116757. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182260/21116811. ------ 1. ==[ start ]==> (((a b)(^c.a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 182261/21116838. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 182262/21116865. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((b a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((b a) b)) REDUCED to normal form. ------ 182263/21116982. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a) b)((^y.a)(^z.a))) 4. ==[ alpha ]==> (((a a) b)((^x.a)(^y.a))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 182264/21117009. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 182265/21117036. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((a (b a))((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> ((a (b a))((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> ((a (b a))((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 182266/21117063. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) a) REDUCED to normal form. ------ 182267/21117117. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 182268/21117342. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)(a a))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 182269/21117621. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((b b)(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> ((b b)(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> ((b b)(a (^y.(a a)))) 6. ==[ alpha ]==> ((b b)(a (^x.(a a)))) REDUCED to normal form. ------ 182270/21117702. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((b a) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a) a)) REDUCED to normal form. ------ 182271/21117729. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1)) b)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a)(^y1.y1)) b)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1)) b)) REDUCED to normal form. ------ 182272/21117936. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(b ((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182273/21118197. ------ 1. ==[ start ]==> (((a b)(a b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(b (^x.(^y.y)))) REDUCED to normal form. ------ 182274/21118305. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 182275/21118332. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 182276/21118359. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 182277/21118386. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((a (b (^x.x)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 182278/21118728. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y)) a)) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 182279/21118773. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.y))((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(a (^y.y)))) REDUCED to normal form. ------ 182280/21118800. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y) a))) 5. ==[ beta ]==> (((a a) a)((^y.y) a)) 6. ==[ alpha ]==> (((a a) a)((^x.x) a)) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 182281/21118854. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (a a))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (a a))(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (a a))(^y1.y1))) REDUCED to normal form. ------ 182282/21118935. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (b ((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 182283/21118971. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> (((a a)(^x.b))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 182284/21119052. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.(y1 y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(x1 x1))) REDUCED to normal form. ------ 182285/21119079. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 182286/21119169. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 182287/21119196. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 182288/21119223. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 182289/21119277. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 182290/21119304. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 182291/21119331. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)(^z.a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.a))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 182292/21119358. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 182293/21119385. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(a a))) REDUCED to normal form. ------ 182294/21119718. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d e)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d e)) 3. ==[ beta ]==> (b (d e)) REDUCED to normal form. ------ 182295/21119961. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(b ((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(b ((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(b ((a a) a))) 5. ==[ beta ]==> ((^y.y)(b ((a a) a))) 6. ==[ alpha ]==> ((^x.x)(b ((a a) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 182296/21119988. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(a (a b))) 3. ==[ beta ]==> ((^y.y)(a (a b))) 4. ==[ alpha ]==> ((^x.x)(a (a b))) 5. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 182297/21120042. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(a (^x1.x1)))) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(a (^z.z)))) 9. ==[ beta ]==> ((b b)((^y.y)(a (^z.z)))) 10. ==[ alpha ]==> ((b b)((^x.x)(a (^y.y)))) 11. ==[ beta ]==> ((b b)(a (^y.y))) 12. ==[ alpha ]==> ((b b)(a (^x.x))) REDUCED to normal form. ------ 182298/21120051. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 182299/21120123. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((a (^x.x))(^z.z))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 182300/21120186. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((a a) a)(^z.z))) REDUCED to normal form. ------ 182301/21120240. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))(^y1.a))) REDUCED to normal form. ------ 182302/21120267. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.(x x)))(a (^z.(z z)))) 6. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.(y y)))) REDUCED to normal form. ------ 182303/21120294. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 182304/21120348. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((a a) a) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a) a)) 5. ==[ beta ]==> ((^y.y)(((a a) a) a)) 6. ==[ alpha ]==> ((^x.x)(((a a) a) a)) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 182305/21120384. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 182306/21120411. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 182307/21120438. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)(^y.(y y)))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 182308/21120465. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 182309/21120600. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (^y.(y y)))) REDUCED to normal form. ------ 182310/21120681. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 182311/21120708. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 182312/21120762. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 182313/21120780. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 182314/21120789. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 6. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 182315/21121185. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (a a)) a)) 3. ==[ beta ]==> (((^y.y) b)((a (a a)) a)) 4. ==[ alpha ]==> (((^x.x) b)((a (a a)) a)) 5. ==[ beta ]==> (b ((a (a a)) a)) REDUCED to normal form. ------ 182316/21121212. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a) a) b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y) a) b)) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a b)) REDUCED to normal form. ------ 182317/21121257. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b ((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(b ((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(b ((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 182318/21121311. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y) a)(a a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y) a)(a a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x) a)(a a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 182319/21121347. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 7. ==[ beta ]==> ((^y.(^z.z)) c) 8. ==[ alpha ]==> ((^x.(^y.y)) c) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182320/21121455. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a)(^z.a))) REDUCED to normal form. ------ 182321/21121536. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a) c)) REDUCED to normal form. ------ 182322/21121563. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.a) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 182323/21121644. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 182324/21121662. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 182325/21121680. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (^y.y))) REDUCED to normal form. ------ 182326/21121707. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 182327/21121734. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 182328/21121761. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b (^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(b (^x.x))) REDUCED to normal form. ------ 182329/21121788. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)(a (^y.(^z.z)))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 182330/21121815. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)(a a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 182331/21121842. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.x)(^y.y))) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 182332/21121869. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a (^z.z))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a (^z.z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 182333/21133377. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 182334/21133401. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (^y.((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> (^x.((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> (^x.((a a)(^z.z))) 6. ==[ alpha ]==> (^x.((a a)(^y.y))) REDUCED to normal form. ------ 182335/21133473. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(a a))(^z.(z z)))) 3. ==[ eta ]==> ((^y.y)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 182336/21133644. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.b)(b a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 182337/21133968. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182338/21134241. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 7. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 8. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 182339/21134250. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 182340/21134655. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (b (^y.((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> (b (^x.((^y.(^z.z)) a))) 7. ==[ beta ]==> (b (^x.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 182341/21134859. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 182342/21135426. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (^y.(((^z.a)(^x1.(a a)))((^z.a)(^x1.(a a))))) 4. ==[ alpha ]==> (^x.(((^y.a)(^z.(a a)))((^x1.a)(^y1.(a a))))) 5. ==[ beta ]==> (^x.(a ((^x1.a)(^y1.(a a))))) 6. ==[ alpha ]==> (^x.(a ((^y.a)(^z.(a a))))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 182343/21135870. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 182344/21136257. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 182345/21136308. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((((a a)(a a)) b)(((a a)(a a)) b))(^y.y)) 4. ==[ alpha ]==> (((((a a)(a a)) b)(((a a)(a a)) b))(^x.x)) REDUCED to normal form. ------ 182346/21137064. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ eta ]==> (b (((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (b (b (^y.(^z.z)))) 6. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 182347/21137373. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(^x1.((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(^x1.((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.((a a)(a a)))) 5. ==[ beta ]==> (^y.((a a)(a a))) 6. ==[ alpha ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 182348/21137613. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 182349/21138075. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 182350/21138504. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182351/21138819. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 182352/21140208. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^b.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(x1 a))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 a))) 4. ==[ alpha ]==> ((^x.x)(^y.(y a))) 5. ==[ beta ]==> (^y.(y a)) 6. ==[ alpha ]==> (^x.(x a)) REDUCED to normal form. ------ 182353/21140487. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(b x1))) 3. ==[ eta ]==> ((((^x.x) b)(^y.(^z.z))) b) 4. ==[ beta ]==> ((b (^y.(^z.z))) b) 5. ==[ alpha ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 182354/21140898. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (a a))(^z.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182355/21140991. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(^y1.((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(^x2.((a a)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x2.((a a)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182356/21141216. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((b c)(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> ((b c)(^x.((^y.y)(a a)))) 5. ==[ beta ]==> ((b c)(^x.(a a))) REDUCED to normal form. ------ 182357/21141243. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 182358/21141459. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 182359/21141684. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 182360/21142503. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 5. ==[ beta ]==> (^y.(^z.y)) 6. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 182361/21142674. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((a a) a))) REDUCED to normal form. ------ 182362/21143301. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^z.(^x1.x1)))(((a a)(^z.(^x1.x1)))(^y.y))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 182363/21143313. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^z.((^x1.x1)(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.x1)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182364/21143907. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.(z z)))) 3. ==[ beta ]==> (b (^y.(^z.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 182365/21144078. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.((^z.z) y))) 3. ==[ eta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 182366/21144150. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.z))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 182367/21144174. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 182368/21144249. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.b)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.b)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.b)) REDUCED to normal form. ------ 182369/21144303. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.x1)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.x1)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.z)) 5. ==[ beta ]==> (((^y.y) b)(^z.z)) 6. ==[ alpha ]==> (((^x.x) b)(^y.y)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182370/21144357. ------ 1. ==[ start ]==> (((a b)(b a))(^c.a)) 2. ==[ alpha ]==> (((a b)(b a))(^x.a)) REDUCED to normal form. ------ 182371/21144384. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 182372/21144432. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (a (((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (a (((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> (a ((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> (a ((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 182373/21144459. ------ 1. ==[ start ]==> (((a a) a)((a b)(b a))) REDUCED to normal form. ------ 182374/21144486. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 182375/21144513. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> (b ((^y.y)((^z.z) b))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y) b))) 7. ==[ beta ]==> (b ((^y.y) b)) 8. ==[ alpha ]==> (b ((^x.x) b)) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 182376/21144540. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 182377/21144567. ------ 1. ==[ start ]==> (((a a) b)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> (((a a) b)(a (b (^y.y)))) 4. ==[ alpha ]==> (((a a) b)(a (b (^x.x)))) REDUCED to normal form. ------ 182378/21144594. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x)) a)((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))(^z.z))) REDUCED to normal form. ------ 182379/21144612. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 182380/21144621. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(a (a (^z.z))))) REDUCED to normal form. ------ 182381/21144639. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 182382/21144666. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a (^x.a))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 182383/21144684. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 182384/21144711. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 182385/21144738. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 182386/21144747. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.a)((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 182387/21144774. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182388/21144909. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.b)(b a))) 3. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 182389/21144927. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 182390/21144954. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 182391/21145017. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.a)(b (^z.z)))((^y.a)(b (^z.z)))) 6. ==[ alpha ]==> (((^x.a)(b (^y.y)))((^z.a)(b (^x1.x1)))) 7. ==[ beta ]==> (a ((^z.a)(b (^x1.x1)))) 8. ==[ alpha ]==> (a ((^x.a)(b (^y.y)))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182392/21145044. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182393/21145098. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 9. ==[ beta ]==> ((^z.z)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182394/21145206. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 182395/21145233. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 182396/21145368. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182397/21145395. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182398/21145458. ------ 1. ==[ start ]==> (((a (a a)) b)(c (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(c (b (^x.x)))) REDUCED to normal form. ------ 182399/21145485. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y) a)(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.x) a)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (a (b ((^y.(^z.z)) a))) 6. ==[ alpha ]==> (a (b ((^x.(^y.y)) a))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 182400/21145503. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z (^x1.x1))))) 7. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 9. ==[ beta ]==> (^y.(y (^z.z))) 10. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 182401/21145512. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a (a (^z.z))))) REDUCED to normal form. ------ 182402/21145539. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 182403/21145566. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 182404/21145593. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 182405/21145620. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) b)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (a a)))) 7. ==[ beta ]==> (((^y.y) b)(a (a a))) 8. ==[ alpha ]==> (((^x.x) b)(a (a a))) 9. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 182406/21145881. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> (a (c (^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (c (^x.(^y.y)))) REDUCED to normal form. ------ 182407/21145917. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y) b)((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.x) b)((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((a a)((^y.(^z.z)) a))) 6. ==[ alpha ]==> (b ((a a)((^x.(^y.y)) a))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 182408/21146043. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((a a)((^y.y)(a (a a)))) 8. ==[ alpha ]==> ((a a)((^x.x)(a (a a)))) 9. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 182409/21146124. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((a (^x.b))(^z.z)) 4. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 182410/21146142. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((a a)(^y.(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a a)(^x.(a a)))) REDUCED to normal form. ------ 182411/21146169. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 182412/21146223. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (a a)) a)((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a (a a)) a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 182413/21146250. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a))(^z.z))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 182414/21146313. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 182415/21146475. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 182416/21146583. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a (a a))) b) REDUCED to normal form. ------ 182417/21146664. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.z))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 5. ==[ beta ]==> (b ((^y.y)(^y.y))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182418/21146691. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 182419/21146862. ------ 1. ==[ start ]==> (((^a.b) b)((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) b)((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 182420/21147078. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a b) b)(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a b) b)(a ((^y.y) b))) 4. ==[ alpha ]==> (((a b) b)(a ((^x.x) b))) 5. ==[ beta ]==> (((a b) b)(a b)) REDUCED to normal form. ------ 182421/21147105. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a a) a)((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (((a a) a)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 182422/21147132. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 182423/21147357. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a b)(^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((a b)(^x.(a a)))) REDUCED to normal form. ------ 182424/21147384. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 182425/21147438. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 182426/21147465. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((a (a a))(((^y.y) a)(^z.z))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) a)(^y.y))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 182427/21147546. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((b (^y.y)) a)) 3. ==[ beta ]==> (((a a)(a a))((b (^y.y)) a)) 4. ==[ alpha ]==> (((a a)(a a))((b (^x.x)) a)) REDUCED to normal form. ------ 182428/21147573. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(a a)) b)) REDUCED to normal form. ------ 182429/21147609. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 182430/21147744. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 182431/21147825. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 182432/21147852. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 182433/21147861. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(c ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(c b)) REDUCED to normal form. ------ 182434/21147888. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(b ((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.b))(b ((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))(b ((a a)(a a)))) REDUCED to normal form. ------ 182435/21147942. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182436/21147969. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(b (a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b (a (^y.y)))) REDUCED to normal form. ------ 182437/21147996. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.a))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 182438/21148023. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((b a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(a (a a)))) REDUCED to normal form. ------ 182439/21148050. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 182440/21148302. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 182441/21148329. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (b a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((a (b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 182442/21148419. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182443/21148500. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 182444/21148608. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 182445/21148635. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.x1)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((a a)(a a))) 6. ==[ alpha ]==> ((^x.x)((a a)(a a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 182446/21148689. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 182447/21148770. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182448/21148878. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 182449/21149031. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.z) b)) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.z) b)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y) b)) 5. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 182450/21149058. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.(^z.z))) c)) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 182451/21149157. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a b)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182452/21149337. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (^x1.(a a)))) 3. ==[ beta ]==> (b (a (^x1.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 182453/21149472. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 182454/21149499. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.b)((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z.b)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((a a) a))) 5. ==[ beta ]==> ((^y.b)((a a) a)) 6. ==[ alpha ]==> ((^x.b)((a a) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 182455/21149553. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((^x1.x1)(a a)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((^z.z)(a a)))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 182456/21149634. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182457/21149769. ------ 1. ==[ start ]==> ((a (^b.b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 182458/21150003. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y) a)) 5. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 182459/21150048. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((b a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182460/21150084. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z)) d)) 3. ==[ beta ]==> ((a b)((^y.(^z.z)) d)) 4. ==[ alpha ]==> ((a b)((^x.(^y.y)) d)) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 182461/21150255. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(c (^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c (^z.a))) 3. ==[ beta ]==> (b (c (^z.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 182462/21150417. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> (b ((^y.(a a))(a (a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))(a (a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 182463/21150444. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.b)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 182464/21150498. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 182465/21150579. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182466/21150921. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> (((a b)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 182467/21151254. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182468/21151362. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182469/21151443. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 182470/21151470. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.x1)(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(b a))) 5. ==[ beta ]==> ((^y.y)(b a)) 6. ==[ alpha ]==> ((^x.x)(b a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 182471/21151524. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 182472/21151605. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 182473/21151722. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(b ((a a)(^x1.x1)))) REDUCED to normal form. ------ 182474/21151749. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (b a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (b a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (b a))) REDUCED to normal form. ------ 182475/21151776. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 182476/21151812. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(a a)) c)) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 182477/21152028. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 182478/21152082. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a b)(^z.a))) REDUCED to normal form. ------ 182479/21152109. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 182480/21152136. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))(a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 182481/21152163. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (a a))(^y.a))) REDUCED to normal form. ------ 182482/21152253. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.y1)((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.y1)((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.x2)((a a)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.x2)((a a)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((a a)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182483/21152334. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (b ((^z.b)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.b)(^y.a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 182484/21152442. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.a)(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182485/21152478. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(b ((^y.y)(a a)))) 3. ==[ beta ]==> ((b c)(b ((^y.y)(a a)))) 4. ==[ alpha ]==> ((b c)(b ((^x.x)(a a)))) 5. ==[ beta ]==> ((b c)(b (a a))) REDUCED to normal form. ------ 182486/21152505. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 182487/21152613. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 182488/21152640. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a (a a))(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (a a))(^x1.x1))) REDUCED to normal form. ------ 182489/21152712. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(b (^z.(a a)))) 3. ==[ beta ]==> (b (b (^z.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 182490/21152721. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a a)(a a))) REDUCED to normal form. ------ 182491/21152946. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 182492/21152973. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a a) a)) REDUCED to normal form. ------ 182493/21153000. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a b) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a b) b)) 3. ==[ beta ]==> ((a ((^y.y) b))((a b) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))((a b) b)) 5. ==[ beta ]==> ((a b)((a b) b)) REDUCED to normal form. ------ 182494/21153216. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.b) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 182495/21153243. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a) c)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a) c)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a) c)) 5. ==[ beta ]==> ((b a)((^y.a) c)) 6. ==[ alpha ]==> ((b a)((^x.a) c)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 182496/21153414. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)(a a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(a a))) 5. ==[ beta ]==> ((^y.y)((^z.b)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 7. ==[ beta ]==> ((^y.b)(a a)) 8. ==[ alpha ]==> ((^x.b)(a a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 182497/21153495. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (a a)))) 5. ==[ beta ]==> (b ((a (a a))(a (a a)))) REDUCED to normal form. ------ 182498/21153603. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b)(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b)(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182499/21153765. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.b))) 5. ==[ beta ]==> ((^y.y)(^z.b)) 6. ==[ alpha ]==> ((^x.x)(^y.b)) 7. ==[ beta ]==> (^y.b) 8. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 182500/21153828. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.y))) REDUCED to normal form. ------ 182501/21153855. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a (a a))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (a a))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (a a))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (a a))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))((^x1.x1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182502/21153900. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 182503/21153909. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 182504/21153936. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)((a a) a))) REDUCED to normal form. ------ 182505/21154008. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))(a (^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(a (^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182506/21154161. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 182507/21154188. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (a a)) c)) REDUCED to normal form. ------ 182508/21154296. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^c.a) a)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a) a)) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 182509/21154323. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 182510/21154458. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((b (a (a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> ((b (a (a a)))(^y.y)) 8. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 182511/21154485. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 182512/21154539. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(^z.(z z)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 182513/21154566. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 182514/21154575. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((^z.z)((^x1.x1)(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182515/21154980. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 7. ==[ beta ]==> ((^y.(y y))(^z.z)) 8. ==[ alpha ]==> ((^x.(x x))(^y.y)) 9. ==[ beta ]==> ((^y.y)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182516/21155007. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 182517/21155034. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182518/21155124. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a (^y.y))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 182519/21155151. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 182520/21155169. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(a (^y.(y y)))) 3. ==[ beta ]==> (b (a (^y.(y y)))) 4. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 182521/21155232. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b c)) REDUCED to normal form. ------ 182522/21155277. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182523/21155313. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 182524/21155340. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 182525/21155394. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182526/21155412. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.a))) REDUCED to normal form. ------ 182527/21155439. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 182528/21155457. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 182529/21155484. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1)) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z)) a)) REDUCED to normal form. ------ 182530/21155511. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a) b)) 3. ==[ beta ]==> ((a (b (^y.y)))((a a) b)) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a) b)) REDUCED to normal form. ------ 182531/21155538. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(^y.y)) a)) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 182532/21155565. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z) b)) 5. ==[ beta ]==> (((^y.y) b)((^z.z) b)) 6. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 7. ==[ beta ]==> (b ((^y.y) b)) 8. ==[ alpha ]==> (b ((^x.x) b)) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 182533/21155592. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 182534/21155619. ------ 1. ==[ start ]==> (((a b)(b a))((a a) a)) REDUCED to normal form. ------ 182535/21155646. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z) a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y) a)) 5. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 182536/21155672. ------ 1. ==[ start ]==> (^a.(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (^x.(((x x)(^y.y))((^z.z)(x x)))) 3. ==[ beta ]==> (^x.(((x x)(^y.y))(x x))) REDUCED to normal form. ------ 182537/21155673. ------ 1. ==[ start ]==> (a (((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (a (((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (a (((a a)(^x.x))(a a))) REDUCED to normal form. ------ 182538/21166938. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a))) a) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a))) a) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 182539/21166944. ------ 1. ==[ start ]==> ((^a.a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 182540/21166971. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((((^y.y)(a a))((a a)(^z.z)))(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((a a)(^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y)(a a))((a a)(^z.z)))) 7. ==[ beta ]==> (((a a)((a a)(^x.x)))((a a)((a a)(^z.z)))) 8. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 182541/21166998. ------ 1. ==[ start ]==> ((^a.b)((a b)(b a))) 2. ==[ alpha ]==> ((^x.b)((a b)(b a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 182542/21167079. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 182543/21167181. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 182544/21167196. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (^y.((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (^x.((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 182545/21167613. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((a b)(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((a b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 182546/21168045. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 182547/21168321. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a) a)(b a))) 3. ==[ beta ]==> (((((a a) a)(b a))(((a a) a)(b a)))(((a a) a)(b a))) REDUCED to normal form. ------ 182548/21168477. ------ 1. ==[ start ]==> ((((a a) a) a)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 182549/21168654. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 182550/21169296. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> ((((^x.x) a)((^y.y)(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((a ((^y.y)(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(^x1.x1))) 7. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 182551/21169428. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((b a)((^z.z)(^x1.x1)))((b a)((^z.z)(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((b a)((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1))))) 5. ==[ beta ]==> (((b a)((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((b a)((^x.x)(^y.y)))((b a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((b a)(^y.y))((b a)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((b a)(^x.x))((b a)((^y.y)(^z.z)))) 9. ==[ beta ]==> (((b a)(^x.x))((b a)(^z.z))) 10. ==[ alpha ]==> (((b a)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 182552/21171537. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(^y.((y y)(y y)))) 5. ==[ beta ]==> (((a a) a)(^y.((y y)(y y)))) 6. ==[ alpha ]==> (((a a) a)(^x.((x x)(x x)))) REDUCED to normal form. ------ 182553/21171696. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a b)((a a) a))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 182554/21172203. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x)(a a))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.z)) 5. ==[ beta ]==> (((a a)(^y.(y y)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 182555/21172536. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.((^z.z) b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^y.b)) REDUCED to normal form. ------ 182556/21172614. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 182557/21173148. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 182558/21173454. ------ 1. ==[ start ]==> (((a b)((a a) a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 182559/21173613. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((((^y.y)(^z.z))((a a) a))(((^y.y)(^z.z))((a a) a)))((((^y.y)(^z.z))((a a) a))(((^y.y)(^z.z))((a a) a)))) 4. ==[ alpha ]==> (((((^x.x)(^y.y))((a a) a))(((^z.z)(^x1.x1))((a a) a)))((((^y1.y1)(^z1.z1))((a a) a))(((^x2.x2)(^y2.y2))((a a) a)))) 5. ==[ beta ]==> ((((^y.y)((a a) a))(((^z.z)(^x1.x1))((a a) a)))((((^y1.y1)(^z1.z1))((a a) a))(((^x2.x2)(^y2.y2))((a a) a)))) 6. ==[ alpha ]==> ((((^x.x)((a a) a))(((^y.y)(^z.z))((a a) a)))((((^x1.x1)(^y1.y1))((a a) a))(((^z1.z1)(^x2.x2))((a a) a)))) 7. ==[ beta ]==> ((((a a) a)(((^y.y)(^z.z))((a a) a)))((((^x1.x1)(^y1.y1))((a a) a))(((^z1.z1)(^x2.x2))((a a) a)))) 8. ==[ alpha ]==> ((((a a) a)(((^x.x)(^y.y))((a a) a)))((((^z.z)(^x1.x1))((a a) a))(((^y1.y1)(^z1.z1))((a a) a)))) 9. ==[ beta ]==> ((((a a) a)((^y.y)((a a) a)))((((^z.z)(^x1.x1))((a a) a))(((^y1.y1)(^z1.z1))((a a) a)))) 10. ==[ alpha ]==> ((((a a) a)((^x.x)((a a) a)))((((^y.y)(^z.z))((a a) a))(((^x1.x1)(^y1.y1))((a a) a)))) 11. ==[ beta ]==> ((((a a) a)((a a) a))((((^y.y)(^z.z))((a a) a))(((^x1.x1)(^y1.y1))((a a) a)))) 12. ==[ alpha ]==> ((((a a) a)((a a) a))((((^x.x)(^y.y))((a a) a))(((^z.z)(^x1.x1))((a a) a)))) 13. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)((a a) a))(((^z.z)(^x1.x1))((a a) a)))) 14. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)((a a) a))(((^y.y)(^z.z))((a a) a)))) 15. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)(((^y.y)(^z.z))((a a) a)))) 16. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a) a)(((^x.x)(^y.y))((a a) a)))) 17. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)((^y.y)((a a) a)))) 18. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a) a)((^x.x)((a a) a)))) 19. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 182560/21174003. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(^y1.a))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 5. ==[ beta ]==> (^y.(^z.a)) 6. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 182561/21174012. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z a))) REDUCED to normal form. ------ 182562/21175038. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 182563/21175281. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 182564/21175854. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182565/21176496. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.b))) REDUCED to normal form. ------ 182566/21176658. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(^x1.((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((a a) a))) 5. ==[ beta ]==> ((^y.y)(^z.((a a) a))) 6. ==[ alpha ]==> ((^x.x)(^y.((a a) a))) 7. ==[ beta ]==> (^y.((a a) a)) 8. ==[ alpha ]==> (^x.((a a) a)) REDUCED to normal form. ------ 182567/21176673. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((a a) a) a)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((a a) a) a)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 182568/21176829. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((x x) x))) REDUCED to normal form. ------ 182569/21177495. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(a (a a)))) 5. ==[ beta ]==> (b (^y.(a (a a)))) 6. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 182570/21177873. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.a))) REDUCED to normal form. ------ 182571/21177945. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.c)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.c)) 3. ==[ beta ]==> (((a a)(^y.y))(^z.c)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.c)) REDUCED to normal form. ------ 182572/21177954. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.z))) REDUCED to normal form. ------ 182573/21177969. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 182574/21178071. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 182575/21178098. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(a a))) 5. ==[ beta ]==> (((^y.y) b)(^z.(a a))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(a a))) 7. ==[ beta ]==> (b (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 182576/21178152. ------ 1. ==[ start ]==> (((a b)(b a))(^a.b)) 2. ==[ alpha ]==> (((a b)(b a))(^x.b)) REDUCED to normal form. ------ 182577/21178179. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(z z))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(z z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(y y))) REDUCED to normal form. ------ 182578/21178206. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.z)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 182579/21178218. ------ 1. ==[ start ]==> ((a a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a a)(((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 182580/21178245. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> ((a (a a))((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((a (a a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 182581/21178272. ------ 1. ==[ start ]==> ((a b)((a b)(b a))) REDUCED to normal form. ------ 182582/21178326. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y) b))) 5. ==[ beta ]==> (((a a)(a a))((^y.y) b)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) b)) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 182583/21178353. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 182584/21178425. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 182585/21178452. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 182586/21178470. ------ 1. ==[ start ]==> ((a (^b.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.a))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 182587/21178551. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.a)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.a)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 182588/21178578. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 182589/21178587. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 182590/21178614. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 182591/21178632. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((b a)(^z.b))) 3. ==[ beta ]==> (((^y.y) a)((b a)(^z.b))) 4. ==[ alpha ]==> (((^x.x) a)((b a)(^y.b))) 5. ==[ beta ]==> (a ((b a)(^y.b))) 6. ==[ alpha ]==> (a ((b a)(^x.b))) REDUCED to normal form. ------ 182592/21178659. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 182593/21178695. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 182594/21178803. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 182595/21178884. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a b)((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a b)((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> ((a b)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a b)(a (a (^x.x)))) REDUCED to normal form. ------ 182596/21178902. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a (^z.z))) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a (^z.z))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a (^z.z))) a)) 5. ==[ beta ]==> ((^y.y)((a (a (^z.z))) a)) 6. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 7. ==[ beta ]==> ((a (a (^y.y))) a) 8. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 182597/21178911. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a (a a)) a)((^z.z)(^y.y))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a)) a)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 182598/21178929. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((a (a a))(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 182599/21178956. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((b (^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 5. ==[ beta ]==> ((b (^y.y)) c) 6. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 182600/21179019. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 182601/21179127. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 182602/21179316. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 182603/21179334. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((^y.(y (^z.z))) a) 6. ==[ alpha ]==> ((^x.(x (^y.y))) a) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 182604/21179460. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 182605/21179487. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((b a)((a a) a))) REDUCED to normal form. ------ 182606/21179514. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(^y.y))(a b))) 5. ==[ beta ]==> ((a a)(((a a)(^y.y))(a b))) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 182607/21179541. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))(a (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 182608/21179568. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)((a b)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a a)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 182609/21179595. ------ 1. ==[ start ]==> ((a ((a a) a))(((a a) a)(b a))) REDUCED to normal form. ------ 182610/21179748. ------ 1. ==[ start ]==> ((((a a) a) a)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 182611/21179766. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a a) a)(((^y.(^z.z)) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a)(^z.z))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 182612/21179793. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((b (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 182613/21179847. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) b)(^z.(z z)))) 7. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(z z)))) 8. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(y y)))) 9. ==[ beta ]==> ((a a)(b (^y.(y y)))) 10. ==[ alpha ]==> ((a a)(b (^x.(x x)))) REDUCED to normal form. ------ 182614/21179856. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a (a a))) REDUCED to normal form. ------ 182615/21179883. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((^y2.y2)(^z2.z2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182616/21179928. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 182617/21180099. ------ 1. ==[ start ]==> (((^a.b) a)((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (b ((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 182618/21180198. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z)) b)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b (^z.z)) b)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z)) b)) IRREDUCIBLE: cycle. ------ 182619/21180261. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.(y y))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(x x))) REDUCED to normal form. ------ 182620/21180288. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 182621/21180369. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 182622/21180396. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x))) b) REDUCED to normal form. ------ 182623/21180423. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.a)((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.a)((^y.a)(^z.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 182624/21180450. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 182625/21180477. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.x))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 182626/21180513. ------ 1. ==[ start ]==> (((a a)(a b))(c ((a a)(a a)))) REDUCED to normal form. ------ 182627/21180540. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(b (b (^y.y)))) REDUCED to normal form. ------ 182628/21180567. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))(a ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((a (^x.x))(a ((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 182629/21180594. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((b (^x.x))(a a))) REDUCED to normal form. ------ 182630/21180621. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(((a a)(a a))(a (^z.z)))) 6. ==[ alpha ]==> (((^x.x) a)(((a a)(a a))(a (^y.y)))) 7. ==[ beta ]==> (a (((a a)(a a))(a (^y.y)))) 8. ==[ alpha ]==> (a (((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 182631/21180648. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b ((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b ((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b a)) REDUCED to normal form. ------ 182632/21180675. ------ 1. ==[ start ]==> (((a b)(a a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a a))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 182633/21180702. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a a))((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a (a a))((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a (a a))((b a)(^y.y))) 6. ==[ alpha ]==> ((a (a a))((b a)(^x.x))) REDUCED to normal form. ------ 182634/21181008. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(a a))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(^z.z)))) 11. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 12. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 182635/21181017. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 182636/21181044. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)((^z.z) a))) 7. ==[ beta ]==> (((^y.y)((^z.z) a))((^y.y)((^z.z) a))) 8. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)((^x1.x1) a))) 9. ==[ beta ]==> (((^y.y) a)((^z.z)((^x1.x1) a))) 10. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.z) a))) 11. ==[ beta ]==> (a ((^y.y)((^z.z) a))) 12. ==[ alpha ]==> (a ((^x.x)((^y.y) a))) 13. ==[ beta ]==> (a ((^y.y) a)) 14. ==[ alpha ]==> (a ((^x.x) a)) 15. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182637/21181071. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 182638/21181089. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 182639/21181314. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (b ((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182640/21181413. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1) b) c)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) c)) 5. ==[ beta ]==> (((^y.y) b) c) 6. ==[ alpha ]==> (((^x.x) b) c) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 182641/21181557. ------ 1. ==[ start ]==> (((a b) c)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.b)(^y.(a a)))) 3. ==[ beta ]==> (((a b) c) b) REDUCED to normal form. ------ 182642/21181584. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 182643/21181665. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 182644/21181692. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 182645/21181791. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.b) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.z) c)) 3. ==[ beta ]==> (b ((^z.z) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 182646/21181890. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((a a)((a a) a))) REDUCED to normal form. ------ 182647/21181917. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a b)(a b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a b)(a b))) REDUCED to normal form. ------ 182648/21181944. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a b))(((a a) a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a (a b))(((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> ((a (a b))(((a a) a)(a a))) REDUCED to normal form. ------ 182649/21181971. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x)(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a) a))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))((a a) a))((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> (((a (a a))((a a) a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a (a a))((a a) a))((a a)(^x.x))) REDUCED to normal form. ------ 182650/21181998. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (a a))(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (a a))(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(b a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(b a))) 7. ==[ beta ]==> ((^y.y)((a (a a))(b a))) 8. ==[ alpha ]==> ((^x.x)((a (a a))(b a))) 9. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 182651/21182025. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((^x.x) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 182652/21182052. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a b) a)((a (^y.y))((^z.z) b))) 4. ==[ alpha ]==> (((a b) a)((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> (((a b) a)((a (^x.x)) b)) REDUCED to normal form. ------ 182653/21182079. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 182654/21182223. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (((a a)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 182655/21182304. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 182656/21182367. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(y y))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((b a)(b a))) REDUCED to normal form. ------ 182657/21182412. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))(^z.z))) 3. ==[ beta ]==> ((b a)((a (^y.y))(^z.z))) 4. ==[ alpha ]==> ((b a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 182658/21182475. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 182659/21182493. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) b) b)) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) b) b)) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) b) b)) 5. ==[ beta ]==> (((a b)(a b))(b b)) REDUCED to normal form. ------ 182660/21182502. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 182661/21182583. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 182662/21182610. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 182663/21182637. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b)(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 182664/21182781. ------ 1. ==[ start ]==> (((a (a a))(a b))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a b))(b ((^x.x) b))) 3. ==[ beta ]==> (((a (a a))(a b))(b b)) REDUCED to normal form. ------ 182665/21182808. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(a ((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(a ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(a ((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 182666/21182835. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z) b)(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) b)(a a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(b (a a))) REDUCED to normal form. ------ 182667/21182862. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 182668/21182889. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((b a)((^y.y) a))) 5. ==[ beta ]==> (((a a) a)((b a)((^y.y) a))) 6. ==[ alpha ]==> (((a a) a)((b a)((^x.x) a))) 7. ==[ beta ]==> (((a a) a)((b a) a)) REDUCED to normal form. ------ 182669/21182916. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 182670/21182970. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)((a a) a))) REDUCED to normal form. ------ 182671/21183249. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((a a)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182672/21183276. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 182673/21183285. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 182674/21183303. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a b)(^z.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.a))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 182675/21183357. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.(a a)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.(a a)))) 9. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(a a)))) 10. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(a a)))) 11. ==[ beta ]==> (((a a)(a a))(^y.(a a))) 12. ==[ alpha ]==> (((a a)(a a))(^x.(a a))) REDUCED to normal form. ------ 182676/21183366. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 182677/21183393. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((^z.(z z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(y y))((a a)(^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 182678/21183438. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 182679/21183447. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 182680/21183474. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 182681/21183501. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 182682/21183546. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((b a) c)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182683/21183753. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(c (b a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(c (b a))) 3. ==[ beta ]==> (((a b)(^y.y))(c (b a))) 4. ==[ alpha ]==> (((a b)(^x.x))(c (b a))) REDUCED to normal form. ------ 182684/21183780. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(b (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(a (a a)))(b (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a)(a (a a)))(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 182685/21183807. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(a ((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a ((^z.z) b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(a ((^y.y) b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a b)) REDUCED to normal form. ------ 182686/21183861. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((b a)(a (^z.z)))) REDUCED to normal form. ------ 182687/21183888. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> ((a b)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 182688/21183897. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) d)) 5. ==[ beta ]==> ((^y.(^z.z)) d) 6. ==[ alpha ]==> ((^x.(^y.y)) d) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182689/21184167. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((b a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182690/21184203. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 182691/21184221. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (b (((^y.y)(a a))(^z.(z z)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(y y)))) 7. ==[ beta ]==> (b ((a a)(^y.(y y)))) 8. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 182692/21184230. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 182693/21184248. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 182694/21184257. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 182695/21184302. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.x1)(^y1.b))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)(^x1.b))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.b)) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.b)) REDUCED to normal form. ------ 182696/21184338. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(x1 x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(z z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(y y))((^z.z)(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182697/21184365. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 182698/21184392. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 182699/21184419. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 182700/21184446. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 182701/21184527. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 182702/21184698. ------ 1. ==[ start ]==> ((((a a) a)(a b))(b (b a))) REDUCED to normal form. ------ 182703/21184725. ------ 1. ==[ start ]==> (((a b)((a a) a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 182704/21184752. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((b a)(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((b a)(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b a)(a a))) 5. ==[ beta ]==> (((a a)(^y.y))((b a)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((b a)(a a))) REDUCED to normal form. ------ 182705/21184779. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 182706/21184833. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b)(a (a a)))) REDUCED to normal form. ------ 182707/21184860. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b (a a))(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b (a a))(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b (a a))(((a a) a)(^y.y))) 6. ==[ alpha ]==> ((b (a a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 182708/21184887. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(^y.y))((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)((a a) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)((a a) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a a) a)) REDUCED to normal form. ------ 182709/21185058. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 182710/21185166. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1)(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182711/21185202. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(y y))(a b))) 3. ==[ beta ]==> ((b b)((^y.(y y))(a b))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(a b))) 5. ==[ beta ]==> ((b b)((a b)(a b))) REDUCED to normal form. ------ 182712/21185229. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 182713/21185283. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(b a)) REDUCED to normal form. ------ 182714/21185328. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a)(^y.y)) b)) 3. ==[ beta ]==> (((b a)(b a))(((a a)(^y.y)) b)) 4. ==[ alpha ]==> (((b a)(b a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 182715/21185391. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 182716/21185418. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 182717/21185472. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.b)(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b)(^y1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 182718/21185526. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 182719/21185616. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x)(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a a)(a (^y.y)))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))((a a)(a (^x.x)))) REDUCED to normal form. ------ 182720/21185643. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a b)((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a b)((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x)) b)((a b) a)) REDUCED to normal form. ------ 182721/21185670. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 182722/21185697. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(b a))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(b a))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(b a))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 8. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 182723/21185724. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a (a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (a a))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((a (a a))((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((a a) a))) REDUCED to normal form. ------ 182724/21185751. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y) a)(a b))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y) a)(a b))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) a)(a b))) 5. ==[ beta ]==> ((((a a) a)(a a))(a (a b))) REDUCED to normal form. ------ 182725/21185778. ------ 1. ==[ start ]==> (((a b)(a b))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((a (^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a b))((a (^x.x))(a a))) REDUCED to normal form. ------ 182726/21185805. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)((a a) a))((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 182727/21186138. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a b) c)) 3. ==[ beta ]==> (b ((a b) c)) REDUCED to normal form. ------ 182728/21186282. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 182729/21186309. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.y))) REDUCED to normal form. ------ 182730/21186354. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(a a)) b)) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a)) b)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a)) b)) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 182731/21186381. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.b) c)) 3. ==[ beta ]==> ((^y.y)((^z.b) c)) 4. ==[ alpha ]==> ((^x.x)((^y.b) c)) 5. ==[ beta ]==> ((^y.b) c) 6. ==[ alpha ]==> ((^x.b) c) 7. ==[ beta ]==> b REDUCED to normal form. ------ 182732/21186525. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(b (^y.(a a)))) REDUCED to normal form. ------ 182733/21186552. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 182734/21186624. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182735/21186660. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 182736/21186687. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 10. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 182737/21186939. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(c ((a a) a))) 3. ==[ beta ]==> (((a a)(a b))(c ((a a) a))) REDUCED to normal form. ------ 182738/21186966. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(b (a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(b (a b))) REDUCED to normal form. ------ 182739/21187020. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a b)(a a))) REDUCED to normal form. ------ 182740/21187047. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((a a) a)(a (^y.y)))) 5. ==[ beta ]==> ((b a)(((a a) a)(a (^y.y)))) 6. ==[ alpha ]==> ((b a)(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 182741/21187074. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z) a)) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y) a)) 7. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 182742/21187128. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 182743/21187218. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a b)(^z.z))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a b)(^z.z))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.z))) 5. ==[ beta ]==> ((^y.y)((a b)(^z.z))) 6. ==[ alpha ]==> ((^x.x)((a b)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 182744/21187299. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 182745/21187407. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a b) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182746/21187524. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182747/21187623. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^c.a) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a) b)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a) b)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a) b)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a) b)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a) b)) 7. ==[ beta ]==> ((b b)((^y.a) b)) 8. ==[ alpha ]==> ((b b)((^x.a) b)) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 182748/21187713. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 182749/21187740. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b (^z.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.a))) REDUCED to normal form. ------ 182750/21187767. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(a (^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.b))) REDUCED to normal form. ------ 182751/21187812. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1)(^x2.x2))(^y2.(^z2.z2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(^y2.(^z2.z2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182752/21187821. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 182753/21187848. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(((^z.z) a)((^z.z) a))) 6. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> ((b (^x.(x x)))(a ((^z.z) a))) 8. ==[ alpha ]==> ((b (^x.(x x)))(a ((^y.y) a))) 9. ==[ beta ]==> ((b (^x.(x x)))(a a)) REDUCED to normal form. ------ 182754/21187875. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 182755/21187929. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.x1)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((a a) a))) 5. ==[ beta ]==> ((^y.y)((^z.z)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((a a) a))) 7. ==[ beta ]==> ((^y.y)((a a) a)) 8. ==[ alpha ]==> ((^x.x)((a a) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 182756/21187947. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((a a) a) a)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((a a) a) a)) REDUCED to normal form. ------ 182757/21188046. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c (a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c (a (a a)))) 3. ==[ beta ]==> (((a (a a)) b)(c (a (a a)))) REDUCED to normal form. ------ 182758/21188073. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b ((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 182759/21188100. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a ((a a) a))) REDUCED to normal form. ------ 182760/21188127. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 182761/21188154. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))((a (a a))(a (^y.y)))) 6. ==[ alpha ]==> (((a a)(a a))((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 182762/21188181. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(a a)) REDUCED to normal form. ------ 182763/21188235. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.x1))) REDUCED to normal form. ------ 182764/21188361. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 182765/21188379. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^z.(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 182766/21188766. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.z)(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(a (a a)))) 5. ==[ beta ]==> (b ((^y.y)(a (a a)))) 6. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 182767/21188784. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (a a)) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a)) a)) 5. ==[ beta ]==> ((^y.y)((a (a a)) a)) 6. ==[ alpha ]==> ((^x.x)((a (a a)) a)) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 182768/21188793. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 6. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 182769/21188811. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a) b)) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a) b)) 5. ==[ beta ]==> ((a (a (^x.x)))(a b)) REDUCED to normal form. ------ 182770/21188820. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 182771/21188892. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(y y)) a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(y y)) a)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(x x)) a)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 182772/21188928. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(c (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(c (^y.(^z.z)))) 7. ==[ beta ]==> (c (^y.(^z.z))) 8. ==[ alpha ]==> (c (^x.(^y.y))) REDUCED to normal form. ------ 182773/21188955. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b (^x1.a))) REDUCED to normal form. ------ 182774/21189036. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 182775/21189081. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(((^x1.x1) a) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182776/21189117. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 182777/21189144. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.a)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 182778/21189198. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182779/21189225. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.a))) REDUCED to normal form. ------ 182780/21189243. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 182781/21189261. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b b)) REDUCED to normal form. ------ 182782/21189315. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b (a a))) 3. ==[ beta ]==> ((a (b (^y.y)))(b (a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(b (a a))) REDUCED to normal form. ------ 182783/21189342. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 182784/21189369. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(a a))) 5. ==[ beta ]==> (((^y.y) b)((a a)(a a))) 6. ==[ alpha ]==> (((^x.x) b)((a a)(a a))) 7. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 182785/21189396. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b a)) REDUCED to normal form. ------ 182786/21189423. ------ 1. ==[ start ]==> (((a b)(b a))(a b)) REDUCED to normal form. ------ 182787/21189450. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a (a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a (a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 182788/21189477. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 182789/21200751. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a))) b) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a))) b) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) b) REDUCED to normal form. ------ 182790/21200775. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182791/21200856. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182792/21201360. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((^y.(y y))((a a)(a a)))(((^y.(y y))((a a)(a a)))((^y.(y y))((a a)(a a))))) 4. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.(y y))((a a)(a a)))((^z.(z z))((a a)(a a))))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.(y y))((a a)(a a)))((^z.(z z))((a a)(a a))))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.(x x))((a a)(a a)))((^y.(y y))((a a)(a a))))) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((((a a)(a a))((a a)(a a)))((^y.(y y))((a a)(a a))))) 8. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((((a a)(a a))((a a)(a a)))((^x.(x x))((a a)(a a))))) 9. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((((a a)(a a))((a a)(a a)))(((a a)(a a))((a a)(a a))))) REDUCED to normal form. ------ 182793/21201435. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a b)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 182794/21201885. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 5. ==[ beta ]==> (^y.(y (y (^z.z)))) 6. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 182795/21202656. ------ 1. ==[ start ]==> ((^a.(a b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.a)((a a)(a a))) b) 4. ==[ alpha ]==> (((^x.a)((a a)(a a))) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 182796/21203505. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 182797/21203901. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(^y.(y (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 182798/21204681. ------ 1. ==[ start ]==> ((^a.(b a))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(a a))(a a))) 3. ==[ eta ]==> (b ((^y.(a a))(a a))) 4. ==[ alpha ]==> (b ((^x.(a a))(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 182799/21205359. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(^y.(^z.(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(a a)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 182800/21205692. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> (b (^x1.((^y1.y1) b))) 4. ==[ alpha ]==> (b (^x.((^y.y) b))) 5. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 182801/21206358. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 182802/21206970. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 182803/21207276. ------ 1. ==[ start ]==> (((a b)((a a) a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 182804/21207834. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^c.(^d.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.a))) REDUCED to normal form. ------ 182805/21208515. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182806/21209328. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^y.(a a))) REDUCED to normal form. ------ 182807/21210651. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 182808/21210813. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.y))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.y))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.x))) REDUCED to normal form. ------ 182809/21210918. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^z.(^x1.x1))(a (a a)))(((^z.(^x1.x1))(a (a a)))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.(^x1.x1))(a (a a)))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(a (a a)))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(a (a a)))(^x1.x1))) 7. ==[ beta ]==> (((^y.(^z.z))(a (a a)))(^x1.x1)) 8. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182810/21211317. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z)))) 5. ==[ beta ]==> (b (^y.(^z.(z z)))) 6. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 182811/21211443. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(y (y y)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(y (y y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(x (x x)))) REDUCED to normal form. ------ 182812/21211524. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.((^z.z) a))) 3. ==[ beta ]==> (b (^y.((^z.z) a))) 4. ==[ alpha ]==> (b (^x.((^y.y) a))) 5. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 182813/21211776. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.c)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.c)) REDUCED to normal form. ------ 182814/21211791. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(c a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(c a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 182815/21211839. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 182816/21211893. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 182817/21211947. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 182818/21211974. ------ 1. ==[ start ]==> (((a b)(b a))(^b.(a a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(a a))) REDUCED to normal form. ------ 182819/21212001. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 182820/21212028. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 182821/21212058. ------ 1. ==[ start ]==> ((a (^a.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 182822/21212085. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 182823/21212112. ------ 1. ==[ start ]==> (((^a.a)(a a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.x)(a a))((a b)(b a))) 3. ==[ beta ]==> ((a a)((a b)(b a))) REDUCED to normal form. ------ 182824/21212139. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 182825/21212193. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182826/21212220. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 182827/21212247. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 182828/21212274. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 182829/21212319. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 182830/21212337. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182831/21212418. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.(^z.z)))) REDUCED to normal form. ------ 182832/21212472. ------ 1. ==[ start ]==> (((a a)(^b.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.a))((b a)(^y.b))) REDUCED to normal form. ------ 182833/21212499. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) REDUCED to normal form. ------ 182834/21212562. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.b)(b a))) 3. ==[ beta ]==> (((a a) a)((^y.b)(b a))) 4. ==[ alpha ]==> (((a a) a)((^x.b)(b a))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 182835/21212616. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 182836/21212643. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 182837/21212715. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((a b)((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a b)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 182838/21212742. ------ 1. ==[ start ]==> (((a (a a)) a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a)) a)((a (a (^x.x))) a)) REDUCED to normal form. ------ 182839/21212769. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 182840/21212796. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((b (^z.z)) c)) REDUCED to normal form. ------ 182841/21212967. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 182842/21213138. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.y)(b ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((^x.x)(b ((^y.(^z.z)) a))) 7. ==[ beta ]==> (b ((^y.(^z.z)) a)) 8. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 182843/21213165. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)(a (a (a (^y.y))))) 5. ==[ beta ]==> (a (a (a (^y.y)))) 6. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 182844/21213174. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a (^z.z))) REDUCED to normal form. ------ 182845/21213219. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 182846/21213462. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 182847/21213516. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> (a (((^z.z) a)((a a)(a a)))) 6. ==[ alpha ]==> (a (((^x.x) a)((a a)(a a)))) 7. ==[ beta ]==> (a (a ((a a)(a a)))) REDUCED to normal form. ------ 182848/21213633. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 182849/21213660. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 182850/21213687. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(b (^y.(y y)))) REDUCED to normal form. ------ 182851/21213714. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182852/21213741. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((b a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 182853/21213804. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 182854/21213831. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a (a a))) b) REDUCED to normal form. ------ 182855/21213885. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 182856/21213912. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)(a a))(b ((^y.y) b))) 6. ==[ alpha ]==> ((((a a) a)(a a))(b ((^x.x) b))) 7. ==[ beta ]==> ((((a a) a)(a a))(b b)) REDUCED to normal form. ------ 182857/21213930. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (b (a (^y.(a a)))) 6. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 182858/21213939. ------ 1. ==[ start ]==> ((a (a b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 182859/21214344. ------ 1. ==[ start ]==> (((a a)(a b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 182860/21214542. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(a a))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(a a))((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182861/21214569. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((a a) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 182862/21214623. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.y)((a b)((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(a a)))) 7. ==[ beta ]==> ((a b)((^y.y)(a a))) 8. ==[ alpha ]==> ((a b)((^x.x)(a a))) 9. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 182863/21214704. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 182864/21214758. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a a)((a (^y.y))((a a)(a a)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 182865/21214785. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((^y.y)((a a)(b (^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 182866/21214848. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 182867/21214875. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b)(^x1.a))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) b)(^x1.a))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)(^z.a))) 7. ==[ beta ]==> ((((^y.y) b)(^z.a))(((^y.y) b)(^z.a))) 8. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z) b)(^x1.a))) 9. ==[ beta ]==> ((b (^y.a))(((^z.z) b)(^x1.a))) 10. ==[ alpha ]==> ((b (^x.a))(((^y.y) b)(^z.a))) 11. ==[ beta ]==> ((b (^x.a))(b (^z.a))) 12. ==[ alpha ]==> ((b (^x.a))(b (^y.a))) REDUCED to normal form. ------ 182868/21214902. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 182869/21214929. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 182870/21214992. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(a b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(a b))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 182871/21215019. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b)) b) REDUCED to normal form. ------ 182872/21215073. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))(b a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 182873/21215100. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))((^y.(y y))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (a a))((^x.(x x))(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 8. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 182874/21215127. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a) a)((^y.a)((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.a)((^y.y) b))) 5. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 182875/21215145. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 182876/21215154. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 182877/21215181. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 182878/21215541. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(b ((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(b ((a a)(a a)))) REDUCED to normal form. ------ 182879/21215622. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (b (((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (b (b (a (^y.y)))) 6. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 182880/21215631. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.b) c)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y) c)) 3. ==[ beta ]==> (((a b)(^x.a)) c) REDUCED to normal form. ------ 182881/21215883. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(c (^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(c (^y.y))) 3. ==[ beta ]==> (((a b) a)(c (^y.y))) 4. ==[ alpha ]==> (((a b) a)(c (^x.x))) REDUCED to normal form. ------ 182882/21215910. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(b (^z.(a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(b (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 182883/21215964. ------ 1. ==[ start ]==> ((a (b a))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((a (b a))((^x.(a a))(a a))) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 182884/21216306. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a)(a a)) a)) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a)(a a)) a)) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(a a)) a)) REDUCED to normal form. ------ 182885/21216333. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) b) b)) 3. ==[ beta ]==> (((a (a a))(^x.b))(b b)) REDUCED to normal form. ------ 182886/21216531. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 182887/21216585. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (a a))((^y.a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (a a))((^x.a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 182888/21216612. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 182889/21216810. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a b)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a b)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)((a a) a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182890/21216891. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a a)((a (a a))((a a)(^z.z)))) 6. ==[ alpha ]==> ((a a)((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 182891/21216972. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)((^x1.x1) b))) 3. ==[ beta ]==> (b ((a a)((^x1.x1) b))) 4. ==[ alpha ]==> (b ((a a)((^x.x) b))) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 182892/21217089. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 182893/21217116. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 182894/21217197. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.(a a))) 6. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 182895/21217224. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.b)((a (a a))(^y.(^z.z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 182896/21217278. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 182897/21217305. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a a)(^z.z))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 182898/21217332. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z) b) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(b a)) REDUCED to normal form. ------ 182899/21217386. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((b a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((b a) c)) REDUCED to normal form. ------ 182900/21217449. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(a a)) REDUCED to normal form. ------ 182901/21217476. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 182902/21217530. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 182903/21217611. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 182904/21217638. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 182905/21217683. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182906/21217728. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 182907/21217755. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(a (a a))) 6. ==[ alpha ]==> (((^x.x)(a a))(a (a a))) 7. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 182908/21217890. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> (b (a ((a a)(^y.y)))) 6. ==[ alpha ]==> (b (a ((a a)(^x.x)))) REDUCED to normal form. ------ 182909/21218007. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 182910/21218034. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> ((b a)(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> ((b a)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 182911/21218061. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 182912/21218088. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 182913/21218169. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> ((^y.(a a))((a (a a))(^z.(a a)))) 6. ==[ alpha ]==> ((^x.(a a))((a (a a))(^y.(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 182914/21218196. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 182915/21218223. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (^a.a))(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 182916/21218250. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 182917/21218277. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 182918/21218394. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 182919/21218448. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 182920/21218475. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 182921/21218502. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.a)(^y.(^z.z)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 182922/21218556. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 182923/21218754. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a a))(a b))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a b))) 5. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 182924/21219033. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (a a))(^y.b))) 3. ==[ beta ]==> ((b b)((a (a a))(^y.b))) 4. ==[ alpha ]==> ((b b)((a (a a))(^x.b))) REDUCED to normal form. ------ 182925/21219060. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a (^y.(a a)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.(a a)))) REDUCED to normal form. ------ 182926/21219141. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((b a) a)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((b a) a)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a) a)) REDUCED to normal form. ------ 182927/21219609. ------ 1. ==[ start ]==> (((a b)(a b))(c (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(c (^x.(a a)))) REDUCED to normal form. ------ 182928/21219636. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(b (^y.(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 182929/21219717. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 182930/21219744. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b)((^z.z) a))) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 182931/21219798. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 182932/21220185. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((b (^x.x))((a a)(a a))) REDUCED to normal form. ------ 182933/21220212. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((^y.y)((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a b)(a (^y.y)))) 5. ==[ beta ]==> ((a b)(a (^y.y))) 6. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 182934/21220248. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a) d)) 3. ==[ beta ]==> ((a (^y.y))((^z.a) d)) 4. ==[ alpha ]==> ((a (^x.x))((^y.a) d)) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 182935/21220266. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(a (a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(a (a a)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (a a))) REDUCED to normal form. ------ 182936/21220347. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (^z.z))(a b))) 3. ==[ beta ]==> (b ((a (^z.z))(a b))) 4. ==[ alpha ]==> (b ((a (^x.x))(a b))) REDUCED to normal form. ------ 182937/21220464. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((a a) a)(^x1.a))) REDUCED to normal form. ------ 182938/21220491. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.a))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((b (^x.a))(^z.(z z))) 8. ==[ alpha ]==> ((b (^x.a))(^y.(y y))) REDUCED to normal form. ------ 182939/21220518. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 182940/21220581. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 182941/21220608. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(a a))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 182942/21220635. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((a b)((^y.(a a))(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.(a a))(^y.y))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 182943/21220662. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 182944/21220689. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.a))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.a))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 182945/21220716. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 182946/21220743. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a b)(a a))(^y.y)) 8. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 182947/21220770. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(a b))((^y.a)(^z.a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.a))) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 182948/21220797. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 182949/21221400. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(b ((a a) a))) 3. ==[ beta ]==> ((^y.y)(b ((a a) a))) 4. ==[ alpha ]==> ((^x.x)(b ((a a) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 182950/21221454. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((a a) a)(a a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((a a) a)(a a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((a a) a)(a a))) 5. ==[ beta ]==> ((b ((^y.y) b))(((a a) a)(a a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((a a) a)(a a))) 7. ==[ beta ]==> ((b b)(((a a) a)(a a))) REDUCED to normal form. ------ 182951/21221463. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^c.a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a) b)) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 182952/21221490. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2)) c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) c)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1)) c)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1)) c)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182953/21221535. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (b (((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)(a (a a)))) 5. ==[ beta ]==> (b (a (a (a a)))) REDUCED to normal form. ------ 182954/21221652. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(^x2.x2))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 182955/21221679. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (a a))(^z.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (a a))(^y.a))) REDUCED to normal form. ------ 182956/21221706. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.(y y)))) REDUCED to normal form. ------ 182957/21221823. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 182958/21221850. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))(^z.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(^y.a))) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.a)(^y.a))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)(^y.a))) 7. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 182959/21221877. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 182960/21221904. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 182961/21221931. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.a)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.a)) REDUCED to normal form. ------ 182962/21222066. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 182963/21222093. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a (^y.a))) 3. ==[ beta ]==> ((b (a (a a)))(a (^y.a))) 4. ==[ alpha ]==> ((b (a (a a)))(a (^x.a))) REDUCED to normal form. ------ 182964/21222120. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 182965/21222174. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((a a)((^y.a)((^z.z) a))) 6. ==[ alpha ]==> ((a a)((^x.a)((^y.y) a))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 182966/21222192. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 182967/21222201. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 182968/21222597. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y) b)((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(^y.(y y)))) 5. ==[ beta ]==> (b ((a a)(^y.(y y)))) 6. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 182969/21222624. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (a a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (a a)) a)) REDUCED to normal form. ------ 182970/21222651. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a) b)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a b)) REDUCED to normal form. ------ 182971/21222723. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a (a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (a (a a)))) REDUCED to normal form. ------ 182972/21222759. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) b)) 5. ==[ beta ]==> ((^y.y)((^z.a) b)) 6. ==[ alpha ]==> ((^x.x)((^y.a) b)) 7. ==[ beta ]==> ((^y.a) b) 8. ==[ alpha ]==> ((^x.a) b) 9. ==[ beta ]==> a REDUCED to normal form. ------ 182973/21222804. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a a)((^y.y) a))) 3. ==[ beta ]==> (b ((a a)((^y.y) a))) 4. ==[ alpha ]==> (b ((a a)((^x.x) a))) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 182974/21222867. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 182975/21222948. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1)) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1)) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 182976/21223029. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 182977/21223047. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(a (^y.y)))) REDUCED to normal form. ------ 182978/21223074. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(c a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(c a)) REDUCED to normal form. ------ 182979/21223092. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 182980/21223119. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 182981/21223146. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 182982/21223173. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 182983/21223200. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b (^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b (^z.z))) 5. ==[ beta ]==> (((^y.y) b)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) b)(b (^y.y))) 7. ==[ beta ]==> (b (b (^y.y))) 8. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 182984/21223227. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 182985/21223254. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a)(a a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.x)(a a))) 3. ==[ beta ]==> (((a b)(b a))(a a)) REDUCED to normal form. ------ 182986/21223281. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 182987/21223308. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a (^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 182988/21223581. ------ 1. ==[ start ]==> ((^a.(^b.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 182989/21233058. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.((a a) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 182990/21234354. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 182991/21234867. ------ 1. ==[ start ]==> ((^a.(^b.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 182992/21234870. ------ 1. ==[ start ]==> ((a (^b.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 182993/21234939. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b (^z.z))(^x1.a))) 3. ==[ eta ]==> ((^y.y)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 182994/21235110. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 182995/21235302. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (a (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(a (a (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 7. ==[ beta ]==> (^y.(a (a (^z.z)))) 8. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 182996/21235434. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 182997/21235734. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 182998/21235743. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 182999/21236166. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 183000/21236505. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((((^y.y) a)(^z.(a a))) b) 4. ==[ alpha ]==> ((((^x.x) a)(^y.(a a))) b) 5. ==[ beta ]==> ((a (^y.(a a))) b) 6. ==[ alpha ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 183001/21236892. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (^y.(((^z.(z z))(^x1.x1))((^z.(z z))(^x1.x1)))) 4. ==[ alpha ]==> (^x.(((^y.(y y))(^z.z))((^x1.(x1 x1))(^y1.y1)))) 5. ==[ beta ]==> (^x.(((^z.z)(^z.z))((^x1.(x1 x1))(^y1.y1)))) 6. ==[ alpha ]==> (^x.(((^y.y)(^z.z))((^x1.(x1 x1))(^y1.y1)))) 7. ==[ beta ]==> (^x.((^z.z)((^x1.(x1 x1))(^y1.y1)))) 8. ==[ alpha ]==> (^x.((^y.y)((^z.(z z))(^x1.x1)))) 9. ==[ beta ]==> (^x.((^z.(z z))(^x1.x1))) 10. ==[ alpha ]==> (^x.((^y.(y y))(^z.z))) 11. ==[ beta ]==> (^x.((^z.z)(^z.z))) 12. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 13. ==[ beta ]==> (^x.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183002/21237363. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 183003/21237774. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((b (^z.z)) a)) 3. ==[ beta ]==> ((((b (^z.z)) a)((b (^z.z)) a))(^y.y)) 4. ==[ alpha ]==> ((((b (^x.x)) a)((b (^y.y)) a))(^z.z)) REDUCED to normal form. ------ 183004/21238146. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(b (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(b (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183005/21238530. ------ 1. ==[ start ]==> ((^a.(b a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(b x))(((a a)(a a))(^y.y))) 3. ==[ eta ]==> (b (((a a)(a a))(^y.y))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.x))) REDUCED to normal form. ------ 183006/21241980. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(^a.(b a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.(b y))) 3. ==[ eta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 183007/21242364. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183008/21242952. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(^y.(a a))) REDUCED to normal form. ------ 183009/21243618. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(z z)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(y y)))) 7. ==[ beta ]==> (^y.(^z.(y y))) 8. ==[ alpha ]==> (^x.(^y.(x x))) REDUCED to normal form. ------ 183010/21243807. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(a z1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1))) a) 4. ==[ beta ]==> ((^y.(^z.z)) a) 5. ==[ alpha ]==> ((^x.(^y.y)) a) 6. ==[ beta ]==> (^y.y) 7. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183011/21244167. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.((a a) a))) REDUCED to normal form. ------ 183012/21244344. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.x1)((a a) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 183013/21244347. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.((a a) a))) REDUCED to normal form. ------ 183014/21244767. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^z.z))(^x1.(x1 x1)))(((a (^z.z))(^x1.(x1 x1)))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a (^z.z))(^x1.(x1 x1)))(^y1.y1))) REDUCED to normal form. ------ 183015/21245184. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(a (a a)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (a a)))) 7. ==[ beta ]==> (^y.(a (a a))) 8. ==[ alpha ]==> (^x.(a (a a))) REDUCED to normal form. ------ 183016/21245292. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 183017/21245481. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183018/21245640. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (^y1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 183019/21245643. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.x1))) REDUCED to normal form. ------ 183020/21245796. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 183021/21245823. ------ 1. ==[ start ]==> (((a b)(b a))(^c.(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 183022/21245877. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.a)) REDUCED to normal form. ------ 183023/21245925. ------ 1. ==[ start ]==> (((^a.a) a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (a (((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> (a (((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (a (((a a)(^x.x))(a a))) REDUCED to normal form. ------ 183024/21245952. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a a) a)((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a) a)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 183025/21245979. ------ 1. ==[ start ]==> (((a a)(^a.a))((a b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a b)(b a))) REDUCED to normal form. ------ 183026/21246006. ------ 1. ==[ start ]==> (((^a.a) b)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (b (((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> (b (((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 183027/21246033. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 183028/21246060. ------ 1. ==[ start ]==> (((a a) b)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 183029/21246087. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) a)(a (b (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a (b (^y.y)))) REDUCED to normal form. ------ 183030/21246114. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 183031/21246132. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 183032/21246141. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(a (a (^z.z))))) REDUCED to normal form. ------ 183033/21246159. ------ 1. ==[ start ]==> ((a (^b.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 183034/21246177. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 183035/21246204. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 183036/21246231. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((a a)((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((a a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 183037/21246321. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))((a a) a))) 6. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))((a a) a))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 183038/21246402. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 183039/21246447. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 183040/21246474. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 183041/21246510. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> (((^y.(y y))((a a)(a a)))((^y.(y y))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(y y))((a a)(a a)))) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(y y))((a a)(a a)))) 8. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(x x))((a a)(a a)))) 9. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 183042/21246537. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 183043/21246591. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a (a (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)((^z.z)(a (a (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 7. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 8. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 183044/21246618. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (a a))((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a a))((^z.z)(^y.y))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 183045/21246726. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 183046/21247005. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 183047/21247023. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 7. ==[ beta ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 183048/21247032. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a (a (a (^z.z))))) REDUCED to normal form. ------ 183049/21247059. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a (^y.a))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 183050/21247086. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 183051/21247113. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 8. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 183052/21247410. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> (b ((a (^y.y))(b (^z.z)))) 6. ==[ alpha ]==> (b ((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 183053/21247437. ------ 1. ==[ start ]==> ((((a a) a) a)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) a)((a a)((^x.(^y.y)) a))) 3. ==[ beta ]==> ((((a a) a) a)((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a) a) a)((a a)(^x.x))) REDUCED to normal form. ------ 183054/21247455. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(a (^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a) a)(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a a) a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 183055/21247635. ------ 1. ==[ start ]==> (((a a)((a a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)((a a) a))(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 183056/21247662. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.(a a)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.(a a)))) REDUCED to normal form. ------ 183057/21247689. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a (a (a a)))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 183058/21247743. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((a (^x.x))(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 183059/21247770. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a (a a))(^x.x))) REDUCED to normal form. ------ 183060/21247797. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> ((a (a b))(a (^y.(a a)))) 4. ==[ alpha ]==> ((a (a b))(a (^x.(a a)))) REDUCED to normal form. ------ 183061/21247806. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.b)((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.a)((a a)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 183062/21247968. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 183063/21247995. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 183064/21248076. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a a)) REDUCED to normal form. ------ 183065/21248157. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183066/21248184. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.z)(^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 183067/21248355. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (b (((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (b (((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (b (b ((^y.y) a))) 6. ==[ alpha ]==> (b (b ((^x.x) a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 183068/21248571. ------ 1. ==[ start ]==> (((a b) b)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) b)((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 183069/21248598. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a a) a)(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (((a a) a)(a ((^y.y) b))) 6. ==[ alpha ]==> (((a a) a)(a ((^x.x) b))) 7. ==[ beta ]==> (((a a) a)(a b)) REDUCED to normal form. ------ 183070/21248625. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 183071/21248652. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a a)(b (^z.z)))) REDUCED to normal form. ------ 183072/21248778. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 183073/21248850. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (((a a)(a a))((a a)(^y.b))) 6. ==[ alpha ]==> (((a a)(a a))((a a)(^x.b))) REDUCED to normal form. ------ 183074/21248877. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a b)(^y.(a a)))) REDUCED to normal form. ------ 183075/21248958. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (a a))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))((a (a a))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (a a))((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 183076/21248985. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x) a)(^y.y))) 5. ==[ beta ]==> ((((a a) a) a)(a (^y.y))) 6. ==[ alpha ]==> ((((a a) a) a)(a (^x.x))) REDUCED to normal form. ------ 183077/21249012. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 183078/21249066. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((b (^y.y)) a)) REDUCED to normal form. ------ 183079/21249102. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 183080/21249237. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 183081/21249345. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183082/21249381. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(c ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(c ((^z.z) b))) 3. ==[ beta ]==> ((a (^y.b))(c ((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.b))(c ((^y.y) b))) 5. ==[ beta ]==> ((a (^x.b))(c b)) REDUCED to normal form. ------ 183083/21249435. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(a (b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (b (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (b (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183084/21249462. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 183085/21249489. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a))(b (a (^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.a))(b (a (^y.y)))) REDUCED to normal form. ------ 183086/21249516. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 183087/21249543. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((b a)(a (a a)))) REDUCED to normal form. ------ 183088/21249822. ------ 1. ==[ start ]==> ((a (b a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((a (b a))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 183089/21249993. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.b)(a b))) 3. ==[ beta ]==> (b ((^z.b)(a b))) 4. ==[ alpha ]==> (b ((^x.b)(a b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 183090/21250101. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)((^y.a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 183091/21250128. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183092/21250182. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(a b))((^y.(a a))(^z.z))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(a a))(^y.y))) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 183093/21250551. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.b) b)) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x) b)) 3. ==[ beta ]==> (((a b)(a (a a))) b) REDUCED to normal form. ------ 183094/21250650. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183095/21250830. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> (b (b (^x1.x1))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 183096/21250992. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 183097/21251127. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> (b ((^x1.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 183098/21251235. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183099/21251541. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183100/21251550. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 183101/21251748. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(d (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(d (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (d (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (d (^x.(^y.y)))) REDUCED to normal form. ------ 183102/21251856. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.(^y2.y2)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183103/21251910. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183104/21251937. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))(a (a a))) 6. ==[ alpha ]==> ((^x.(a a))(a (a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 183105/21252072. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (b ((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 183106/21252441. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1))) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1))) a)) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 183107/21252855. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183108/21252936. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 183109/21252963. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183110/21253098. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(y y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 183111/21253206. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183112/21253215. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(c ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(c (a a))) REDUCED to normal form. ------ 183113/21253242. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b ((a a)(^z.z)))) REDUCED to normal form. ------ 183114/21253269. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(a (b a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(a (b a))) REDUCED to normal form. ------ 183115/21253332. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(a a)) c)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a)) c)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a)) c)) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 183116/21253575. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 183117/21253602. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b)(^z.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((a b)(^z.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b)(^y.a))) REDUCED to normal form. ------ 183118/21253629. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 183119/21253656. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^x.x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 183120/21253746. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))((^z2.z2)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))((^z2.z2)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183121/21253827. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 183122/21253971. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c (a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c (a b))) 3. ==[ beta ]==> ((b c)(c (a b))) REDUCED to normal form. ------ 183123/21253998. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(b ((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(b (a a))) REDUCED to normal form. ------ 183124/21254106. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))(((a a) a) a)) REDUCED to normal form. ------ 183125/21254133. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(a (a a)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 183126/21254205. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(c (^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(c (^z.b))) 3. ==[ beta ]==> (b (c (^z.b))) 4. ==[ alpha ]==> (b (c (^x.b))) REDUCED to normal form. ------ 183127/21254214. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (^y.y))(a b))) REDUCED to normal form. ------ 183128/21254241. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))((a a)(a a))) REDUCED to normal form. ------ 183129/21254313. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183130/21254439. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 183131/21254466. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 183132/21254493. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(a a)) a)) 5. ==[ beta ]==> ((a b)(((^y.y)(a a)) a)) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a)) a)) 7. ==[ beta ]==> ((a b)((a a) a)) REDUCED to normal form. ------ 183133/21254520. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a b) b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a b) b)) REDUCED to normal form. ------ 183134/21254547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((a a) a) c)) 3. ==[ beta ]==> (((^y.y)(b a))(((a a) a) c)) 4. ==[ alpha ]==> (((^x.x)(b a))(((a a) a) c)) 5. ==[ beta ]==> ((b a)(((a a) a) c)) REDUCED to normal form. ------ 183135/21254709. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(a a)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a a)) REDUCED to normal form. ------ 183136/21254736. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.b) b)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.b) b)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.b) b)) 5. ==[ beta ]==> ((b a)((^y.b) b)) 6. ==[ alpha ]==> ((b a)((^x.b) b)) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 183137/21254907. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(a (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(a a)))) 5. ==[ beta ]==> ((^y.y)(a (^z.(a a)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(a a)))) 7. ==[ beta ]==> (a (^y.(a a))) 8. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 183138/21254988. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183139/21255096. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183140/21255231. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 183141/21255258. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183142/21255321. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a)(a a))) REDUCED to normal form. ------ 183143/21255348. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(a (^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(a (^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183144/21255402. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (a (a a)))) REDUCED to normal form. ------ 183145/21255429. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 183146/21255456. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)((a a) a))) REDUCED to normal form. ------ 183147/21255636. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)((a a) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((a a) a)) REDUCED to normal form. ------ 183148/21255654. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((a a) a) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((a a) a) a)) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a) a)) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a) a)) REDUCED to normal form. ------ 183149/21255681. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y))) b) REDUCED to normal form. ------ 183150/21255816. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^c.a) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a) a)) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 183151/21255843. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z)) b)) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z)) b)) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y)) b)) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 183152/21255870. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(c c)) REDUCED to normal form. ------ 183153/21255978. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 183154/21256032. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(^z.a))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.a))) 7. ==[ beta ]==> ((a a)(a (^y.a))) 8. ==[ alpha ]==> ((a a)(a (^x.a))) REDUCED to normal form. ------ 183155/21256059. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 183156/21256068. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (((^z.(^x1.x1))(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183157/21256473. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a (a a)))) 7. ==[ beta ]==> ((^y.y)(a (a a))) 8. ==[ alpha ]==> ((^x.x)(a (a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 183158/21256500. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 183159/21256527. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 183160/21256581. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(y y))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(x x))) REDUCED to normal form. ------ 183161/21256617. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a a))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a a))) 7. ==[ beta ]==> (((^y.y) a)(a a)) 8. ==[ alpha ]==> (((^x.x) a)(a a)) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 183162/21256644. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 183163/21256662. ------ 1. ==[ start ]==> (((^a.b)(b a))(b (^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(b (^y.a))) 3. ==[ beta ]==> (b (b (^y.a))) 4. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 183164/21256725. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c b)) REDUCED to normal form. ------ 183165/21256770. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183166/21256806. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c (a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (a a))) REDUCED to normal form. ------ 183167/21256833. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b (a (^y.y)))) REDUCED to normal form. ------ 183168/21256887. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183169/21256905. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 183170/21256914. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a)(a (^z.z)))) REDUCED to normal form. ------ 183171/21256932. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.a))) REDUCED to normal form. ------ 183172/21256950. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 183173/21256977. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 183174/21257004. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z)) a)) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z)) a)) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y)) a)) REDUCED to normal form. ------ 183175/21257031. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a) b)) REDUCED to normal form. ------ 183176/21257058. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) a)) 7. ==[ beta ]==> (b ((^y.(^z.z)) a)) 8. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183177/21257085. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z) b)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 183178/21257112. ------ 1. ==[ start ]==> (((a b)(b a))((a a)(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))((a a)(^x.x))) REDUCED to normal form. ------ 183179/21257139. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a) a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 183180/21257166. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 183181/21257192. ------ 1. ==[ start ]==> (^a.((b a)(a b))) 2. ==[ alpha ]==> (^x.((b x)(x b))) REDUCED to normal form. ------ 183182/21257193. ------ 1. ==[ start ]==> (a ((b a)(a b))) REDUCED to normal form. ------ 183183/21268221. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 183184/21268491. ------ 1. ==[ start ]==> ((^a.a)((b a)(a b))) 2. ==[ alpha ]==> ((^x.x)((b a)(a b))) 3. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 183185/21268518. ------ 1. ==[ start ]==> ((^a.(a a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((^z.z)(a a)))(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(((a a)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(((a a)(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 183186/21268545. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 183187/21268626. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((((^z.z)(^x1.x1))((^y1.y1) b))(^y.y)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.x1)) 5. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.z)) 7. ==[ beta ]==> (((^y.y) b)(^z.z)) 8. ==[ alpha ]==> (((^x.x) b)(^y.y)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183188/21269187. ------ 1. ==[ start ]==> (((a (a a)) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 183189/21269619. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 183190/21269868. ------ 1. ==[ start ]==> ((^a.((a a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a b)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a b)((a a)(^y.y)))((a b)((a a)(^y.y))))((a b)((a a)(^y.y)))) 4. ==[ alpha ]==> ((((a b)((a a)(^x.x)))((a b)((a a)(^y.y))))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 183191/21270201. ------ 1. ==[ start ]==> ((^a.(^a.b))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.b))((b a)(^z.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 183192/21270870. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> (((a (a a))(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 183193/21270975. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a (^z.(^x1.x1)))(a (a a)))((a (^z.(^x1.x1)))(a (a a))))) 4. ==[ alpha ]==> ((^x.x)(((a (^y.(^z.z)))(a (a a)))((a (^x1.(^y1.y1)))(a (a a))))) 5. ==[ beta ]==> (((a (^y.(^z.z)))(a (a a)))((a (^x1.(^y1.y1)))(a (a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 183194/21272751. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 183195/21273111. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.((z z)(z z)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(^z.((z z)(z z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.((y y)(y y)))) REDUCED to normal form. ------ 183196/21273243. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^x1.x1)(a a))((^y1.y1)(^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.x1))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 183197/21273777. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 183198/21273846. ------ 1. ==[ start ]==> ((^a.(^b.b))((b a) c)) 2. ==[ alpha ]==> ((^x.(^y.y))((b a) c)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183199/21274161. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a)(a (^z.z)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 183200/21274722. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 183201/21275028. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(z (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 183202/21275160. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((((a a) a)((^y.y)(^z.z)))(((a a) a)((^y.y)(^z.z))))((((a a) a)((^y.y)(^z.z)))(((a a) a)((^y.y)(^z.z))))) 4. ==[ alpha ]==> (((((a a) a)((^x.x)(^y.y)))(((a a) a)((^z.z)(^x1.x1))))((((a a) a)((^y1.y1)(^z1.z1)))(((a a) a)((^x2.x2)(^y2.y2))))) 5. ==[ beta ]==> (((((a a) a)(^y.y))(((a a) a)((^z.z)(^x1.x1))))((((a a) a)((^y1.y1)(^z1.z1)))(((a a) a)((^x2.x2)(^y2.y2))))) 6. ==[ alpha ]==> (((((a a) a)(^x.x))(((a a) a)((^y.y)(^z.z))))((((a a) a)((^x1.x1)(^y1.y1)))(((a a) a)((^z1.z1)(^x2.x2))))) 7. ==[ beta ]==> (((((a a) a)(^x.x))(((a a) a)(^z.z)))((((a a) a)((^x1.x1)(^y1.y1)))(((a a) a)((^z1.z1)(^x2.x2))))) 8. ==[ alpha ]==> (((((a a) a)(^x.x))(((a a) a)(^y.y)))((((a a) a)((^z.z)(^x1.x1)))(((a a) a)((^y1.y1)(^z1.z1))))) 9. ==[ beta ]==> (((((a a) a)(^x.x))(((a a) a)(^y.y)))((((a a) a)(^x1.x1))(((a a) a)((^y1.y1)(^z1.z1))))) 10. ==[ alpha ]==> (((((a a) a)(^x.x))(((a a) a)(^y.y)))((((a a) a)(^z.z))(((a a) a)((^x1.x1)(^y1.y1))))) 11. ==[ beta ]==> (((((a a) a)(^x.x))(((a a) a)(^y.y)))((((a a) a)(^z.z))(((a a) a)(^y1.y1)))) 12. ==[ alpha ]==> (((((a a) a)(^x.x))(((a a) a)(^y.y)))((((a a) a)(^z.z))(((a a) a)(^x1.x1)))) REDUCED to normal form. ------ 183203/21275586. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(y1 a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.(y1 a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(x1 a))) REDUCED to normal form. ------ 183204/21277296. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(z z))) REDUCED to normal form. ------ 183205/21277401. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (a a))(a (a a)))) 3. ==[ eta ]==> ((^y.(^z.z))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183206/21277683. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183207/21278403. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((y y) y))) REDUCED to normal form. ------ 183208/21278538. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))(^x.(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 183209/21279069. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(a (a a)))) REDUCED to normal form. ------ 183210/21279516. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1) c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 183211/21279519. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.c)) REDUCED to normal form. ------ 183212/21279591. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.c)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.c)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.c)) REDUCED to normal form. ------ 183213/21279645. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(z (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(y (^z.z)))) 7. ==[ beta ]==> (b (^y.(y (^z.z)))) 8. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 183214/21279726. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 183215/21279753. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(z z))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(z z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(y y))) REDUCED to normal form. ------ 183216/21279792. ------ 1. ==[ start ]==> ((a a)((b a)(a b))) REDUCED to normal form. ------ 183217/21279819. ------ 1. ==[ start ]==> ((a (a a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 183218/21279846. ------ 1. ==[ start ]==> ((a b)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> ((a b)((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((a b)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 183219/21279900. ------ 1. ==[ start ]==> (((a a)(a a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 183220/21279927. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (a (^x.x)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z) b)) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) b)) 7. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 183221/21280026. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 183222/21280080. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 183223/21280125. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.a)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.a)((b (^y.y))(^z.a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 183224/21280152. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 183225/21280161. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 183226/21280188. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 183227/21280215. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 183228/21280233. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 183229/21280377. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 183230/21280458. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 183231/21280476. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 7. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 8. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 183232/21280485. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> (((a (a a)) a)(a (a (^y.y)))) 4. ==[ alpha ]==> (((a (a a)) a)(a (a (^x.x)))) REDUCED to normal form. ------ 183233/21280503. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a (a (^y.y))) a)) 3. ==[ beta ]==> ((a (a a))((a (a (^y.y))) a)) 4. ==[ alpha ]==> ((a (a a))((a (a (^x.x))) a)) REDUCED to normal form. ------ 183234/21280512. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 183235/21280530. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((^y.(^z.z)) a) b) 6. ==[ alpha ]==> (((^x.(^y.y)) a) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 183236/21280701. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 183237/21280836. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(a a))(^y.(a a)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 183238/21280917. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 183239/21281034. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (a (a a)))) REDUCED to normal form. ------ 183240/21281061. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 183241/21281088. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b a)((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) a))((b a)((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((b a)((a a) a))) 5. ==[ beta ]==> ((a a)((b a)((a a) a))) REDUCED to normal form. ------ 183242/21281115. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 183243/21281142. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a a)(((^y.y)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((a a)((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> ((a a)((a a)((^x.x)(a a)))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 183244/21281169. ------ 1. ==[ start ]==> ((a ((a a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 183245/21281295. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(c (^y.(^z.z)))) 5. ==[ beta ]==> (b (c (^y.(^z.z)))) 6. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 183246/21281367. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a)(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.x1)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183247/21281421. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(a a))(^z.a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a)(a a))(^z.a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))(^y.a))) 7. ==[ beta ]==> ((a a)(((a a)(a a))(^y.a))) 8. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 183248/21281430. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a a)) REDUCED to normal form. ------ 183249/21281457. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183250/21281484. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 183251/21281502. ------ 1. ==[ start ]==> ((a (^a.b))((b a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.b))((b a)(^y.a))) REDUCED to normal form. ------ 183252/21281673. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (b ((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> (b (((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> (b (((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> (b (b ((^y.y) b))) 8. ==[ alpha ]==> (b (b ((^x.x) b))) 9. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 183253/21281691. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.b)(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 183254/21281772. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.(^x1.x1)) a) a)) IRREDUCIBLE: cycle. ------ 183255/21281835. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a))(^y.a))) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 183256/21281862. ------ 1. ==[ start ]==> (((a b) a)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a b) a)(^y.(y y))) 4. ==[ alpha ]==> (((a b) a)(^x.(x x))) REDUCED to normal form. ------ 183257/21281889. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 183258/21281943. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 183259/21281970. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 183260/21281997. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.a)((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 183261/21282051. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 183262/21282141. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(b (b (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(b (b (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(b (b (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(b (b (^y.y)))) REDUCED to normal form. ------ 183263/21282168. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 183264/21282195. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((b (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((b (^z.z))(a a))) 5. ==[ beta ]==> (((^y.y) a)((b (^z.z))(a a))) 6. ==[ alpha ]==> (((^x.x) a)((b (^y.y))(a a))) 7. ==[ beta ]==> (a ((b (^y.y))(a a))) 8. ==[ alpha ]==> (a ((b (^x.x))(a a))) REDUCED to normal form. ------ 183265/21282222. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 183266/21282249. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) b)((^y.y) a))) 3. ==[ beta ]==> (((a b)(a a))(b ((^y.y) a))) 4. ==[ alpha ]==> (((a b)(a a))(b ((^x.x) a))) 5. ==[ beta ]==> (((a b)(a a))(b a)) REDUCED to normal form. ------ 183267/21282276. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 183268/21282510. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.(a a)))) REDUCED to normal form. ------ 183269/21282582. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b (^y1.y1))(^z1.z1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b (^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b (^x1.x1))(^y1.y1))) 7. ==[ beta ]==> (((^y.y)(^z.z))((b (^x1.x1))(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z))(^x1.x1))) 9. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 11. ==[ beta ]==> ((b (^y.y))(^z.z)) 12. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 183270/21282645. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((^z.z) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y) a)) 5. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 183271/21282663. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 183272/21282672. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 183273/21282888. ------ 1. ==[ start ]==> (((^a.b) c)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) c)((^y.a)((^z.z) b))) 3. ==[ beta ]==> (b ((^y.a)((^z.z) b))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 183274/21282987. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((^y.y)(((a a)(a a)) b)) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a)) b)) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 183275/21283131. ------ 1. ==[ start ]==> (((a b) c)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b) c)((^x.(a a))(^y.b))) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 183276/21283158. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 183277/21283239. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.(^y1.(^z1.z1)))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 183278/21283266. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.b))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 183279/21283365. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(a a)) b)) 3. ==[ beta ]==> (b ((^z.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 183280/21283464. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 183281/21283491. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(a a))((a a)((a a) a))) REDUCED to normal form. ------ 183282/21283518. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a b)(a b))) 3. ==[ beta ]==> ((a (a b))((a b)(a b))) REDUCED to normal form. ------ 183283/21283545. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((a a) a)((^x.x)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(((a a) a)(a a))) REDUCED to normal form. ------ 183284/21283572. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((a a)(^x1.x1)))) 9. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.x1))) 10. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z))) 11. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 12. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 13. ==[ beta ]==> ((a a)(^y.y)) 14. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 183285/21283599. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a (a a))(b a))) REDUCED to normal form. ------ 183286/21283626. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) a)(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b) a)(((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a b) a)(a (a (^y.(^z.z))))) 6. ==[ alpha ]==> (((a b) a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 183287/21283653. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 183288/21283680. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 183289/21283797. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((b a)(^z.(z z)))) 5. ==[ beta ]==> (b ((b a)(^z.(z z)))) 6. ==[ alpha ]==> (b ((b a)(^x.(x x)))) REDUCED to normal form. ------ 183290/21283878. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a b)(^z.b))) 3. ==[ beta ]==> (b ((a b)(^z.b))) 4. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 183291/21283941. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 183292/21283986. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b a)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((b a)(a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((b a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 183293/21284013. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z))) 5. ==[ beta ]==> ((a (^y.y))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 183294/21284049. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))((a a)(a a))) REDUCED to normal form. ------ 183295/21284067. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a)(a a)) a)) 3. ==[ beta ]==> (((a b)(a b))(((a a)(a a)) a)) REDUCED to normal form. ------ 183296/21284076. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 183297/21284130. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 183298/21284184. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 183299/21284211. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 183300/21284355. ------ 1. ==[ start ]==> (((a (a a))(a b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a b))(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 183301/21284382. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(b ((^z.z) b))) 3. ==[ beta ]==> (((^y.y)((a a) a))(b ((^z.z) b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(b ((^y.y) b))) 5. ==[ beta ]==> (((a a) a)(b ((^y.y) b))) 6. ==[ alpha ]==> (((a a) a)(b ((^x.x) b))) 7. ==[ beta ]==> (((a a) a)(b b)) REDUCED to normal form. ------ 183302/21284409. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(a ((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(a ((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a ((a a)(a a)))) REDUCED to normal form. ------ 183303/21284436. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x) b)(a a))) 3. ==[ beta ]==> (((a b)(a (a a)))(b (a a))) REDUCED to normal form. ------ 183304/21284463. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 183305/21284490. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((b a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((b a) a)) REDUCED to normal form. ------ 183306/21284544. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 183307/21284823. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((b a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183308/21284850. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 183309/21284877. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 183310/21284931. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((a a) a)(^z.b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a) a)(^z.b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a) a)(^z.b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a) a)(^z.b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a)(^y.b))) 7. ==[ beta ]==> (((a a)(a a))(((a a) a)(^y.b))) 8. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.b))) REDUCED to normal form. ------ 183311/21284940. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 183312/21284967. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 183313/21285021. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(b a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 183314/21285048. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 183315/21285075. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.x1) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) b) REDUCED to normal form. ------ 183316/21285120. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183317/21285129. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 183318/21285147. ------ 1. ==[ start ]==> ((a (^b.b))((b a) c)) 2. ==[ alpha ]==> ((a (^x.x))((b a) c)) REDUCED to normal form. ------ 183319/21285381. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 183320/21285435. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 183321/21285462. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a)(a (^y.y)))) 3. ==[ beta ]==> ((a b)((b a)(a (^y.y)))) 4. ==[ alpha ]==> ((a b)((b a)(a (^x.x)))) REDUCED to normal form. ------ 183322/21285741. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.(^x2.x2)))(^y2.y2))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.(^x2.x2)))(^y2.y2))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183323/21285750. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 183324/21285795. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (b (((a a)(^y.y))(^z.a))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 183325/21285804. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 183326/21285822. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(z z))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(y y))) 7. ==[ beta ]==> ((a a)(^y.(y y))) 8. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 183327/21285831. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 183328/21285912. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(a b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 183329/21285939. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.b))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((((a a) a)(^x.b))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((((a a) a)(^x.b))((a a)(a a))) REDUCED to normal form. ------ 183330/21285957. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 183331/21285966. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 183332/21285993. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 183333/21286020. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 183334/21286065. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((b a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183335/21286101. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 183336/21286272. ------ 1. ==[ start ]==> ((((a a) a)(a b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(c ((a a)(^x.x)))) REDUCED to normal form. ------ 183337/21286299. ------ 1. ==[ start ]==> (((a b)((a a) a))(b (b a))) REDUCED to normal form. ------ 183338/21286326. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(a (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^y.y))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 183339/21286353. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((b a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((b a)(a a))) REDUCED to normal form. ------ 183340/21286407. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a) a)) REDUCED to normal form. ------ 183341/21286434. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a b)(a (a a)))) 3. ==[ beta ]==> ((b (a a))((a b)(a (a a)))) REDUCED to normal form. ------ 183342/21286461. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((a a) a)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((a a) a)(^x.x))) REDUCED to normal form. ------ 183343/21286632. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((b a)(^z.z))) 3. ==[ beta ]==> (b ((b a)(^z.z))) 4. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 183344/21286740. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((a a) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183345/21286776. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 183346/21286803. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(a b))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a b)(a b))) REDUCED to normal form. ------ 183347/21286821. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.(a a)))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.(a a)))) REDUCED to normal form. ------ 183348/21286848. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 183349/21286857. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 183350/21286884. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.y1)(b a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.y1)(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(b a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 183351/21286902. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((b a) a)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((b a) a)) 3. ==[ beta ]==> (((b a)(b a))((b a) a)) REDUCED to normal form. ------ 183352/21286965. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 183353/21286992. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 183354/21287046. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 183355/21287100. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 183356/21287127. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 183357/21287190. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 183358/21287217. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(a (^z.z)))) 6. ==[ alpha ]==> (((a (^x.x)) b)((a a)(a (^y.y)))) REDUCED to normal form. ------ 183359/21287244. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a b)((^x1.x1) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a b)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a b) a)) REDUCED to normal form. ------ 183360/21287271. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 183361/21287298. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 11. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 12. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 183362/21287325. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a (a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (a a))((a a) a))) REDUCED to normal form. ------ 183363/21287352. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(a b))) 3. ==[ beta ]==> (((a b)(a b))(a (a b))) REDUCED to normal form. ------ 183364/21287379. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((a (^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)((a a) a))((a (^x.x))(a a))) REDUCED to normal form. ------ 183365/21287406. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 183366/21287631. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (^x2.x2))(^y2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x2.x2))(^y2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183367/21287712. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> (b (((^z.z)(a a)) b)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) b)) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 183368/21287856. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(^z.b))) 3. ==[ beta ]==> ((b c)((^y.a)(^z.b))) 4. ==[ alpha ]==> ((b c)((^x.a)(^y.b))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 183369/21287883. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 183370/21287928. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 183371/21287955. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(a a)) b)) 3. ==[ beta ]==> ((^y.y)((^z.(a a)) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(a a)) b)) 5. ==[ beta ]==> ((^y.(a a)) b) 6. ==[ alpha ]==> ((^x.(a a)) b) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 183372/21288099. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(c (^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(c (^y.b))) REDUCED to normal form. ------ 183373/21288126. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(b (^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(b (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(b (^y.(a a)))) REDUCED to normal form. ------ 183374/21288198. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183375/21288207. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 183376/21288234. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 183377/21288261. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 183378/21288594. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a (a a))) REDUCED to normal form. ------ 183379/21288621. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a b)(a a))) 3. ==[ beta ]==> ((b ((^y.y) a))((a b)(a a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a b)(a a))) 5. ==[ beta ]==> ((b a)((a b)(a a))) REDUCED to normal form. ------ 183380/21288648. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 183381/21288702. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(a (a a)))) REDUCED to normal form. ------ 183382/21288873. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (b ((^y.y)(^z.a))) 6. ==[ alpha ]==> (b ((^x.x)(^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 183383/21288981. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183384/21289098. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> (a ((^y.(y y))(^z.(z z)))) 6. ==[ alpha ]==> (a ((^x.(x x))(^y.(y y)))) 7. ==[ beta ]==> (a ((^y.(y y))(^y.(y y)))) 8. ==[ alpha ]==> (a ((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 183385/21289197. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.b) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.b) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.b) a)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.b) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.b) a)) 7. ==[ beta ]==> ((b b)((^y.b) a)) 8. ==[ alpha ]==> ((b b)((^x.b) a)) 9. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 183386/21289287. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d (^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d (^z.(z z)))) REDUCED to normal form. ------ 183387/21289314. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 183388/21289341. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (^z.a))) REDUCED to normal form. ------ 183389/21289386. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((a a) a)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183390/21289395. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 183391/21289422. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 183392/21289449. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(a ((^z.z) a))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a ((^y.y) a))) 7. ==[ beta ]==> ((((a a)(a a))(^x.a))(a a)) REDUCED to normal form. ------ 183393/21289503. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183394/21289674. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(b ((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(b a))(b (^y.y))) 4. ==[ alpha ]==> ((((a a) a)(b a))(b (^x.x))) REDUCED to normal form. ------ 183395/21289701. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 183396/21289728. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(a a))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(a a))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(a a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(a a))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 183397/21289755. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 183398/21289809. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(a (a a)))) REDUCED to normal form. ------ 183399/21289836. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b (a (a a)))((a a)(^y.y))) 6. ==[ alpha ]==> ((b (a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 183400/21289935. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 183401/21289953. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^z.z))(^x1.(x1 x1)))(^y.y)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 183402/21290340. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183403/21290358. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(^y.(y y))) 8. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 183404/21290367. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a (a a))) REDUCED to normal form. ------ 183405/21290385. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (a a)) a)) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a a)) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a a)) a)) REDUCED to normal form. ------ 183406/21290394. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 183407/21290412. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1) a) b)) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a) b)) 5. ==[ beta ]==> (((^y.y) a) b) 6. ==[ alpha ]==> (((^x.x) a) b) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 183408/21290547. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z)) c)) 3. ==[ beta ]==> (b ((^y.(^z.z)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183409/21290610. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 183410/21290655. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183411/21290691. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 183412/21290718. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 183413/21290790. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 183414/21290799. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 183415/21290817. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a) c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1) c)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) c) REDUCED to normal form. ------ 183416/21290862. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b b)) REDUCED to normal form. ------ 183417/21290889. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a c)) 3. ==[ beta ]==> ((a (b (^y.y)))(a c)) 4. ==[ alpha ]==> ((a (b (^x.x)))(a c)) REDUCED to normal form. ------ 183418/21290916. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b (a a))) REDUCED to normal form. ------ 183419/21290943. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (a (^z.z)))) 5. ==[ beta ]==> (((^y.y) b)(a (a (^z.z)))) 6. ==[ alpha ]==> (((^x.x) b)(a (a (^y.y)))) 7. ==[ beta ]==> (b (a (a (^y.y)))) 8. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 183420/21290970. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 183421/21290997. ------ 1. ==[ start ]==> (((a b)(b a))(b a)) REDUCED to normal form. ------ 183422/21291024. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a b)) REDUCED to normal form. ------ 183423/21291051. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a (a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (a a))) REDUCED to normal form. ------ 183424/21291342. ------ 1. ==[ start ]==> ((^a.(^b.a))(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (^x.(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 183425/21294249. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((^z.(z (^x1.x1)))(^z.(z (^x1.x1))))(^y.y)) 4. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(z (^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (((^z.(z (^x1.x1)))(^y.y))(^y1.y1)) 6. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.x1)) 7. ==[ beta ]==> (((^z.z)(^y.y))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183426/21302115. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 183427/21302403. ------ 1. ==[ start ]==> ((^a.(^a.a))((b a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)(a b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183428/21302484. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(b a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183429/21302646. ------ 1. ==[ start ]==> ((^a.(^b.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> (^y.((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> (^x.((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 183430/21302649. ------ 1. ==[ start ]==> ((a (^b.a))(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 183431/21302667. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 183432/21302988. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.(^z.z))((^x1.x1) b))(((^y.(^z.z))((^x1.x1) b))((^y.(^z.z))((^x1.x1) b)))) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.(^y1.y1))((^z1.z1) b))((^x2.(^y2.y2))((^z2.z2) b)))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))((^z1.z1) b))((^x2.(^y2.y2))((^z2.z2) b)))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((^x1.x1) b))((^y1.(^z1.z1))((^x2.x2) b)))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1) b))((^y1.(^z1.z1))((^x2.x2) b))) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))((^z1.z1) b))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) b))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 11. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 12. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183433/21303339. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183434/21304284. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((^y.(y y))((^z.z) b)) b) 4. ==[ alpha ]==> (((^x.(x x))((^y.y) b)) b) 5. ==[ beta ]==> ((((^y.y) b)((^y.y) b)) b) 6. ==[ alpha ]==> ((((^x.x) b)((^y.y) b)) b) 7. ==[ beta ]==> ((b ((^y.y) b)) b) 8. ==[ alpha ]==> ((b ((^x.x) b)) b) 9. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 183435/21305553. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> ((((^z.z)(b (^x1.x1)))((^z.z)(b (^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((((^x.x)(b (^y.y)))((^z.z)(b (^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (((b (^y.y))((^z.z)(b (^x1.x1))))(^y1.y1)) 6. ==[ alpha ]==> (((b (^x.x))((^y.y)(b (^z.z))))(^x1.x1)) 7. ==[ beta ]==> (((b (^x.x))(b (^z.z)))(^x1.x1)) 8. ==[ alpha ]==> (((b (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 183436/21305556. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 183437/21306654. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 183438/21307014. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 183439/21307680. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^c.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 183440/21308931. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 183441/21310143. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183442/21310533. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 183443/21310983. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((a b)(^y.((^z.z)(a a)))) 6. ==[ alpha ]==> ((a b)(^x.((^y.y)(a a)))) 7. ==[ beta ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 183444/21311199. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 183445/21311397. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a b))) 5. ==[ beta ]==> ((^y.y)(^z.(a b))) 6. ==[ alpha ]==> ((^x.x)(^y.(a b))) 7. ==[ beta ]==> (^y.(a b)) 8. ==[ alpha ]==> (^x.(a b)) REDUCED to normal form. ------ 183446/21311802. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(z b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(z b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(z b))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(z b))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(y b))) 7. ==[ beta ]==> ((b b)(^y.(y b))) 8. ==[ alpha ]==> ((b b)(^x.(x b))) REDUCED to normal form. ------ 183447/21312144. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.((a a) a))) REDUCED to normal form. ------ 183448/21312306. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 183449/21312546. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((^z.a)((^x1.x1) a))(((^z.a)((^x1.x1) a))(^y.y))) 4. ==[ alpha ]==> (((^x.a)((^y.y) a))(((^z.a)((^x1.x1) a))(^y1.y1))) 5. ==[ beta ]==> (a (((^z.a)((^x1.x1) a))(^y1.y1))) 6. ==[ alpha ]==> (a (((^x.a)((^y.y) a))(^z.z))) 7. ==[ beta ]==> (a (a (^z.z))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 183450/21313419. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 183451/21313422. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(a (^y1.y1)))) REDUCED to normal form. ------ 183452/21313440. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.y))) REDUCED to normal form. ------ 183453/21313494. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 183454/21313548. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 183455/21313602. ------ 1. ==[ start ]==> (((a b)(b a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 183456/21313629. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(a a))) REDUCED to normal form. ------ 183457/21313656. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 183458/21313713. ------ 1. ==[ start ]==> ((a (^a.a))((b a)(a b))) 2. ==[ alpha ]==> ((a (^x.x))((b a)(a b))) REDUCED to normal form. ------ 183459/21313740. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 183460/21313767. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a a)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 183461/21313794. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a b)(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(b a))) REDUCED to normal form. ------ 183462/21313848. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183463/21313875. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 183464/21313902. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a (b (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 183465/21313929. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 183466/21313956. ------ 1. ==[ start ]==> ((a (^b.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 183467/21313974. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 183468/21313992. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 183469/21314001. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(^y.y))) REDUCED to normal form. ------ 183470/21314073. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 183471/21314100. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 183472/21314127. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 183473/21314154. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)(^x1.b))) REDUCED to normal form. ------ 183474/21314181. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 183475/21314217. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 183476/21314244. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 183477/21314289. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 183478/21314298. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a (a (a a)))(^y.y)) 4. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 183479/21314397. ------ 1. ==[ start ]==> (((a (a a)) a)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 183480/21314424. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a (^y.y))) a)) REDUCED to normal form. ------ 183481/21314451. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.a)) b) REDUCED to normal form. ------ 183482/21314478. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b (^x1.x1)) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 183483/21314541. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 183484/21314649. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 183485/21314820. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.y)(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.x)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183486/21314856. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((a (^y.a))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((a (^x.a))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((a (^x.a))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.a))(a (^y.y))) REDUCED to normal form. ------ 183487/21314874. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 183488/21315117. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(b a))) 5. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 183489/21315171. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (a a))((^z.z) b))) 5. ==[ beta ]==> (a ((a (a a))((^z.z) b))) 6. ==[ alpha ]==> (a ((a (a a))((^x.x) b))) 7. ==[ beta ]==> (a ((a (a a)) b)) REDUCED to normal form. ------ 183490/21315252. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a) a)((a a)((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a a) a)((a a)((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 183491/21315288. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 183492/21315315. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 183493/21315342. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 183494/21315369. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183495/21315396. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 183496/21315486. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 183497/21315513. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> (((a (a a)) a) b) REDUCED to normal form. ------ 183498/21315567. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 183499/21315585. ------ 1. ==[ start ]==> (((^a.b) a)((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b) a)((a (a a))(^y.y))) 3. ==[ beta ]==> (b ((a (a a))(^y.y))) 4. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 183500/21315594. ------ 1. ==[ start ]==> ((a (a b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a b))((^x.(x x))((^y.y) b))) 3. ==[ beta ]==> ((a (a b))(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> ((a (a b))(b ((^y.y) b))) 6. ==[ alpha ]==> ((a (a b))(b ((^x.x) b))) 7. ==[ beta ]==> ((a (a b))(b b)) REDUCED to normal form. ------ 183501/21315747. ------ 1. ==[ start ]==> ((((a a) a) b)(((a a)(a a)) c)) REDUCED to normal form. ------ 183502/21315999. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a a)(a b))((^y.y)(^y.y))) 4. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 183503/21316026. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 183504/21316152. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.b) b)((^y.(a a)) c)) 3. ==[ beta ]==> (b ((^y.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 183505/21316197. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((^y.(a a))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.(a a))((a (^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 183506/21316224. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 183507/21316278. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(a b))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(a b))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a b))) 7. ==[ beta ]==> (((^y.y)(a a))(a b)) 8. ==[ alpha ]==> (((^x.x)(a a))(a b)) 9. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 183508/21316359. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (b ((^y.y)(b a))) 6. ==[ alpha ]==> (b ((^x.x)(b a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 183509/21316413. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> ((a a)(((^y.y) a)((^z.z) b))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y) b))) 7. ==[ beta ]==> ((a a)(a ((^y.y) b))) 8. ==[ alpha ]==> ((a a)(a ((^x.x) b))) 9. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 183510/21316440. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 183511/21316503. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 183512/21316530. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(((a a)(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((((a a)(a a))(^y.(^z.z)))(((a a)(a a))(^y.(^z.z)))) 8. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 183513/21316557. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(b (^z.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(b (^y.a))) REDUCED to normal form. ------ 183514/21316584. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) REDUCED to normal form. ------ 183515/21316611. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 183516/21316674. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 183517/21316701. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 183518/21316755. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(b a))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(b a))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 183519/21316782. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a) a)((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 183520/21316800. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 183521/21316809. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 183522/21316836. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 183523/21316863. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(b (^z.z))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 183524/21317277. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((a a)(a a))(a a))) 3. ==[ beta ]==> (b (((a a)(a a))(a a))) REDUCED to normal form. ------ 183525/21317286. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a)) b)) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 183526/21317313. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1) c)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) c)) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) c) REDUCED to normal form. ------ 183527/21317592. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (^y.(a a)))) REDUCED to normal form. ------ 183528/21317853. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 183529/21317961. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 183530/21317988. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a)(a a)) a)) REDUCED to normal form. ------ 183531/21318042. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1))) c)) REDUCED to normal form. ------ 183532/21318186. ------ 1. ==[ start ]==> (((a a)(b a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 183533/21318213. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 183534/21318267. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(a b)) a) REDUCED to normal form. ------ 183535/21318294. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 183536/21318465. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183537/21318546. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a a)(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)((^y.y)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(a a)))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 183538/21318627. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 183539/21318744. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((b a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((b a)(^z.a))) REDUCED to normal form. ------ 183540/21318771. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((a a)(^x1.x1))(^y1.(y1 y1)))) REDUCED to normal form. ------ 183541/21318852. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a) a)(^y.b))) REDUCED to normal form. ------ 183542/21318879. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 183543/21318960. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 183544/21318987. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)(^z.z))) REDUCED to normal form. ------ 183545/21319041. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1))) b)) REDUCED to normal form. ------ 183546/21319104. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 183547/21319131. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 183548/21319158. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.b)(^z.a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.b)(^y.a))) 5. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 183549/21319185. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(^z.b))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.b))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.b))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 183550/21319212. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 183551/21319239. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 183552/21319293. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 183553/21319338. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.x1) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183554/21319383. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(a (^z.z)))) 3. ==[ beta ]==> ((^y.y)((b a)(a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)((b a)(a (^y.y)))) 5. ==[ beta ]==> ((b a)(a (^y.y))) 6. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 183555/21319410. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((a a)(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 183556/21319545. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (b ((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 183557/21319662. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 183558/21319689. ------ 1. ==[ start ]==> ((((^a.a) b) a)((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((b a)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 183559/21319716. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 183560/21319743. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(^y1.(y1 y1)))) REDUCED to normal form. ------ 183561/21319824. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))(^x1.b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 183562/21319851. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 183563/21319878. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 183564/21319932. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 183565/21319986. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((b a) b)) REDUCED to normal form. ------ 183566/21320013. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a)(^z.z)) c)) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z)) c)) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y)) c)) REDUCED to normal form. ------ 183567/21320049. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 183568/21320076. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) b) REDUCED to normal form. ------ 183569/21320103. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (b a))((^y.a)(^z.a))) 4. ==[ alpha ]==> ((a (b a))((^x.a)(^y.a))) 5. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 183570/21320130. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 183571/21320157. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(^z.(a a)))) 7. ==[ beta ]==> ((a a)((^y.(y y))(^z.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.(x x))(^y.(a a)))) 9. ==[ beta ]==> ((a a)((^y.(a a))(^y.(a a)))) 10. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(a a)))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 183572/21320184. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a b)) a) REDUCED to normal form. ------ 183573/21320238. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 183574/21320409. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((a a) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a a) a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a a) a)) 7. ==[ beta ]==> ((^y.y)((a a) a)) 8. ==[ alpha ]==> ((^x.x)((a a) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 183575/21320688. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> ((b b)((^y.y)(^z.a))) 6. ==[ alpha ]==> ((b b)((^x.x)(^y.a))) 7. ==[ beta ]==> ((b b)(^y.a)) 8. ==[ alpha ]==> ((b b)(^x.a)) REDUCED to normal form. ------ 183576/21320715. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((a (a a))(^x.b))) REDUCED to normal form. ------ 183577/21320769. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 183578/21320877. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(a a)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a) c)) REDUCED to normal form. ------ 183579/21321318. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 183580/21321399. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((b (a (^x.x)))(a a)) REDUCED to normal form. ------ 183581/21321426. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 183582/21321453. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 183583/21321840. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(a ((a a)(^z.z)))) 3. ==[ beta ]==> ((b (^y.y))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 183584/21321867. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a a))) 5. ==[ beta ]==> (((^y.y)(a a))(a a)) 6. ==[ alpha ]==> (((^x.x)(a a))(a a)) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 183585/21321903. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b) c)) 3. ==[ beta ]==> ((a (^y.y))((^z.b) c)) 4. ==[ alpha ]==> ((a (^x.x))((^y.b) c)) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 183586/21321921. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((a a) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((a a) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a) a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a) a) a)) REDUCED to normal form. ------ 183587/21322002. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (b (((^z.z) a)((a a) a))) 4. ==[ alpha ]==> (b (((^x.x) a)((a a) a))) 5. ==[ beta ]==> (b (a ((a a) a))) REDUCED to normal form. ------ 183588/21322119. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 183589/21322146. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((b (^y.a))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((b (^x.a))(((a a) a)(^y.a))) REDUCED to normal form. ------ 183590/21322173. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 183591/21322236. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 183592/21322263. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 183593/21322290. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((a b)((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a b)((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> ((a b)((^y.y)(a a))) 8. ==[ alpha ]==> ((a b)((^x.x)(a a))) 9. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 183594/21322317. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 183595/21322344. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 183596/21322398. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 183597/21322425. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a b))((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a b))((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a b))(^y.y)) 8. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 183598/21322452. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 183599/21322506. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(a a))) REDUCED to normal form. ------ 183600/21322704. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a b))) 5. ==[ beta ]==> ((^y.y)((a a)(a b))) 6. ==[ alpha ]==> ((^x.x)((a a)(a b))) 7. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 183601/21323055. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(c ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> (c ((^y.y)(^z.z))) 6. ==[ alpha ]==> (c ((^x.x)(^y.y))) 7. ==[ beta ]==> (c (^y.y)) 8. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 183602/21323109. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(a (a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(a (a b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(a (a b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(a (a b))) 5. ==[ beta ]==> ((b ((^y.y) b))(a (a b))) 6. ==[ alpha ]==> ((b ((^x.x) b))(a (a b))) 7. ==[ beta ]==> ((b b)(a (a b))) REDUCED to normal form. ------ 183603/21323118. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b) a)) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 183604/21323190. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (b ((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x) a))) 5. ==[ beta ]==> (b ((a (a a)) a)) REDUCED to normal form. ------ 183605/21323199. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a)) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z)) d)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(d d)) REDUCED to normal form. ------ 183606/21323307. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a) a)(^y1.y1))) REDUCED to normal form. ------ 183607/21323334. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b (^x.(x x)))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 183608/21323361. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (a a))(^y.a))) REDUCED to normal form. ------ 183609/21323415. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 183610/21323451. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.z)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((a a) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 183611/21323478. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 183612/21323505. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 183613/21323532. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y))(^z.a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(^y.a))) 5. ==[ beta ]==> (((a (a a)) b)((^y.a)(^y.a))) 6. ==[ alpha ]==> (((a (a a)) b)((^x.a)(^y.a))) 7. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 183614/21323559. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.a)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 183615/21323586. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 183616/21323613. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.a)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 183617/21323748. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 183618/21323829. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> ((a a)((^y.(y y))(a (^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(a (^y.y)))) 7. ==[ beta ]==> ((a a)((a (^y.y))(a (^y.y)))) 8. ==[ alpha ]==> ((a a)((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 183619/21323847. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.a))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.a))) REDUCED to normal form. ------ 183620/21323856. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 183621/21324252. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.a))) 5. ==[ beta ]==> (b ((a (^y.y))(^z.a))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 183622/21324279. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a)(^y.(y y)))) REDUCED to normal form. ------ 183623/21324306. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (a a)) a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (a a)) a)) REDUCED to normal form. ------ 183624/21324378. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b ((^y.y) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b ((^x.x) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b a)) REDUCED to normal form. ------ 183625/21324414. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z)) a)) 5. ==[ beta ]==> ((^y.y)((^z.(z z)) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(y y)) a)) 7. ==[ beta ]==> ((^y.(y y)) a) 8. ==[ alpha ]==> ((^x.(x x)) a) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 183626/21324441. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 183627/21324459. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y))(a (^z.z)))) 3. ==[ beta ]==> (b ((a (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 183628/21324522. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.z))) REDUCED to normal form. ------ 183629/21324567. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b c)) 3. ==[ beta ]==> ((^y.(^z.z))(b c)) 4. ==[ alpha ]==> ((^x.(^y.y))(b c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183630/21324603. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a) a)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 183631/21324630. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y)) b)) REDUCED to normal form. ------ 183632/21324684. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183633/21324702. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (^z.z))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 183634/21324711. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 183635/21324729. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(a (^x1.x1)))) REDUCED to normal form. ------ 183636/21324747. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a (^b.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (^y.a))) REDUCED to normal form. ------ 183637/21324774. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 183638/21324801. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a (b (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 183639/21324828. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 183640/21324855. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> (b (^y.(^z.z))) 10. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 183641/21324882. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b (^z.z))) REDUCED to normal form. ------ 183642/21324909. ------ 1. ==[ start ]==> (((a b)(b a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 183643/21324936. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 183644/21324963. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 183645/21336576. ------ 1. ==[ start ]==> ((^a.(^b.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (^x.(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 183646/21336648. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183647/21336918. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.x1))((((^y.y)(^z.z))(^x1.x1))(((^y.y)(^z.z))(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((((^x1.x1)(^y1.y1))(^z1.z1))(((^x2.x2)(^y2.y2))(^z2.z2)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((((^x1.x1)(^y1.y1))(^z1.z1))(((^x2.x2)(^y2.y2))(^z2.z2)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((((^z.z)(^x1.x1))(^y1.y1))(((^z1.z1)(^x2.x2))(^y2.y2)))) 7. ==[ beta ]==> ((^y.y)((((^z.z)(^x1.x1))(^y1.y1))(((^z1.z1)(^x2.x2))(^y2.y2)))) 8. ==[ alpha ]==> ((^x.x)((((^y.y)(^z.z))(^x1.x1))(((^y1.y1)(^z1.z1))(^x2.x2)))) 9. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.x1))(((^y1.y1)(^z1.z1))(^x2.x2))) 10. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 11. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 13. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 14. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 15. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 16. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 17. ==[ beta ]==> ((^y.y)(^z.z)) 18. ==[ alpha ]==> ((^x.x)(^y.y)) 19. ==[ beta ]==> (^y.y) 20. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183648/21337038. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((a (a a))(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((a (a a))(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 183649/21337143. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183650/21337479. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.a))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 183651/21337902. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 183652/21338034. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 183653/21338214. ------ 1. ==[ start ]==> ((^a.(a b))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((^x.(x b))((a (a a))(^y.y))) 3. ==[ beta ]==> (((a (a a))(^y.y)) b) 4. ==[ alpha ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 183654/21338307. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.((^x1.(^y1.y1)) a))) IRREDUCIBLE: cycle. ------ 183655/21338601. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2)))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.(^x3.(^y3.y3)))))) 5. ==[ beta ]==> (^x.((^z.z)((^x2.(^y2.y2))(^z2.(^x3.(^y3.y3)))))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2)))))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183656/21339882. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 183657/21340602. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.((a a)(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.((a a)(a a)))) REDUCED to normal form. ------ 183658/21340788. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.b)(^z1.b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 183659/21341679. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183660/21341961. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183661/21341994. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 183662/21342276. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183663/21343167. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 183664/21343437. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^b.(b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(y a))) 3. ==[ beta ]==> (((b a)(b a))(^y.(y a))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(x a))) REDUCED to normal form. ------ 183665/21344073. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183666/21344463. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 183667/21344913. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(^z.(a a)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 183668/21345732. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.z))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.z))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.z))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.z))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.y))) 7. ==[ beta ]==> ((b b)(^y.(^z.y))) 8. ==[ alpha ]==> ((b b)(^x.(^y.x))) REDUCED to normal form. ------ 183669/21345741. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(y b))) REDUCED to normal form. ------ 183670/21345921. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183671/21346053. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 183672/21346476. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((((^z.z) a)(^x1.a))((((^z.z) a)(^x1.a))(^y.y))) 4. ==[ alpha ]==> ((((^x.x) a)(^y.a))((((^z.z) a)(^x1.a))(^y1.y1))) 5. ==[ beta ]==> ((a (^y.a))((((^z.z) a)(^x1.a))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.a))((((^y.y) a)(^z.a))(^x1.x1))) 7. ==[ beta ]==> ((a (^x.a))((a (^z.a))(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.a))((a (^y.a))(^z.z))) REDUCED to normal form. ------ 183673/21346920. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(a (a a)))) REDUCED to normal form. ------ 183674/21347037. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(z (z z)))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (y y)))) 7. ==[ beta ]==> (^y.(y (y y))) 8. ==[ alpha ]==> (^x.(x (x x))) REDUCED to normal form. ------ 183675/21347307. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.y1)) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183676/21347349. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 183677/21347370. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.c)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.c)) REDUCED to normal form. ------ 183678/21347424. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 183679/21347478. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.b)) 5. ==[ beta ]==> (((^y.y) b)(^z.b)) 6. ==[ alpha ]==> (((^x.x) b)(^y.b)) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 183680/21347532. ------ 1. ==[ start ]==> (((a b)(b a))(^b.b)) 2. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 183681/21347661. ------ 1. ==[ start ]==> (((^a.a) a)((b a)(a b))) 2. ==[ alpha ]==> (((^x.x) a)((b a)(a b))) 3. ==[ beta ]==> (a ((b a)(a b))) REDUCED to normal form. ------ 183682/21347688. ------ 1. ==[ start ]==> (((a a) a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 183683/21347715. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.x))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 183684/21347742. ------ 1. ==[ start ]==> (((^a.a) b)((a b)(b a))) 2. ==[ alpha ]==> (((^x.x) b)((a b)(b a))) 3. ==[ beta ]==> (b ((a b)(b a))) REDUCED to normal form. ------ 183685/21347769. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 183686/21347796. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a) b)((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y) b))) 5. ==[ beta ]==> (((a a) b)((^y.y) b)) 6. ==[ alpha ]==> (((a a) b)((^x.x) b)) 7. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 183687/21347823. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 183688/21347850. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 183689/21347877. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 183690/21347895. ------ 1. ==[ start ]==> ((a (^b.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 183691/21347940. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 183692/21347967. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 183693/21348057. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (a ((^y.y)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 183694/21348084. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183695/21348210. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a a))(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 183696/21348237. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 183697/21348246. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.(^z.z))((^x1.x1) b))((^y.(^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))((^z1.z1) b))) 7. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) b))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 9. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 10. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183698/21348273. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 183699/21348327. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183700/21348354. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((a (a a))((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> ((a (a a))(a (a (^y.y)))) 6. ==[ alpha ]==> ((a (a a))(a (a (^x.x)))) REDUCED to normal form. ------ 183701/21348381. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 7. ==[ beta ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183702/21348462. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 183703/21348597. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183704/21348678. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183705/21348741. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(c (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (b (^z.z)))) REDUCED to normal form. ------ 183706/21348768. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(b (^z.z))) REDUCED to normal form. ------ 183707/21348795. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((a (^y.a))(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((a (^x.a))(a (a (a (^y.y))))) REDUCED to normal form. ------ 183708/21348822. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 183709/21348849. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((b (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((b (^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 183710/21349146. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (b (((^y.y) a)((a a)(a a)))) 6. ==[ alpha ]==> (b (((^x.x) a)((a a)(a a)))) 7. ==[ beta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 183711/21349173. ------ 1. ==[ start ]==> ((((a a) a) a)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 183712/21349218. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(a (^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(y (^z.z))))) 5. ==[ beta ]==> (a (^y.(y (^z.z)))) 6. ==[ alpha ]==> (a (^x.(x (^y.y)))) REDUCED to normal form. ------ 183713/21349353. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 183714/21349371. ------ 1. ==[ start ]==> (((a a)((a a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a a)((a a) a))((b a)(^x.a))) REDUCED to normal form. ------ 183715/21349398. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 183716/21349425. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (a (a a)))((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((a (a (a a)))((a a)(^x.(a a)))) REDUCED to normal form. ------ 183717/21349452. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 183718/21349506. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 183719/21349533. ------ 1. ==[ start ]==> ((a (a b))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((a (a b))((a (a a))(^x.x))) REDUCED to normal form. ------ 183720/21349542. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.b)((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.b)((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 183721/21349623. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)((^x1.(^y1.y1)) a))) IRREDUCIBLE: cycle. ------ 183722/21349704. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 183723/21349731. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((a b)(^y.(y y))) 6. ==[ alpha ]==> ((a b)(^x.(x x))) REDUCED to normal form. ------ 183724/21349758. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183725/21349893. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.a)(^z.a))) 3. ==[ beta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 183726/21349920. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 183727/21350091. ------ 1. ==[ start ]==> (((^a.b) b)(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> (b (((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> (b (((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 183728/21350100. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a)) c)) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 183729/21350307. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(^y.y))(b a))) 3. ==[ beta ]==> (((a b) b)((^y.y)(b a))) 4. ==[ alpha ]==> (((a b) b)((^x.x)(b a))) 5. ==[ beta ]==> (((a b) b)(b a)) REDUCED to normal form. ------ 183730/21350334. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a) a)((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a) a)((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 183731/21350361. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a ((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a b)) REDUCED to normal form. ------ 183732/21350379. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(c (^z.(a a)))) 3. ==[ beta ]==> ((^y.y)(c (^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(a a)))) 5. ==[ beta ]==> (c (^y.(a a))) 6. ==[ alpha ]==> (c (^x.(a a))) REDUCED to normal form. ------ 183733/21350388. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.z))((a a)(a a)))) REDUCED to normal form. ------ 183734/21350514. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 183735/21350613. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a a)(^z.b))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((a a)(^y.b))) REDUCED to normal form. ------ 183736/21350640. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a b)(^y.(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((a b)(^y.(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((a b)(^x.(a a)))) REDUCED to normal form. ------ 183737/21350721. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a (a a))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) a)((a (a a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a) a)((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 183738/21350748. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 183739/21350973. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183740/21351135. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.a)(^y.y))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 183741/21351171. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(b ((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b ((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(b ((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b ((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183742/21351198. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(a (b (^y.y)))) REDUCED to normal form. ------ 183743/21351225. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 183744/21351252. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 183745/21351279. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a (^z.(^x1.x1))) a)) REDUCED to normal form. ------ 183746/21351648. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 5. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 183747/21351729. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (b ((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((a a) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 183748/21351837. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y))(b a))) 3. ==[ beta ]==> ((b a)((^y.(y y))(b a))) 4. ==[ alpha ]==> ((b a)((^x.(x x))(b a))) 5. ==[ beta ]==> ((b a)((b a)(b a))) REDUCED to normal form. ------ 183749/21351864. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.a)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(a (^y.(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 183750/21351918. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (((a b)(a b))((a a)(a a))) REDUCED to normal form. ------ 183751/21351999. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 183752/21352107. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)(^y1.b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 183753/21352287. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(a a)) a)) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 183754/21352314. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z) b)) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z) b)) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y) b)) 5. ==[ beta ]==> (((a a) a)((^y.y) b)) 6. ==[ alpha ]==> (((a a) a)((^x.x) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 183755/21352386. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183756/21352566. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (c (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 183757/21352674. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(a (^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183758/21352728. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183759/21352782. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.b)((a a) a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.b)((a a) a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.b)((a a) a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.b)((a a) a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b)((a a) a))) 7. ==[ beta ]==> (((a a)(a a))((^y.b)((a a) a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.b)((a a) a))) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 183760/21352863. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (b (((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 183761/21352971. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183762/21352998. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 183763/21353016. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((b a) c)) REDUCED to normal form. ------ 183764/21353277. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(a ((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183765/21353286. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) a) REDUCED to normal form. ------ 183766/21353313. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 183767/21353592. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(a (^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183768/21353727. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 183769/21353808. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> (b ((^y.(y y))((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> (b (((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (b ((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 183770/21353916. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183771/21354204. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.z))) REDUCED to normal form. ------ 183772/21354483. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 183773/21354591. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.b)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183774/21354672. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(a b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(a b))) 5. ==[ beta ]==> (((a a)(a a))((a b)(a b))) REDUCED to normal form. ------ 183775/21354699. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 183776/21354753. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.y)(b a))) 3. ==[ beta ]==> (((b a)(b a))((^y.y)(b a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.x)(b a))) 5. ==[ beta ]==> (((b a)(b a))(b a)) REDUCED to normal form. ------ 183777/21354834. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 183778/21354942. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183779/21354978. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c ((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(c (a a))) REDUCED to normal form. ------ 183780/21355005. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(b ((a a)(^y.y)))) REDUCED to normal form. ------ 183781/21355068. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z)) b)) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 183782/21355095. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(a a)) c)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a)) c)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a)) c)) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 183783/21355311. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 183784/21355338. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 183785/21355365. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((a b)(^x.a))) REDUCED to normal form. ------ 183786/21355392. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 183787/21355482. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.a)(a b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.a)(a b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.a)(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.a)(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183788/21355563. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183789/21355671. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183790/21355707. ------ 1. ==[ start ]==> ((((^a.a) b) c)(d ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(d ((a a) a))) 3. ==[ beta ]==> ((b c)(d ((a a) a))) REDUCED to normal form. ------ 183791/21355734. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(c (a b))) REDUCED to normal form. ------ 183792/21355779. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 183793/21355842. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((a (^y.y))((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(a (^y.y)))) REDUCED to normal form. ------ 183794/21355869. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((a a) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(((a a) a) a)) REDUCED to normal form. ------ 183795/21355950. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a ((a a) a))) REDUCED to normal form. ------ 183796/21355977. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (^z.z))(a b))) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z))(a b))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(a b))) REDUCED to normal form. ------ 183797/21356049. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183798/21356175. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a (^z.a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.a))) REDUCED to normal form. ------ 183799/21356202. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 183800/21356229. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)(^y.(a a)))) 5. ==[ beta ]==> ((a b)((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((a b)((a a)(^x.(a a)))) REDUCED to normal form. ------ 183801/21356256. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((a a) a)) REDUCED to normal form. ------ 183802/21356283. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a b) b)) 3. ==[ beta ]==> (((^y.y)(b a))((a b) b)) 4. ==[ alpha ]==> (((^x.x)(b a))((a b) b)) 5. ==[ beta ]==> ((b a)((a b) b)) REDUCED to normal form. ------ 183803/21356472. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(a a)) a)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(a a)) a)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(a a)) a)) 5. ==[ beta ]==> ((b a)((^y.(a a)) a)) 6. ==[ alpha ]==> ((b a)((^x.(a a)) a)) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 183804/21356499. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.b) b)) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 183805/21356643. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (^z.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b (^z.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.b))) 5. ==[ beta ]==> ((^y.y)(b (^z.b))) 6. ==[ alpha ]==> ((^x.x)(b (^y.b))) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 183806/21356724. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 183807/21356832. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183808/21356967. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(z z)))) 7. ==[ beta ]==> ((^y.(y y))(^z.(z z))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) 9. ==[ beta ]==> ((^y.(y y))(^y.(y y))) 10. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) IRREDUCIBLE: cycle. ------ 183809/21356994. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 183810/21357048. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.z)(^x1.b))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.z)(^x1.b))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.y)(^z.b))) 7. ==[ beta ]==> ((b b)((^y.y)(^z.b))) 8. ==[ alpha ]==> ((b b)((^x.x)(^y.b))) 9. ==[ beta ]==> ((b b)(^y.b)) 10. ==[ alpha ]==> ((b b)(^x.b)) REDUCED to normal form. ------ 183811/21357057. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(a (a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (a b))) REDUCED to normal form. ------ 183812/21357084. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((a a) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a)(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a)(a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183813/21357138. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 183814/21357165. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a (a (a a)))) REDUCED to normal form. ------ 183815/21357192. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 183816/21357237. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(a (^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183817/21357372. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 183818/21357417. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((a a) a) a)) REDUCED to normal form. ------ 183819/21357444. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y)(^z.z)) b)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(^y.y)) b)) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.y) b)) 6. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x) b)) 7. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 183820/21357471. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (a a)) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (a a)) c)) 3. ==[ beta ]==> (((a (a a)) b)((a (a a)) c)) REDUCED to normal form. ------ 183821/21357606. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 183822/21357768. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)((a (a a))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 183823/21357795. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a (^z.a))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.a))) REDUCED to normal form. ------ 183824/21357804. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> (((^z.a)((^x1.x1) a))(^y.y)) 6. ==[ alpha ]==> (((^x.a)((^y.y) a))(^z.z)) 7. ==[ beta ]==> (a (^z.z)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 183825/21358191. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c c)) 3. ==[ beta ]==> (((^y.y) b)(c c)) 4. ==[ alpha ]==> (((^x.x) b)(c c)) 5. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 183826/21358209. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183827/21358236. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (a a))) REDUCED to normal form. ------ 183828/21358263. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(y1 y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((^y.(y y))(^z.z)) 6. ==[ alpha ]==> ((^x.(x x))(^y.y)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183829/21358317. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 183830/21358353. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a (a a)))) 5. ==[ beta ]==> ((^y.y)(a (a (a a)))) 6. ==[ alpha ]==> ((^x.x)(a (a (a a)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 183831/21358380. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 183832/21358398. ------ 1. ==[ start ]==> (((^a.b)(b a))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(c (^y.(^z.z)))) 3. ==[ beta ]==> (b (c (^y.(^z.z)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 183833/21358506. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183834/21358623. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a ((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a ((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a ((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183835/21358650. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (^z.z))(a a))) REDUCED to normal form. ------ 183836/21358668. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 183837/21358713. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 183838/21358740. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 183839/21358767. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a (^x.x)) a)) REDUCED to normal form. ------ 183840/21358794. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a) b)) 5. ==[ beta ]==> (((^y.y) b)((a a) b)) 6. ==[ alpha ]==> (((^x.x) b)((a a) b)) 7. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 183841/21358821. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 183842/21358848. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a) b)) 2. ==[ alpha ]==> (((a b)(b a))((^x.x) b)) 3. ==[ beta ]==> (((a b)(b a)) b) REDUCED to normal form. ------ 183843/21358875. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a)(^z.z))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 183844/21358902. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a) a)) REDUCED to normal form. ------ 183845/21358955. ------ 1. ==[ start ]==> (^a.((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (^x.((x (^y.(^z.z)))((x x) x))) REDUCED to normal form. ------ 183846/21358956. ------ 1. ==[ start ]==> (a ((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (a ((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 183847/21362874. ------ 1. ==[ start ]==> ((^a.(b a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.((a a)(a a)))) 3. ==[ eta ]==> (b (^y.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 183848/21370275. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a)) a) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a)) a) REDUCED to normal form. ------ 183849/21370281. ------ 1. ==[ start ]==> ((^a.a)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 183850/21370308. ------ 1. ==[ start ]==> ((^a.(a a))((b a)(a b))) 2. ==[ alpha ]==> ((^x.(x x))((b a)(a b))) 3. ==[ beta ]==> (((b a)(a b))((b a)(a b))) REDUCED to normal form. ------ 183851/21370335. ------ 1. ==[ start ]==> ((^a.b)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 183852/21370416. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(a (^z.(^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 183853/21370572. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 183854/21370776. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 183855/21371004. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 183856/21371436. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 183857/21371658. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((((^y.y)(a a))((^z.z)(a a)))(((^y.y)(a a))((^z.z)(a a))))(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(a a))))(((^y1.y1)(a a))((^z1.z1)(a a)))) 5. ==[ beta ]==> ((((a a)((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(a a))))(((^y1.y1)(a a))((^z1.z1)(a a)))) 6. ==[ alpha ]==> ((((a a)((^x.x)(a a)))(((^y.y)(a a))((^z.z)(a a))))(((^x1.x1)(a a))((^y1.y1)(a a)))) 7. ==[ beta ]==> ((((a a)(a a))(((^y.y)(a a))((^z.z)(a a))))(((^x1.x1)(a a))((^y1.y1)(a a)))) 8. ==[ alpha ]==> ((((a a)(a a))(((^x.x)(a a))((^y.y)(a a))))(((^z.z)(a a))((^x1.x1)(a a)))) 9. ==[ beta ]==> ((((a a)(a a))((a a)((^y.y)(a a))))(((^z.z)(a a))((^x1.x1)(a a)))) 10. ==[ alpha ]==> ((((a a)(a a))((a a)((^x.x)(a a))))(((^y.y)(a a))((^z.z)(a a)))) 11. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y)(a a))((^z.z)(a a)))) 12. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x)(a a))((^y.y)(a a)))) 13. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)((^y.y)(a a)))) 14. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)((^x.x)(a a)))) 15. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 183858/21371868. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) REDUCED to normal form. ------ 183859/21371991. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 183860/21372687. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))((^z.z) a))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(^x1.(^y1.y1))) 5. ==[ beta ]==> (((^y.y)((^z.z) a))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.x1))) 7. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 183861/21372765. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((((^z.z) b)((^x1.x1) a))(((^z.z) b)((^x1.x1) a)))) 4. ==[ alpha ]==> ((^x.x)((((^y.y) b)((^z.z) a))(((^x1.x1) b)((^y1.y1) a)))) 5. ==[ beta ]==> ((((^y.y) b)((^z.z) a))(((^x1.x1) b)((^y1.y1) a))) 6. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z) b)((^x1.x1) a))) 7. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) b)((^x1.x1) a))) 8. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) b)((^z.z) a))) 9. ==[ beta ]==> ((b a)(((^y.y) b)((^z.z) a))) 10. ==[ alpha ]==> ((b a)(((^x.x) b)((^y.y) a))) 11. ==[ beta ]==> ((b a)(b ((^y.y) a))) 12. ==[ alpha ]==> ((b a)(b ((^x.x) a))) 13. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 183862/21374196. ------ 1. ==[ start ]==> ((^a.(b a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((a a)((a a)(a a)))) 3. ==[ eta ]==> (b ((a a)((a a)(a a)))) REDUCED to normal form. ------ 183863/21374199. ------ 1. ==[ start ]==> ((a (b a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((a (b a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 183864/21374559. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 183865/21374568. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.((a a)(a a)))) REDUCED to normal form. ------ 183866/21374928. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.((x x)(x x)))) REDUCED to normal form. ------ 183867/21375033. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x1.x1))(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.z))) REDUCED to normal form. ------ 183868/21375636. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183869/21375918. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183870/21375927. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^z.b)) REDUCED to normal form. ------ 183871/21375951. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 183872/21376242. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 183873/21376845. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 183874/21376950. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a b)(a (a a)))) 3. ==[ beta ]==> ((((a b)(a (a a)))((a b)(a (a a))))(((a b)(a (a a)))((a b)(a (a a))))) REDUCED to normal form. ------ 183875/21377394. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(^z.a))) 3. ==[ beta ]==> (((b a)(b a))(^y.(^z.a))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 183876/21377682. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^a.(b a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.(b x))) 3. ==[ eta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 183877/21379113. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((b a)(^y.((^z.z)(y y)))) 6. ==[ alpha ]==> ((b a)(^x.((^y.y)(x x)))) 7. ==[ beta ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 183878/21379191. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183879/21379698. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 183880/21379887. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.b))) REDUCED to normal form. ------ 183881/21380010. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 183882/21380220. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.((z z) z))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.((z z) z))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.((y y) y))) 5. ==[ beta ]==> (((a a)(a a))(^y.((y y) y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.((x x) x))) REDUCED to normal form. ------ 183883/21380886. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(a (a a)))) REDUCED to normal form. ------ 183884/21380994. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 7. ==[ beta ]==> (^y.(^z.(z z))) 8. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 183885/21381102. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 183886/21381183. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 183887/21381264. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183888/21381306. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 183889/21381462. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 183890/21381489. ------ 1. ==[ start ]==> (((a b)(b a))(^c.(a a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(a a))) REDUCED to normal form. ------ 183891/21381543. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.b)) REDUCED to normal form. ------ 183892/21381597. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 183893/21381609. ------ 1. ==[ start ]==> ((a a)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 183894/21381636. ------ 1. ==[ start ]==> ((a (a a))((b a)(a b))) REDUCED to normal form. ------ 183895/21381663. ------ 1. ==[ start ]==> ((a b)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a b)(((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> ((a b)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 183896/21381717. ------ 1. ==[ start ]==> (((a a)(a a))((a b)(b a))) REDUCED to normal form. ------ 183897/21381744. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 183898/21381879. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 183899/21381897. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 183900/21381942. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.a)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 183901/21381969. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 183902/21382023. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a (((^y.y) b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.x) b)(^y.(^z.z)))) 7. ==[ beta ]==> (a (b (^y.(^z.z)))) 8. ==[ alpha ]==> (a (b (^x.(^y.y)))) REDUCED to normal form. ------ 183903/21382032. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 183904/21382059. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 183905/21382104. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 183906/21382212. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.x1))(((^y.y)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 9. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 10. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 11. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 12. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 13. ==[ beta ]==> ((^y.y)(^z.z)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183907/21382239. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.(a a))) 6. ==[ alpha ]==> ((a (a a))(^x.(a a))) REDUCED to normal form. ------ 183908/21382275. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a b)((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 183909/21382302. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a)) a)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 183910/21382320. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((a (a a))((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a (a a))((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 183911/21382329. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a (a (^y.y)))) REDUCED to normal form. ------ 183912/21382347. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 5. ==[ beta ]==> ((a (a (^y.y))) a) 6. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 183913/21382356. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^y1.y1)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 183914/21382401. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(a a))((b (^y.y)) c)) 3. ==[ beta ]==> (((a a)(a a))((b (^y.y)) c)) 4. ==[ alpha ]==> (((a a)(a a))((b (^x.x)) c)) REDUCED to normal form. ------ 183915/21382653. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 183916/21382761. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.a))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a (^x.a))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 183917/21382779. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z (^x1.x1))) a)) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 183918/21382851. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.x))(((a a)(a a)) a)) REDUCED to normal form. ------ 183919/21382878. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(b (a (a a)))) REDUCED to normal form. ------ 183920/21382905. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a a)((a (^x.(^y.y)))(^x1.x1))) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 183921/21382932. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((b a)((a a) a))) REDUCED to normal form. ------ 183922/21382959. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y))(a b))) 5. ==[ beta ]==> ((a a)(((a a)(^y.y))(a b))) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 183923/21382986. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((a ((a a) a))((a a)(a a))) REDUCED to normal form. ------ 183924/21383193. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 183925/21383238. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)((b (^y.y))(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 183926/21383301. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(a (a a))) REDUCED to normal form. ------ 183927/21383319. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 183928/21383490. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 183929/21383508. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))(^z.z))) 3. ==[ beta ]==> ((^y.b)((a (a a))(^z.z))) 4. ==[ alpha ]==> ((^x.b)((a (a a))(^y.y))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 183930/21383670. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((a a)(a a)) c)) 3. ==[ beta ]==> (b (((a a)(a a)) c)) REDUCED to normal form. ------ 183931/21383679. ------ 1. ==[ start ]==> (((a b) a)((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 183932/21383706. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.(z z))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(y y))) REDUCED to normal form. ------ 183933/21383814. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 183934/21383841. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 183935/21383868. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 183936/21383985. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(b (b (^x.x)))) REDUCED to normal form. ------ 183937/21384012. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((^y.y) a)(a ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> (((^x.x) a)(a ((^y.(^z.z)) a))) 7. ==[ beta ]==> (a (a ((^y.(^z.z)) a))) 8. ==[ alpha ]==> (a (a ((^x.(^y.y)) a))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 183938/21384039. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((b (^y.y))(a a))) REDUCED to normal form. ------ 183939/21384066. ------ 1. ==[ start ]==> (((a b)(a a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 183940/21384093. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> ((a (a a))(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> ((a (a a))(b ((^y.y) a))) 6. ==[ alpha ]==> ((a (a a))(b ((^x.x) a))) 7. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 183941/21384354. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(c (^z.(a a)))) REDUCED to normal form. ------ 183942/21384462. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 183943/21384480. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (b (((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.a))) 5. ==[ beta ]==> (b (b (^y.a))) 6. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 183944/21384489. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1) a)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) a)) 5. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 183945/21384516. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 183946/21384705. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 183947/21384804. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((b (^x1.x1)) a)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) a)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) a)) 5. ==[ beta ]==> ((b (^y.y)) a) 6. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 183948/21384948. ------ 1. ==[ start ]==> (((a b) c)((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 183949/21384975. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(^z.b))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.b))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 183950/21385002. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 183951/21385083. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.b))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.b))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 183952/21385137. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183953/21385281. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((b a)(a (a a)))) REDUCED to normal form. ------ 183954/21385308. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 183955/21385335. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((a (a b))(((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> ((a (a b))(((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> ((a (a b))((a a)((a a) a))) REDUCED to normal form. ------ 183956/21385362. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a b)(a b))) REDUCED to normal form. ------ 183957/21385389. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)((^z.z)(a a)))) 7. ==[ beta ]==> ((^y.y)(((a a) a)((^z.z)(a a)))) 8. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(a a)))) 9. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 10. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 11. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 183958/21385416. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((^x.x)(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a (a a)))((a a)(^y.y))) 6. ==[ alpha ]==> ((((a a) a)(a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 183959/21385443. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (a a))(b a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a (a a))(b a))) 3. ==[ beta ]==> (((a b) a)((a (a a))(b a))) REDUCED to normal form. ------ 183960/21385470. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 183961/21385497. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^y.y)) b)) REDUCED to normal form. ------ 183962/21385524. ------ 1. ==[ start ]==> ((a (b a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 183963/21385614. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(^y1.a))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 183964/21385695. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (b ((a a)(^y.a))) 6. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 183965/21385758. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 183966/21385830. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 183967/21385866. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 183968/21385884. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a a)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a b))((a a)(^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))((a a)(^x.(a a)))) REDUCED to normal form. ------ 183969/21385893. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a a)(a a))) REDUCED to normal form. ------ 183970/21385947. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 183971/21385965. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (^y.(^z.z))) c)) 3. ==[ beta ]==> (b ((a (^y.(^z.z))) c)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 183972/21385974. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 183973/21386226. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(b ((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(b ((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b ((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(b b)) REDUCED to normal form. ------ 183974/21386253. ------ 1. ==[ start ]==> (((a b)(a (a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 183975/21386280. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) b)(a a))) 5. ==[ beta ]==> (((a a) a)(((^y.y) b)(a a))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b)(a a))) 7. ==[ beta ]==> (((a a) a)(b (a a))) REDUCED to normal form. ------ 183976/21386307. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 183977/21386361. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 183978/21386640. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183979/21386649. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.x1))) REDUCED to normal form. ------ 183980/21386667. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((b a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 183981/21386694. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 183982/21386748. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a b)(^z.a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a b)(^z.a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a b)(^z.a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a b)(^z.a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)(^y.a))) 7. ==[ beta ]==> (((a a)(a a))((a b)(^y.a))) 8. ==[ alpha ]==> (((a a)(a a))((a b)(^x.a))) REDUCED to normal form. ------ 183983/21386757. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.b)((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) b) REDUCED to normal form. ------ 183984/21386784. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(a b))) 5. ==[ beta ]==> ((^y.b)((^z.a)(a b))) 6. ==[ alpha ]==> ((^x.b)((^y.a)(a b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 183985/21386829. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 183986/21386838. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(((a a)(^x1.x1))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 183987/21386865. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.a)(b a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.a)(b a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.a)(b a))) 5. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 183988/21386892. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 183989/21386937. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1) b) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183990/21386946. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 183991/21386964. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 183992/21387243. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 183993/21387252. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(a ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a b)) REDUCED to normal form. ------ 183994/21387279. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 183995/21387288. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) b) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) b) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 183996/21387567. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a (^z.z))) REDUCED to normal form. ------ 183997/21387594. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 183998/21387612. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> (b ((b a)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 183999/21387639. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 184000/21387693. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 184001/21387729. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)((a a) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)((a a) a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)((a a) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184002/21387756. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 184003/21387774. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a (a a))(^y.(a a)))) 3. ==[ beta ]==> (b ((a (a a))(^y.(a a)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 184004/21387783. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a b)(^x.a))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a b)(^x.a))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a b)(^x.a))((a a)(a a))) REDUCED to normal form. ------ 184005/21387810. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 184006/21387837. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 184007/21387882. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a (^y1.(^z1.z1))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184008/21387891. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 184009/21388116. ------ 1. ==[ start ]==> (((a b)((a a) a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(c ((a a)(^x.x)))) REDUCED to normal form. ------ 184010/21388143. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(b (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(b (b a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(b (b a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(b (b a))) 5. ==[ beta ]==> (((a a)(^y.y))(b (b a))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (b a))) REDUCED to normal form. ------ 184011/21388170. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 184012/21388224. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a)(^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 184013/21388251. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> ((b (a a))((a a)((^y.y) a))) 6. ==[ alpha ]==> ((b (a a))((a a)((^x.x) a))) 7. ==[ beta ]==> ((b (a a))((a a) a)) REDUCED to normal form. ------ 184014/21388278. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a b)(a (a a)))) REDUCED to normal form. ------ 184015/21388557. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184016/21388593. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 184017/21388620. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 184018/21388638. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a (a a))(^y.b))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(^y.b))) 4. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.b))) REDUCED to normal form. ------ 184019/21388665. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(a a))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(a a))) 7. ==[ beta ]==> (a (^y.(a a))) 8. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 184020/21388674. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 184021/21388701. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 184022/21388782. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 184023/21388800. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(a a)) c)) 3. ==[ beta ]==> (b (((^y.y)(a a)) c)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) c)) 5. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 184024/21388809. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 184025/21388863. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 184026/21388917. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.b)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.b)(^y1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 184027/21388944. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 184028/21389007. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(a (b a))) REDUCED to normal form. ------ 184029/21389034. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a)(^z.z))(a a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(^z.z))(a a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 184030/21389061. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(a (^z.z)))) REDUCED to normal form. ------ 184031/21389088. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(b a))((a b)((^x.x) a))) 3. ==[ beta ]==> (((a (a a))(b a))((a b) a)) REDUCED to normal form. ------ 184032/21389115. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)(a (a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(a (a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 184033/21389142. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(a a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.z))) 8. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.y))) 9. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 10. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 184034/21389169. ------ 1. ==[ start ]==> (((a b)(a b))((a (a a))((a a) a))) REDUCED to normal form. ------ 184035/21389196. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y) a)(a b))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y) a)(a b))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) a)(a b))) 5. ==[ beta ]==> (((a a)((a a) a))(a (a b))) REDUCED to normal form. ------ 184036/21389223. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a (^z.z))(a a))) REDUCED to normal form. ------ 184037/21389448. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2) a)(^y2.b))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2) a)(^y2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184038/21389529. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((a a)(^z.z)) a)) 3. ==[ beta ]==> (b (((a a)(^z.z)) a)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 184039/21389673. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((b c)((^y.(y y))(^z.a))) 4. ==[ alpha ]==> ((b c)((^x.(x x))(^y.a))) 5. ==[ beta ]==> ((b c)((^y.a)(^y.a))) 6. ==[ alpha ]==> ((b c)((^x.a)(^y.a))) 7. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 184040/21389700. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)(^y.b))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 184041/21389826. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.b) c)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b) c)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b) c)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 184042/21389943. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(c (^z.b))) 3. ==[ beta ]==> (((a a)(^y.b))(c (^z.b))) 4. ==[ alpha ]==> (((a a)(^x.b))(c (^y.b))) REDUCED to normal form. ------ 184043/21390015. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184044/21390024. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a a)) REDUCED to normal form. ------ 184045/21390051. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 184046/21390411. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(b (a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(b (a b))) REDUCED to normal form. ------ 184047/21390438. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)(a ((^y.y)(a a)))) 6. ==[ alpha ]==> ((b a)(a ((^x.x)(a a)))) 7. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 184048/21390465. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a b)(a a))) REDUCED to normal form. ------ 184049/21390519. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((a (^x.x))((^z.z) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 184050/21390690. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 184051/21390798. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184052/21390915. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 184053/21391023. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.b))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.b)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.b)) REDUCED to normal form. ------ 184054/21391095. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184055/21391158. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 184056/21391212. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.b))) REDUCED to normal form. ------ 184057/21391239. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^c.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(a a))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 184058/21391266. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 184059/21391320. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a (a a)))) 7. ==[ beta ]==> ((^y.a)(a (a a))) 8. ==[ alpha ]==> ((^x.a)(a (a a))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 184060/21391338. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 184061/21391491. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c (a (a a)))) REDUCED to normal form. ------ 184062/21391518. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(b (^z.z))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 184063/21391545. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(a ((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(a ((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a ((a a) a))) 5. ==[ beta ]==> (((a a)(a a))(a ((a a) a))) REDUCED to normal form. ------ 184064/21391572. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(a a)) REDUCED to normal form. ------ 184065/21391626. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a)((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a ((^y1.y1) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((^x1.x1) a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 184066/21391653. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (^y.y))(a (a a)))) 3. ==[ beta ]==> ((b (a (a a)))((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> ((b (a (a a)))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 184067/21391680. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a a)(^y.y))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((a a)(^x.x))) REDUCED to normal form. ------ 184068/21391752. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a (^z.z))(a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 184069/21391770. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> ((((^z.z) a)(^x1.a))(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.z)) 7. ==[ beta ]==> ((a (^y.a))(^z.z)) 8. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 184070/21392157. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(a (^z.z)))) 5. ==[ beta ]==> (b ((^y.a)(a (^z.z)))) 6. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 184071/21392175. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.a))) 7. ==[ beta ]==> ((a (^y.y))(^z.a)) 8. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 184072/21392184. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 184073/21392202. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a a)(^z.(z z)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 184074/21392211. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a (a a))) REDUCED to normal form. ------ 184075/21392229. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (a a)) a)) 3. ==[ beta ]==> ((^y.y)((a (a a)) a)) 4. ==[ alpha ]==> ((^x.x)((a (a a)) a)) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 184076/21392319. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((^y.y)(^z.(z z))) 8. ==[ alpha ]==> ((^x.x)(^y.(y y))) 9. ==[ beta ]==> (^y.(y y)) 10. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 184077/21392364. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a) b)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a) b)) 3. ==[ beta ]==> (b ((^y.a) b)) 4. ==[ alpha ]==> (b ((^x.a) b)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 184078/21392427. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.(z z)))) REDUCED to normal form. ------ 184079/21392472. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184080/21392508. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1) a)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 184081/21392535. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 184082/21392589. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184083/21392607. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.a) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a) a)) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 184084/21392634. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 184085/21392652. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(a (^y.y)))) REDUCED to normal form. ------ 184086/21392706. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b b)) 3. ==[ beta ]==> ((a (b (^y.y)))(b b)) 4. ==[ alpha ]==> ((a (b (^x.x)))(b b)) REDUCED to normal form. ------ 184087/21392760. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b (a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b (a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b (a a))) 5. ==[ beta ]==> (((^y.y) b)(b (a a))) 6. ==[ alpha ]==> (((^x.x) b)(b (a a))) 7. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 184088/21392787. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (a (^z.z)))) REDUCED to normal form. ------ 184089/21392814. ------ 1. ==[ start ]==> (((a b)(b a))((a a)(a a))) REDUCED to normal form. ------ 184090/21392841. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b a)) REDUCED to normal form. ------ 184091/21392868. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a b)) REDUCED to normal form. ------ 184092/21392922. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a a)) REDUCED to normal form. ------ 184093/21404250. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a)) b) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a)) b) REDUCED to normal form. ------ 184094/21404274. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184095/21404355. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184096/21404517. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (^x.((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (^x.((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> (^x.((a (^y.y))(^z.z))) REDUCED to normal form. ------ 184097/21404565. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 184098/21404589. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(z (^x1.x1)))(a a))) 3. ==[ eta ]==> ((^y.y)((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 184099/21405438. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 184100/21406155. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.z))(a (^x1.(^y1.y1)))) b) 4. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1)))) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 184101/21407424. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((((^z.(^x1.x1))((a a)(a a)))((^z.(^x1.x1))((a a)(a a))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))((a a)(a a))))(^y1.y1)) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1))((a a)(a a))))(^y1.y1)) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))((a a)(a a))))(^x1.x1)) 7. ==[ beta ]==> (((^y.(^z.z))((a a)(a a)))(^x1.x1)) 8. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184102/21407841. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 184103/21408180. ------ 1. ==[ start ]==> ((^a.(b a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(b (^y.(a a)))) 3. ==[ eta ]==> (b (b (^y.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 184104/21408552. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.(a a)))) REDUCED to normal form. ------ 184105/21408912. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.(a a)))) REDUCED to normal form. ------ 184106/21409911. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 184107/21410829. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 184108/21411108. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^c.(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(b a))) 3. ==[ beta ]==> (b (^z.(b a))) 4. ==[ alpha ]==> (b (^x.(b a))) REDUCED to normal form. ------ 184109/21412014. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184110/21412431. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.((y y)(^z.z)))) 5. ==[ beta ]==> (^y.((y y)(^z.z))) 6. ==[ alpha ]==> (^x.((x x)(^y.y))) REDUCED to normal form. ------ 184111/21412881. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 184112/21413097. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.(a a)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(a a)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 184113/21414042. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.((a a) a))) REDUCED to normal form. ------ 184114/21414204. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.a))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.a))) REDUCED to normal form. ------ 184115/21414417. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^z.(z z))(a (^x1.x1)))(((^z.(z z))(a (^x1.x1)))(^y.y))) 4. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.(z z))(a (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.(z z))(a (^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(z z))(a (^x1.x1)))(^y1.y1))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a (^x1.x1))(a (^x1.x1)))(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a (^z.z))(a (^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 184116/21414978. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.d)) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.d)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.d)) 5. ==[ beta ]==> ((^y.y)(^z.d)) 6. ==[ alpha ]==> ((^x.x)(^y.d)) 7. ==[ beta ]==> (^y.d) 8. ==[ alpha ]==> (^x.d) REDUCED to normal form. ------ 184117/21415167. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 184118/21415266. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.(x (^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.z)) 5. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 184119/21415290. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184120/21415338. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.z))) REDUCED to normal form. ------ 184121/21415392. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(a (^y.y)))) REDUCED to normal form. ------ 184122/21415446. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 184123/21415500. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 184124/21415527. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(a a))) REDUCED to normal form. ------ 184125/21415581. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.x1))) REDUCED to normal form. ------ 184126/21415611. ------ 1. ==[ start ]==> ((a (^a.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 184127/21415638. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((b a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(a b))) 3. ==[ beta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 184128/21415665. ------ 1. ==[ start ]==> (((^a.a)(a a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 184129/21415692. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 184130/21415746. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184131/21415773. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 184132/21415800. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 184133/21415827. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 184134/21415854. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.a))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 184135/21415872. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 184136/21415899. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 184137/21415926. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((a a)((a a)(^y.y))) 6. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 184138/21415971. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b (^y.y))(^z.a))) REDUCED to normal form. ------ 184139/21415998. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 184140/21416025. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 184141/21416079. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b a)(^z.b))) 3. ==[ beta ]==> ((a (^y.y))((b a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(^y.b))) REDUCED to normal form. ------ 184142/21416142. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 184143/21416169. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.b)(b a))) 3. ==[ beta ]==> ((a (a a))((^y.b)(b a))) 4. ==[ alpha ]==> ((a (a a))((^x.b)(b a))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 184144/21416187. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 184145/21416322. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 184146/21416349. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (a (^z.z))) a)) REDUCED to normal form. ------ 184147/21416376. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a) b)) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 184148/21416403. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((b (^y.y)) c)) REDUCED to normal form. ------ 184149/21416466. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 184150/21416772. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(a (a (a (^z.z))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(a (a (a (^z.z))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (a (a (^z.z))))) REDUCED to normal form. ------ 184151/21416781. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 184152/21417015. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)((a a)(^y.y))) 6. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 184153/21417069. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (a (((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (a ((^y.y)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (a ((^x.x)(a (^y.(^z.z))))) 9. ==[ beta ]==> (a (a (^y.(^z.z)))) 10. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 184154/21417150. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a a) a)((a (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> (((a a) a)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 184155/21417177. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a a)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 184156/21417213. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 8. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 184157/21417240. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 184158/21417267. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(^x1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184159/21417294. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(b (^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 184160/21417330. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 184161/21417411. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 184162/21417438. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 184163/21417483. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 184164/21417492. ------ 1. ==[ start ]==> ((a (a b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 184165/21417645. ------ 1. ==[ start ]==> ((((a a) a) b)((b (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a) b)((b (^x.x)) b)) REDUCED to normal form. ------ 184166/21417672. ------ 1. ==[ start ]==> (((a b) a)(((a a)(a a)) c)) REDUCED to normal form. ------ 184167/21417897. ------ 1. ==[ start ]==> (((a a)(a b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 184168/21417924. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 184169/21417951. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 184170/21418095. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184171/21418122. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a (a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 184172/21418176. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))((a a) a))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))((a a) a))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((a a) a))) 7. ==[ beta ]==> (((a a)(^y.y))((a a) a)) 8. ==[ alpha ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 184173/21418257. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 184174/21418311. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a a)((a (a a))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a a)((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 184175/21418338. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (((^y.y) a)((^z.z) b)) 6. ==[ alpha ]==> (((^x.x) a)((^y.y) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 184176/21418392. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a a)(b (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a a)(b (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)(b (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a a)(b (^x1.x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(b (^z.z)))) 9. ==[ beta ]==> ((^y.y)((a a)(b (^z.z)))) 10. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 11. ==[ beta ]==> ((a a)(b (^y.y))) 12. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 184177/21418428. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y y))((b (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))((b (^y.y))(^z.z))) 7. ==[ beta ]==> (((b (^y.y))(^z.z))((b (^y.y))(^z.z))) 8. ==[ alpha ]==> (((b (^x.x))(^y.y))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 184178/21418455. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 184179/21418482. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b (^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 184180/21418509. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 184181/21418572. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 184182/21418599. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(a a))(a b))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(a a))(a b))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(a a))(a b))) 5. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 184183/21418626. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 184184/21418680. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((((a a) a) a)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 184185/21418698. ------ 1. ==[ start ]==> (((^a.b) c)((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)((a (a a))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((a (a a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 184186/21418707. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 184187/21418734. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)((^y.y) b))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 184188/21418761. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 184189/21419175. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(a (b (^z.z)))) 3. ==[ beta ]==> (b (a (b (^z.z)))) 4. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 184190/21419238. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) c) REDUCED to normal form. ------ 184191/21419517. ------ 1. ==[ start ]==> ((a (b a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))(b (^x.(a a)))) REDUCED to normal form. ------ 184192/21419751. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 184193/21419859. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 184194/21419886. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 184195/21419940. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 184196/21419967. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 184197/21420084. ------ 1. ==[ start ]==> (((a a)(b a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.b)(^y.b))) 3. ==[ beta ]==> (((a a)(b a)) b) REDUCED to normal form. ------ 184198/21420138. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 184199/21420192. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a) a)((^y.a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a) a)((^x.a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 184200/21420219. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 184201/21420246. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.(a a))) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.(a a))) REDUCED to normal form. ------ 184202/21420363. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184203/21420444. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a) a)(a b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a) a)(a b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a) a)(a b))) 5. ==[ beta ]==> ((a a)(((a a) a)(a b))) REDUCED to normal form. ------ 184204/21420525. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> (b (((^x1.x1) a)(b a))) 4. ==[ alpha ]==> (b (((^x.x) a)(b a))) 5. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 184205/21420642. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 184206/21420669. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((b a)(^x1.a))) REDUCED to normal form. ------ 184207/21420750. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a b)(^y.a))) REDUCED to normal form. ------ 184208/21420777. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a) a)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a) a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)(^z.b))) 5. ==[ beta ]==> ((^y.b)(((a a) a)(^z.b))) 6. ==[ alpha ]==> ((^x.b)(((a a) a)(^y.b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 184209/21420831. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 184210/21420885. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 184211/21420939. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(b a)) REDUCED to normal form. ------ 184212/21420975. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 184213/21421056. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 184214/21421083. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a b)((^y.b)(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.b)(^y.a))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 184215/21421137. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 184216/21421245. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 184217/21421281. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 184218/21421308. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((b a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(a (^y.y)))) 5. ==[ beta ]==> ((b a)(a (^y.y))) 6. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 184219/21421443. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a b))) 5. ==[ beta ]==> (b ((^y.y)(a b))) 6. ==[ alpha ]==> (b ((^x.x)(a b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 184220/21421551. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184221/21421587. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 184222/21421614. ------ 1. ==[ start ]==> (((a a)(^b.b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 184223/21421641. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.a))) REDUCED to normal form. ------ 184224/21421722. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a) a)(^z.a))) 5. ==[ beta ]==> ((^y.(a a))(((a a) a)(^z.a))) 6. ==[ alpha ]==> ((^x.(a a))(((a a) a)(^y.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184225/21421749. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)(^z.b))) 5. ==[ beta ]==> ((((a a) a)(^x.b))(^z.b)) 6. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.b)) REDUCED to normal form. ------ 184226/21421776. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 184227/21421803. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 184228/21421884. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.(^z1.z1))) a)) REDUCED to normal form. ------ 184229/21421911. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((b a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((b a) b)) 3. ==[ beta ]==> ((b (^y.y))((b a) b)) 4. ==[ alpha ]==> ((b (^x.x))((b a) b)) REDUCED to normal form. ------ 184230/21421947. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 184231/21421974. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a a)) REDUCED to normal form. ------ 184232/21422001. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 184233/21422055. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.b))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.b))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 184234/21422082. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a b))((^y.(a a))(^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a b))((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((((a a) a)(a b))(a a)) REDUCED to normal form. ------ 184235/21422109. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)((a a) a)) a) REDUCED to normal form. ------ 184236/21422163. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 184237/21422307. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 184238/21422442. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a a)(b a))) 3. ==[ beta ]==> (b ((a a)(b a))) REDUCED to normal form. ------ 184239/21422586. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> ((b b)(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b b)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 184240/21422667. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(a a)))) REDUCED to normal form. ------ 184241/21422775. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 184242/21422802. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a)) c)) 3. ==[ beta ]==> (((a b)(^x.b))((a a) c)) REDUCED to normal form. ------ 184243/21423297. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 184244/21423324. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a a)) REDUCED to normal form. ------ 184245/21423351. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 184246/21423738. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(b ((^z.z)(a a)))) 3. ==[ beta ]==> ((b (^y.y))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(b ((^y.y)(a a)))) 5. ==[ beta ]==> ((b (^x.x))(b (a a))) REDUCED to normal form. ------ 184247/21423765. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(a ((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.x)(a ((a a)(^y.y)))) 5. ==[ beta ]==> (a ((a a)(^y.y))) 6. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 184248/21423801. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(a a)) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a)) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a)) b)) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 184249/21423819. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a b)(a (^y1.y1)))) REDUCED to normal form. ------ 184250/21423828. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.b) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.b) c)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 184251/21423900. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((a (a a))(^y.y))) 6. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 184252/21424017. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 184253/21424044. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 184254/21424071. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((a a) a)(^z.a))) REDUCED to normal form. ------ 184255/21424134. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.z))) 9. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 10. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 184256/21424161. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 184257/21424188. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(a b))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(a b))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 184258/21424215. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(a a))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 184259/21424242. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((b a)((^y.(a a))(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.(a a))(^y.y))) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 184260/21424269. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 184261/21424296. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)(^z.a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.a))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 184262/21424323. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 184263/21424350. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 184264/21424404. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 184265/21424431. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.(a a)))) 7. ==[ beta ]==> ((b a)(^y.(a a))) 8. ==[ alpha ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 184266/21424602. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a) a))) 7. ==[ beta ]==> ((a (^y.y))((a a) a)) 8. ==[ alpha ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 184267/21425007. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b ((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b ((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b ((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(b ((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(b ((a a) a))) 7. ==[ beta ]==> ((b b)(b ((a a) a))) REDUCED to normal form. ------ 184268/21425043. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184269/21425088. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b ((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 184270/21425097. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 184271/21425196. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184272/21425232. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((a a) a)(^z.z))) 3. ==[ beta ]==> ((b (^y.(y y)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 184273/21425259. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 184274/21425313. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(z z)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(z z))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(y y))) 9. ==[ beta ]==> (a (^y.(y y))) 10. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 184275/21425349. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 184276/21425376. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a a) a)) REDUCED to normal form. ------ 184277/21425430. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 184278/21425457. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.a)(^x1.a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.a))) 9. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 184279/21425484. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 184280/21425511. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 184281/21425646. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c (^y.(y y)))) 3. ==[ beta ]==> ((b (a (a a)))(c (^y.(y y)))) 4. ==[ alpha ]==> ((b (a (a a)))(c (^x.(x x)))) REDUCED to normal form. ------ 184282/21425673. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 184283/21425727. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(a a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 184284/21425745. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 184285/21425754. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 184286/21426150. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (((^y.y) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 184287/21426177. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y))(^z.a))) REDUCED to normal form. ------ 184288/21426204. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)(^z.(z z)))) REDUCED to normal form. ------ 184289/21426339. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 184290/21426357. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y) a)(a a))) 3. ==[ beta ]==> (b (((^y.y) a)(a a))) 4. ==[ alpha ]==> (b (((^x.x) a)(a a))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 184291/21426501. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(^x1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 184292/21426528. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((^y.y) a) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 184293/21426600. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a ((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.y))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 184294/21426609. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^b.a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.a) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 184295/21426627. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 184296/21426645. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b (^y.(^z.z)))) REDUCED to normal form. ------ 184297/21426672. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a (^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a (^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.a))) REDUCED to normal form. ------ 184298/21426699. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 184299/21426726. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (^x.x))) REDUCED to normal form. ------ 184300/21426753. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> (b ((^y.(^z.z))(^x1.x1))) 8. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184301/21426780. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 184302/21426807. ------ 1. ==[ start ]==> (((a b)(b a))(b (^a.a))) 2. ==[ alpha ]==> (((a b)(b a))(b (^x.x))) REDUCED to normal form. ------ 184303/21426834. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 184304/21426861. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 184305/21426915. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a (^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (^z.z))) REDUCED to normal form. ------ 184306/21438567. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 184307/21438600. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (a (^z.z)))(^x1.x1))) 3. ==[ eta ]==> ((^y.y)((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 184308/21438870. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^y.(^z.(^x1.x1))))((((a a) a)(^y.(^z.(^x1.x1))))(((a a) a)(^y.(^z.(^x1.x1)))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((((a a) a)(^x1.(^y1.(^z1.z1))))(((a a) a)(^x2.(^y2.(^z2.z2)))))) REDUCED to normal form. ------ 184309/21439017. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 184310/21439449. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 184311/21439458. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 184312/21439863. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 184313/21439986. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)(a (a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 184314/21440166. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) b) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) b) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1)))) b) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1)))) b) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1))) b) 8. ==[ alpha ]==> ((^x.(^y.(^z.z))) b) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184315/21440553. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (^y.(((^z.a)(^x1.a))((^z.a)(^x1.a)))) 4. ==[ alpha ]==> (^x.(((^y.a)(^z.a))((^x1.a)(^y1.a)))) 5. ==[ beta ]==> (^x.(a ((^x1.a)(^y1.a)))) 6. ==[ alpha ]==> (^x.(a ((^y.a)(^z.a)))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 184316/21441078. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 184317/21441474. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 184318/21441861. ------ 1. ==[ start ]==> (((a b)(^b.a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(b (^z.z)))) REDUCED to normal form. ------ 184319/21442740. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184320/21443607. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(a a))(^y1.y1)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184321/21443631. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184322/21443946. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.b) a)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.z) a)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 184323/21444237. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 184324/21444552. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184325/21446025. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a b)(^z.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184326/21446199. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.((a a)(^y.y)))) REDUCED to normal form. ------ 184327/21446442. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184328/21447720. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(z1 b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(z1 b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(y1 b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184329/21447882. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((a a) a))) REDUCED to normal form. ------ 184330/21448005. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a)(a (a a)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 184331/21448053. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 184332/21448428. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^z.(^x1.x1)))(((a (a a))(^z.(^x1.x1)))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a (a a))(^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 184333/21448899. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.(a (a a)))) 3. ==[ beta ]==> ((^y.y)(^y1.(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a a)))) 5. ==[ beta ]==> (^y.(a (a a))) 6. ==[ alpha ]==> (^x.(a (a a))) REDUCED to normal form. ------ 184334/21449016. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(x1 (x1 x1)))) REDUCED to normal form. ------ 184335/21449097. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^z.a)) REDUCED to normal form. ------ 184336/21449277. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 184337/21449286. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 184338/21449301. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(c (^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(c (^y1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184339/21449349. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.c)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.c)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.c)) REDUCED to normal form. ------ 184340/21449511. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.z)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.z)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 184341/21449592. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.a)) REDUCED to normal form. ------ 184342/21449640. ------ 1. ==[ start ]==> (((^a.a) a)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x) a)((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (a ((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> (a ((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 184343/21449667. ------ 1. ==[ start ]==> (((a a) a)((b a)(a b))) REDUCED to normal form. ------ 184344/21449694. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 184345/21449721. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (b (((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> (b ((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> (b ((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 184346/21449748. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 184347/21449775. ------ 1. ==[ start ]==> (((a a) b)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 184348/21449802. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z) b)) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y) b)) 7. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 184349/21449829. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 184350/21449856. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (b (^z.z)))) REDUCED to normal form. ------ 184351/21449910. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 184352/21449946. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a a)((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> ((a a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 184353/21449955. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.a)((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.a)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 184354/21450063. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184355/21450135. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 184356/21450216. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 184357/21450252. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184358/21450306. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 7. ==[ beta ]==> ((^y.a)(b (^z.z))) 8. ==[ alpha ]==> ((^x.a)(b (^y.y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 184359/21450333. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 184360/21450360. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 184361/21450576. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184362/21450603. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184363/21450774. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.a))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.a))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (^x.a))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.a))(b (^y.y))) REDUCED to normal form. ------ 184364/21450792. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 184365/21450801. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (a (a (^z.z))))) REDUCED to normal form. ------ 184366/21450828. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(^y1.y1)) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(a a))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a a))) 7. ==[ beta ]==> (((^y.(^z.z)) a)(a a)) 8. ==[ alpha ]==> (((^x.(^y.y)) a)(a a)) 9. ==[ beta ]==> ((^y.y)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184367/21451125. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))((^y.y) b))) 5. ==[ beta ]==> (b ((a (a a))((^y.y) b))) 6. ==[ alpha ]==> (b ((a (a a))((^x.x) b))) 7. ==[ beta ]==> (b ((a (a a)) b)) REDUCED to normal form. ------ 184368/21451152. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 184369/21451206. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 184370/21451332. ------ 1. ==[ start ]==> ((a (^a.b))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a (^x.b))(a (a a))) REDUCED to normal form. ------ 184371/21451350. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 184372/21451377. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)(^z.a))) REDUCED to normal form. ------ 184373/21451404. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> ((a (a (a a)))(((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> ((a (a (a a)))(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 184374/21451431. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a (a a)) a)((a a)(^y.(a a)))) 6. ==[ alpha ]==> (((a (a a)) a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 184375/21451458. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 184376/21451512. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a b))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a b))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 184377/21451521. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 184378/21451602. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(b (^y1.y1)))) IRREDUCIBLE: cycle. ------ 184379/21451710. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 184380/21451737. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(z z))) 6. ==[ alpha ]==> ((^x.x)(^y.(y y))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 184381/21451872. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 184382/21451899. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 184383/21452070. ------ 1. ==[ start ]==> (((^a.b) b)((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b) b)((b (^y.y))(a a))) 3. ==[ beta ]==> (b ((b (^y.y))(a a))) 4. ==[ alpha ]==> (b ((b (^x.x))(a a))) REDUCED to normal form. ------ 184384/21452286. ------ 1. ==[ start ]==> (((a b) b)(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 184385/21452313. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (((a a) a)((^y.y)(b a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(b a))) 7. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 184386/21452340. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 184387/21452367. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a ((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(a ((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.b))(a b)) REDUCED to normal form. ------ 184388/21452421. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)(b (^z.z)))) REDUCED to normal form. ------ 184389/21452493. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 184390/21452565. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 184391/21452592. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 184392/21452619. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> ((a ((a a) a))((a a)(^y.b))) 6. ==[ alpha ]==> ((a ((a a) a))((a a)(^x.b))) REDUCED to normal form. ------ 184393/21452646. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a b)(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a b)(^y.(a a)))) REDUCED to normal form. ------ 184394/21452727. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 184395/21452754. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^y.y))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 184396/21452817. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(b (^z.z)))) 5. ==[ beta ]==> ((^y.y)(b (^z.z))) 6. ==[ alpha ]==> ((^x.x)(b (^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184397/21453033. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 184398/21453114. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(^z.z))) 8. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 184399/21453150. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(c ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(c ((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(c ((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(c ((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))(c ((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))(c ((^z.z) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184400/21453177. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b ((a a)(a a)))) REDUCED to normal form. ------ 184401/21453204. ------ 1. ==[ start ]==> (((a b)(^b.a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(a (b (^y.y)))) REDUCED to normal form. ------ 184402/21453231. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 184403/21453258. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b (a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (a (^z.z)))) REDUCED to normal form. ------ 184404/21453627. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (b ((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 184405/21453708. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184406/21453816. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 184407/21453843. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(b a))) 5. ==[ beta ]==> ((^y.(y y))(b a)) 6. ==[ alpha ]==> ((^x.(x x))(b a)) 7. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 184408/21453897. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 184409/21453978. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 184410/21454086. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 184411/21454320. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 184412/21454365. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((b a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184413/21454653. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.y1)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184414/21454680. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 184415/21454761. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(a a))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(a a))((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))((^y.y)(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 184416/21454842. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184417/21454950. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184418/21454977. ------ 1. ==[ start ]==> ((a (^b.b))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 184419/21454995. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 184420/21455022. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((b a) c)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((b a) c)) REDUCED to normal form. ------ 184421/21455256. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(b (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184422/21455292. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.b) a)) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.y) a)) 3. ==[ beta ]==> ((a b)((^y.y) a)) 4. ==[ alpha ]==> ((a b)((^x.x) a)) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 184423/21455571. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(b (^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184424/21455580. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 184425/21455625. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a a))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 184426/21455706. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 184427/21455787. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184428/21455895. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.y1)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184429/21455967. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a)(^y.y)) c)) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y)) c)) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x)) c)) REDUCED to normal form. ------ 184430/21456264. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y)) c)) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 184431/21456570. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184432/21456651. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 184433/21456678. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a b))) 5. ==[ beta ]==> ((^y.(y y))(a b)) 6. ==[ alpha ]==> ((^x.(x x))(a b)) 7. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 184434/21456732. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 184435/21456813. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184436/21456921. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184437/21457101. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(a a)) c)) 3. ==[ beta ]==> (((a (a a))(b a))(a a)) REDUCED to normal form. ------ 184438/21457317. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 184439/21457344. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 184440/21457371. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a b)(^y.a))) REDUCED to normal form. ------ 184441/21457461. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(x2 x2))((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184442/21457542. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 184443/21457758. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 184444/21457821. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 184445/21457848. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a b)(a (^x1.x1)))) REDUCED to normal form. ------ 184446/21457929. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a (a a))(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((a (a a))(^y.y))) REDUCED to normal form. ------ 184447/21457956. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> (((a a)(^x.b))(a ((a a) a))) REDUCED to normal form. ------ 184448/21458154. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 184449/21458208. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((a b)((a (^y.y))(^z.b))) 6. ==[ alpha ]==> ((a b)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 184450/21458235. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a)(^z.(a a)))) REDUCED to normal form. ------ 184451/21458262. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(a a)) a)) 5. ==[ beta ]==> ((b a)(((^y.y)(a a)) a)) 6. ==[ alpha ]==> ((b a)(((^x.x)(a a)) a)) 7. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 184452/21458289. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a b) b)) REDUCED to normal form. ------ 184453/21458316. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((a a) a) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((a a) a) c)) 3. ==[ beta ]==> (((a b)(a a))(((a a) a) c)) REDUCED to normal form. ------ 184454/21458478. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 184455/21458622. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c (^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(c (^z.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(c (^z.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.a))) 5. ==[ beta ]==> ((^y.y)(c (^z.a))) 6. ==[ alpha ]==> ((^x.x)(c (^y.a))) 7. ==[ beta ]==> (c (^y.a)) 8. ==[ alpha ]==> (c (^x.a)) REDUCED to normal form. ------ 184456/21458703. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(a a))) 3. ==[ beta ]==> (b ((^x1.b)(a a))) 4. ==[ alpha ]==> (b ((^x.b)(a a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 184457/21458811. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184458/21458946. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184459/21458973. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(z z))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) 7. ==[ beta ]==> ((^y.(y y))(^y.(y y))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) IRREDUCIBLE: cycle. ------ 184460/21459027. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.a))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.a))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 184461/21459036. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b ((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b ((a a) a))) REDUCED to normal form. ------ 184462/21459063. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(a (a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(a (a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (a b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184463/21459117. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 184464/21459144. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a (a a)) a)) REDUCED to normal form. ------ 184465/21459171. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (a (a a)))) REDUCED to normal form. ------ 184466/21459216. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(b (^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184467/21459225. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)((a a) a))) REDUCED to normal form. ------ 184468/21459351. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 184469/21459369. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 184470/21459396. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 184471/21459423. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((a a) a) a)) 3. ==[ beta ]==> ((a ((a a)(a a)))(((a a) a) a)) REDUCED to normal form. ------ 184472/21459450. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y)(^z.z)) b)) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y)) b)) 5. ==[ beta ]==> (((a (a a)) b)((^y.y) b)) 6. ==[ alpha ]==> (((a (a a)) b)((^x.x) b)) 7. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 184473/21459585. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^c.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 184474/21459747. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.z))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 184475/21459774. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 184476/21459783. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> (((^z.(z z))(a (^x1.x1)))(^y.y)) 6. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.z)) 7. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.z)) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 184477/21460188. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z)))) 7. ==[ beta ]==> ((^y.a)(a (^z.z))) 8. ==[ alpha ]==> ((^x.a)(a (^y.y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 184478/21460215. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 184479/21460242. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.y1)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(a (a a))) 6. ==[ alpha ]==> ((^x.x)(a (a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 184480/21460296. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 184481/21460332. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b ((^z.z) a))) 5. ==[ beta ]==> ((^y.y)(b ((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)(b ((^y.y) a))) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 184482/21460359. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (a (a a)))) REDUCED to normal form. ------ 184483/21460440. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))((a a) a)) REDUCED to normal form. ------ 184484/21460485. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184485/21460521. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b c)) REDUCED to normal form. ------ 184486/21460602. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b (a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184487/21460620. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 184488/21460629. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a ((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a a)) REDUCED to normal form. ------ 184489/21460647. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(c (^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(c (^x1.x1))) REDUCED to normal form. ------ 184490/21460665. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 184491/21460719. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 184492/21460746. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 184493/21460773. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z)) a)) 5. ==[ beta ]==> (((^y.y) b)((a (^z.z)) a)) 6. ==[ alpha ]==> (((^x.x) b)((a (^y.y)) a)) 7. ==[ beta ]==> (b ((a (^y.y)) a)) 8. ==[ alpha ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 184494/21460800. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a) b)) REDUCED to normal form. ------ 184495/21460827. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y)) a)) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 184496/21460854. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z) b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z) b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y) b)) 5. ==[ beta ]==> (((a a)((a a)(^x.x))) b) REDUCED to normal form. ------ 184497/21460881. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a a)(^y.y))) REDUCED to normal form. ------ 184498/21460935. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a)) a) REDUCED to normal form. ------ 184499/21460961. ------ 1. ==[ start ]==> (^a.(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (^x.(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (^x.(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (^x.(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (^x.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 184500/21460962. ------ 1. ==[ start ]==> (a (((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (a (((^x.x) b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (a (b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (a (b ((^x.x)(^y.y)))) 5. ==[ beta ]==> (a (b (^y.y))) 6. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 184501/21466635. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 184502/21472308. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a))) a) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z))) a) 3. ==[ beta ]==> ((b ((^y.y)(^z.z))) a) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y))) a) 5. ==[ beta ]==> ((b (^y.y)) a) 6. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 184503/21472314. ------ 1. ==[ start ]==> ((^a.a)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184504/21472341. ------ 1. ==[ start ]==> ((^a.(a a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))((a a) a))((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a (^z.(^x1.x1)))((a a) a))) REDUCED to normal form. ------ 184505/21472368. ------ 1. ==[ start ]==> ((^a.b)((b a)(a b))) 2. ==[ alpha ]==> ((^x.b)((b a)(a b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 184506/21472449. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a b)(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a b)(b a))) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 184507/21472809. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b a)(^z.b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 184508/21473064. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 184509/21473133. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184510/21473496. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 184511/21473691. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a)(^y.y))(a b))) 3. ==[ beta ]==> (((((a a)(^y.y))(a b))(((a a)(^y.y))(a b)))(((a a)(^y.y))(a b))) 4. ==[ alpha ]==> (((((a a)(^x.x))(a b))(((a a)(^y.y))(a b)))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 184512/21473928. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 184513/21474024. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 184514/21474747. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((((a a) a)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 184515/21474798. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((^y.y)((((a a)(a a))(a (^z.z)))(((a a)(a a))(a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)((((a a)(a a))(a (^y.y)))(((a a)(a a))(a (^z.z))))) 5. ==[ beta ]==> ((((a a)(a a))(a (^y.y)))(((a a)(a a))(a (^z.z)))) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 184516/21475512. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184517/21476229. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.y))((^z.z) b))) 3. ==[ eta ]==> (b ((a (^y.y))((^z.z) b))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 184518/21476988. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.((y y)(y y)))) 5. ==[ beta ]==> (((a a) a)(^y.((y y)(y y)))) 6. ==[ alpha ]==> (((a a) a)(^x.((x x)(x x)))) REDUCED to normal form. ------ 184519/21477066. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((b a)((^x1.x1) a))) 3. ==[ beta ]==> (((b a)((^x1.x1) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((b a)((^x.x) a))(^y.(^z.z))) 5. ==[ beta ]==> (((b a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((b a) a)(^x.(^y.y))) REDUCED to normal form. ------ 184520/21477654. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 184521/21477669. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a) b) a)) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184522/21477984. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(a ((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(a ((^z.z) b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 184523/21477987. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.((^z.z) b))) 3. ==[ beta ]==> ((a b)(^y.((^z.z) b))) 4. ==[ alpha ]==> ((a b)(^x.((^y.y) b))) 5. ==[ beta ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 184524/21478302. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^a.(^b.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(^z.z))) 3. ==[ beta ]==> ((b a)(^y.(^z.z))) 4. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 184525/21478599. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(a (^z1.(^x2.x2))))) REDUCED to normal form. ------ 184526/21478983. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (((((^y.y)(a a))((^z.z) a))(((^y.y)(a a))((^z.z) a)))((((^y.y)(a a))((^z.z) a))(((^y.y)(a a))((^z.z) a)))) 4. ==[ alpha ]==> (((((^x.x)(a a))((^y.y) a))(((^z.z)(a a))((^x1.x1) a)))((((^y1.y1)(a a))((^z1.z1) a))(((^x2.x2)(a a))((^y2.y2) a)))) 5. ==[ beta ]==> ((((a a)((^y.y) a))(((^z.z)(a a))((^x1.x1) a)))((((^y1.y1)(a a))((^z1.z1) a))(((^x2.x2)(a a))((^y2.y2) a)))) 6. ==[ alpha ]==> ((((a a)((^x.x) a))(((^y.y)(a a))((^z.z) a)))((((^x1.x1)(a a))((^y1.y1) a))(((^z1.z1)(a a))((^x2.x2) a)))) 7. ==[ beta ]==> ((((a a) a)(((^y.y)(a a))((^z.z) a)))((((^x1.x1)(a a))((^y1.y1) a))(((^z1.z1)(a a))((^x2.x2) a)))) 8. ==[ alpha ]==> ((((a a) a)(((^x.x)(a a))((^y.y) a)))((((^z.z)(a a))((^x1.x1) a))(((^y1.y1)(a a))((^z1.z1) a)))) 9. ==[ beta ]==> ((((a a) a)((a a)((^y.y) a)))((((^z.z)(a a))((^x1.x1) a))(((^y1.y1)(a a))((^z1.z1) a)))) 10. ==[ alpha ]==> ((((a a) a)((a a)((^x.x) a)))((((^y.y)(a a))((^z.z) a))(((^x1.x1)(a a))((^y1.y1) a)))) 11. ==[ beta ]==> ((((a a) a)((a a) a))((((^y.y)(a a))((^z.z) a))(((^x1.x1)(a a))((^y1.y1) a)))) 12. ==[ alpha ]==> ((((a a) a)((a a) a))((((^x.x)(a a))((^y.y) a))(((^z.z)(a a))((^x1.x1) a)))) 13. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)((^y.y) a))(((^z.z)(a a))((^x1.x1) a)))) 14. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)((^x.x) a))(((^y.y)(a a))((^z.z) a)))) 15. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)(((^y.y)(a a))((^z.z) a)))) 16. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a) a)(((^x.x)(a a))((^y.y) a)))) 17. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)((a a)((^y.y) a)))) 18. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a) a)((a a)((^x.x) a)))) 19. ==[ beta ]==> ((((a a) a)((a a) a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 184527/21479742. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.(b z))) 3. ==[ eta ]==> (((a (^x.x))((^y.y) b)) b) 4. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 184528/21480237. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 184529/21481173. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 184530/21481224. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((a a) a)(a (^x1.x1)))) 3. ==[ eta ]==> ((^y.(^z.z))(((a a) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184531/21481758. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.y1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184532/21481947. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.b))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.b))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.b))) REDUCED to normal form. ------ 184533/21482043. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 184534/21482280. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((y y) y))) REDUCED to normal form. ------ 184535/21483054. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.(y1 y1)))) REDUCED to normal form. ------ 184536/21483243. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 184537/21483324. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.a))) REDUCED to normal form. ------ 184538/21483339. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184539/21483468. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.c)) 5. ==[ beta ]==> (((^y.y) b)(^z.c)) 6. ==[ alpha ]==> (((^x.x) b)(^y.c)) 7. ==[ beta ]==> (b (^y.c)) 8. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 184540/21483522. ------ 1. ==[ start ]==> (((a b)(b a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 184541/21483630. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(z z))) REDUCED to normal form. ------ 184542/21483657. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.x1)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.z)) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 184543/21483669. ------ 1. ==[ start ]==> ((a a)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a a)(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a a)(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 184544/21483696. ------ 1. ==[ start ]==> ((a (a a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 184545/21483723. ------ 1. ==[ start ]==> ((a b)((b a)(a b))) REDUCED to normal form. ------ 184546/21483777. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a a))((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 184547/21483804. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a b)(b a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a b)(b a))) REDUCED to normal form. ------ 184548/21483939. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 184549/21483957. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 184550/21483966. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 184551/21484002. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((^y.a)((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((^x.a)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 184552/21484029. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184553/21484083. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (a (((a a)(a a))(^y.(y y)))) 6. ==[ alpha ]==> (a (((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 184554/21484092. ------ 1. ==[ start ]==> (((a a)(^b.a))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 184555/21484110. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 184556/21484119. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 184557/21484146. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 184558/21484164. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((b a)(^y.b))) REDUCED to normal form. ------ 184559/21484254. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.b)(b a))) 3. ==[ beta ]==> ((a a)((^y.b)(b a))) 4. ==[ alpha ]==> ((a a)((^x.b)(b a))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 184560/21484272. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(y y))(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(x x))(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a)(^y.(^z.(^x1.x1))))(((a a) a)(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((a a) a)(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 184561/21484299. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184562/21484335. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a b)((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((a b)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 184563/21484362. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.a)(b (^y.y)))) 3. ==[ beta ]==> (((a (a a)) a) a) REDUCED to normal form. ------ 184564/21484389. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 184565/21484407. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 184566/21484416. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (a (^z.z)))) REDUCED to normal form. ------ 184567/21484443. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^y1.y1)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 184568/21484461. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a a)(a a))(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> (((a a)(a a))(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> (((a a)(a a))((^y.y) b)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) b)) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 184569/21484488. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 184570/21484578. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((b b)((^y.(^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((b b)((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 184571/21484713. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 184572/21484740. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 184573/21484767. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 184574/21484848. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 184575/21484911. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 184576/21484938. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(((a a)(a a)) a)) REDUCED to normal form. ------ 184577/21484965. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> ((a a)(((^y.y) b)(a (a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)(a (a a)))) 7. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 184578/21484992. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 184579/21485019. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((b a)((a a) a))) 5. ==[ beta ]==> ((a a)((b a)((a a) a))) REDUCED to normal form. ------ 184580/21485046. ------ 1. ==[ start ]==> ((a ((a a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a ((a a) a))(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 184581/21485280. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(y y)))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 184582/21485298. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(^x1.x1)) a)(^y1.y1))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a)(^y1.y1))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a)(^x1.x1))) 7. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.x1))) 8. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.z))) 9. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 10. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 11. ==[ beta ]==> ((a a)(^y.y)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 184583/21485379. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.b))(b (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.b))(b (^y.(y y)))) REDUCED to normal form. ------ 184584/21485550. ------ 1. ==[ start ]==> (((^a.b) a)((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.a)(b a))) 3. ==[ beta ]==> (b ((^y.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 184585/21485568. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 184586/21485730. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.y))((b (^z.z)) b)) 3. ==[ beta ]==> (b ((b (^z.z)) b)) 4. ==[ alpha ]==> (b ((b (^x.x)) b)) REDUCED to normal form. ------ 184587/21485757. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.x)(a b))(((a a)(a a)) c)) 3. ==[ beta ]==> ((a b)(((a a)(a a)) c)) REDUCED to normal form. ------ 184588/21485766. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 184589/21485820. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 184590/21485874. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 184591/21485901. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 184592/21485928. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 184593/21486072. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(b (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(b (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (b (^z.z)))) 6. ==[ alpha ]==> (((^x.x) a)(b (b (^y.y)))) 7. ==[ beta ]==> (a (b (b (^y.y)))) 8. ==[ alpha ]==> (a (b (b (^x.x)))) REDUCED to normal form. ------ 184594/21486099. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 184595/21486126. ------ 1. ==[ start ]==> (((a b)(a a))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(a a))((b (^x.x))(a a))) REDUCED to normal form. ------ 184596/21486153. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> ((a (a a))(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 184597/21486162. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a)) c)) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a)) c)) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a)) c)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184598/21486540. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 184599/21486549. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 184600/21486576. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 184601/21486765. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z))(b a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184602/21487008. ------ 1. ==[ start ]==> (((a b) c)((^d.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 184603/21487035. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 184604/21487062. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 184605/21487116. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 184606/21487197. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184607/21487341. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 184608/21487368. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((b a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((b a)(a (a a)))) REDUCED to normal form. ------ 184609/21487395. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a b))(((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 184610/21487422. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x)(a a))((a a) a))) 3. ==[ beta ]==> (((a (a a))((a a) a))((a a)((a a) a))) REDUCED to normal form. ------ 184611/21487449. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)(a b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a b)(a b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(a b))) 7. ==[ beta ]==> ((^y.y)((a b)(a b))) 8. ==[ alpha ]==> ((^x.x)((a b)(a b))) 9. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 184612/21487476. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((a a) a)((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 184613/21487503. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a b) a)((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (((a b) a)((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> (((a b) a)((a a)(^y.y))) 8. ==[ alpha ]==> (((a b) a)((a a)(^x.x))) REDUCED to normal form. ------ 184614/21487530. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((a (a a))(b a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a (a a))(b a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a (a a))(b a))) REDUCED to normal form. ------ 184615/21487557. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 184616/21487584. ------ 1. ==[ start ]==> ((a (b a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))((a (^x.x))((^y.y) b))) 3. ==[ beta ]==> ((a (b a))((a (^x.x)) b)) REDUCED to normal form. ------ 184617/21487674. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (((^z.z) b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b (((^x.x) b)(^y.(^z.z)))) 7. ==[ beta ]==> (b (b (^y.(^z.z)))) 8. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 184618/21487755. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 184619/21487818. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.b)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) b) REDUCED to normal form. ------ 184620/21487863. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a)(^y.(^z.z))) 8. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 184621/21487926. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 184622/21487944. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.y))(^z.z))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.y))(^z.z))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 184623/21487953. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 184624/21488007. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 184625/21488025. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y) b) b)) 3. ==[ beta ]==> (b (((^y.y) b) b)) 4. ==[ alpha ]==> (b (((^x.x) b) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 184626/21488034. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 184627/21488061. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 184628/21488313. ------ 1. ==[ start ]==> (((a b)(a (a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (a a)))(b ((^x.x) b))) 3. ==[ beta ]==> (((a b)(a (a a)))(b b)) REDUCED to normal form. ------ 184629/21488340. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(a ((a a)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(a ((a a)(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(a ((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 184630/21488367. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(b (a a))) REDUCED to normal form. ------ 184631/21488421. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((b a)((^z.z) a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((b a) a)) REDUCED to normal form. ------ 184632/21488700. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1) b)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) b)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184633/21488709. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 184634/21488727. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 184635/21488736. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 184636/21488754. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.a))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 184637/21488808. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))((a a)(^y.(^z.z)))) 10. ==[ alpha ]==> (((a a)(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 184638/21488817. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 184639/21488844. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.b)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)((a a) a))) 5. ==[ beta ]==> ((^y.b)((^z.b)((a a) a))) 6. ==[ alpha ]==> ((^x.b)((^y.b)((a a) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 184640/21488889. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (b (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 184641/21488898. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 184642/21488925. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(((a a)(^z.z))((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 184643/21488952. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 184644/21488997. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184645/21489006. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 184646/21489024. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a) b) a)) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) b) a)) 3. ==[ beta ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 184647/21489303. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184648/21489312. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 184649/21489339. ------ 1. ==[ start ]==> ((a ((^a.a) b))(a ((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(a ((^y.y) b))) 3. ==[ beta ]==> ((a b)(a ((^y.y) b))) 4. ==[ alpha ]==> ((a b)(a ((^x.x) b))) 5. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 184650/21489348. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.b) a)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) a)) 3. ==[ beta ]==> ((^y.y)((^z.z) a)) 4. ==[ alpha ]==> ((^x.x)((^y.y) a)) 5. ==[ beta ]==> ((^y.y) a) 6. ==[ alpha ]==> ((^x.x) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 184651/21489375. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.(^y2.y2))) b)) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.(^y2.y2))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) b) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) b) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184652/21489627. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 184653/21489654. ------ 1. ==[ start ]==> ((((^a.a) b) a)(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)(a (^y.y))) 3. ==[ beta ]==> ((b a)(a (^y.y))) 4. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 184654/21489672. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.x1))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 184655/21489681. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 184656/21489699. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((b a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 184657/21489753. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 184658/21489789. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.b)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.b)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184659/21489816. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 184660/21489834. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> (b ((^y.y)(^z.b))) 6. ==[ alpha ]==> (b ((^x.x)(^y.b))) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 184661/21489843. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 184662/21489870. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(((^x1.x1)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((^x1.x1)(a a)))) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((^z.z)(a a)))) 9. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 184663/21489897. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 184664/21489942. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184665/21489951. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) REDUCED to normal form. ------ 184666/21489978. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 184667/21490230. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(b (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(b (b a))) REDUCED to normal form. ------ 184668/21490284. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((b a)(a a))) REDUCED to normal form. ------ 184669/21490311. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((b (a a))(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((b (a a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 184670/21490338. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(a a))((^y.y) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a)((^y.y) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a a)((^x.x) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a a) a)) REDUCED to normal form. ------ 184671/21490617. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1)(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184672/21490653. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.b)(a (a a)))) 3. ==[ beta ]==> ((b b)((^y.b)(a (a a)))) 4. ==[ alpha ]==> ((b b)((^x.b)(a (a a)))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 184673/21490725. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a (a a))(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.b))) 5. ==[ beta ]==> ((a (a a))(^y.b)) 6. ==[ alpha ]==> ((a (a a))(^x.b)) REDUCED to normal form. ------ 184674/21490734. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a b)(a b))) REDUCED to normal form. ------ 184675/21490761. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.a)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.a)((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 184676/21490779. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 184677/21490860. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a)(^y.y)) b)) 3. ==[ beta ]==> (b (((a a)(^y.y)) b)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) b)) REDUCED to normal form. ------ 184678/21490869. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 184679/21490923. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 184680/21490977. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 184681/21491004. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.b)(^x1.b))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.b)(^x1.b))) 7. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 184682/21491031. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) a) REDUCED to normal form. ------ 184683/21491067. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 184684/21491094. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(a (b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(a (b a))) 3. ==[ beta ]==> (((a (^x.x)) b)(a (b a))) REDUCED to normal form. ------ 184685/21491121. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 184686/21491148. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))(b a))((a a)(a (^y.y)))) 4. ==[ alpha ]==> (((a (a a))(b a))((a a)(a (^x.x)))) REDUCED to normal form. ------ 184687/21491175. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a b)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^y.y))((a b)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((a b)((^y.y) a))) 7. ==[ beta ]==> (((a a)(^x.x))((a b) a)) REDUCED to normal form. ------ 184688/21491202. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 184689/21491229. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a b)(a b))(^y.y)) 8. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 184690/21491256. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a (a a))((a a) a))) 3. ==[ beta ]==> (((a a)((a a) a))((a (a a))((a a) a))) REDUCED to normal form. ------ 184691/21491283. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (a b))) REDUCED to normal form. ------ 184692/21491337. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 184693/21491589. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 184694/21491733. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 184695/21491760. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(x x))(^y.a))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.a)(^y.a))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)(^y.a))) 5. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 184696/21491886. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(a a)) b)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(a a)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(a a)) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 184697/21492111. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(a a))(a a))) 3. ==[ beta ]==> ((b (^y.a))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(a a))(a a))) 5. ==[ beta ]==> ((b (^x.a))(a a)) REDUCED to normal form. ------ 184698/21492138. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 184699/21492498. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(b (a b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(b (a b))) 3. ==[ beta ]==> ((b ((^y.y) a))(b (a b))) 4. ==[ alpha ]==> ((b ((^x.x) a))(b (a b))) 5. ==[ beta ]==> ((b a)(b (a b))) REDUCED to normal form. ------ 184700/21492525. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(a ((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a (a a))) REDUCED to normal form. ------ 184701/21492579. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 184702/21492750. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)(^x1.x1))) 3. ==[ beta ]==> (b ((a b)(^x1.x1))) 4. ==[ alpha ]==> (b ((a b)(^x.x))) REDUCED to normal form. ------ 184703/21492858. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184704/21493083. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 184705/21493110. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1)(^x2.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)(^x2.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184706/21493155. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a) b)) 3. ==[ beta ]==> (b ((^z.a) b)) 4. ==[ alpha ]==> (b ((^x.a) b)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 184707/21493272. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.a))) REDUCED to normal form. ------ 184708/21493299. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a (^z.b))) 3. ==[ beta ]==> ((b (^y.(y y)))(a (^z.b))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.b))) REDUCED to normal form. ------ 184709/21493326. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^c.a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 184710/21493380. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) a))) 7. ==[ beta ]==> ((^y.(y y))((^z.z) a)) 8. ==[ alpha ]==> ((^x.(x x))((^y.y) a)) 9. ==[ beta ]==> (((^y.y) a)((^y.y) a)) 10. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 11. ==[ beta ]==> (a ((^y.y) a)) 12. ==[ alpha ]==> (a ((^x.x) a)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184711/21493398. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.(z z)))) REDUCED to normal form. ------ 184712/21493578. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c (a (a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (a (a a)))) REDUCED to normal form. ------ 184713/21493605. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 8. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 184714/21493632. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a ((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a ((a a) a))) REDUCED to normal form. ------ 184715/21493686. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a))(a (^x1.x1)))) REDUCED to normal form. ------ 184716/21493713. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> ((b (a (a a)))(a ((^y.y) a))) 6. ==[ alpha ]==> ((b (a (a a)))(a ((^x.x) a))) 7. ==[ beta ]==> ((b (a (a a)))(a a)) REDUCED to normal form. ------ 184717/21493740. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (^y.y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 184718/21493812. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 184719/21493830. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^z.(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 184720/21494217. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(z z))(a a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(a a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(a a))) 5. ==[ beta ]==> (b ((^y.(y y))(a a))) 6. ==[ alpha ]==> (b ((^x.(x x))(a a))) 7. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 184721/21494235. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 184722/21494244. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 184723/21494262. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 184724/21494271. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 184725/21494289. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(y y)))) 5. ==[ beta ]==> ((a a)(^y.(y y))) 6. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 184726/21494343. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y) a) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y) a) b)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x) a) b)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a b)) REDUCED to normal form. ------ 184727/21494379. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184728/21494406. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.(y1 y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 184729/21494424. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(y y)) a)) 3. ==[ beta ]==> (b ((^y.(y y)) a)) 4. ==[ alpha ]==> (b ((^x.(x x)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 184730/21494487. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (^z.a))) REDUCED to normal form. ------ 184731/21494532. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184732/21494568. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 184733/21494595. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y) a)) 5. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 184734/21494649. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184735/21494676. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.a)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.a)) REDUCED to normal form. ------ 184736/21494694. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 184737/21494712. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (^y.y))(a a))) REDUCED to normal form. ------ 184738/21494739. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(a (^z.z)))) REDUCED to normal form. ------ 184739/21494766. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(c a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(c a)) 3. ==[ beta ]==> ((a (b (^y.y)))(c a)) 4. ==[ alpha ]==> ((a (b (^x.x)))(c a)) REDUCED to normal form. ------ 184740/21494793. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b b)) REDUCED to normal form. ------ 184741/21494820. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a c)) 5. ==[ beta ]==> (((^y.y) b)(a c)) 6. ==[ alpha ]==> (((^x.x) b)(a c)) 7. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 184742/21494847. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b (a a))) REDUCED to normal form. ------ 184743/21494874. ------ 1. ==[ start ]==> (((a b)(b a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(a (a (^x.x)))) REDUCED to normal form. ------ 184744/21494901. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a)(a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a)(a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)(a a))) REDUCED to normal form. ------ 184745/21494928. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b a)) REDUCED to normal form. ------ 184746/21494982. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a (a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (a a))) REDUCED to normal form. ------ 184747/21495009. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a a)) 5. ==[ beta ]==> ((b (^y.y))(a a)) 6. ==[ alpha ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 184748/21495345. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ eta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 184749/21500691. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^b.(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 184750/21506046. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> ((^x.(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184751/21506364. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a))) b) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z))) b) 3. ==[ beta ]==> ((b ((^y.y)(^z.z))) b) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y))) b) 5. ==[ beta ]==> ((b (^y.y)) b) 6. ==[ alpha ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 184752/21506388. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184753/21506469. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184754/21506631. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (^y.(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> (^x.(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (^x.(a (b (^z.z)))) 6. ==[ alpha ]==> (^x.(a (b (^y.y)))) REDUCED to normal form. ------ 184755/21506703. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(a (^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> ((^y.y)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 184756/21506706. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 184757/21506973. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.b)(b a))) 3. ==[ beta ]==> (((^y.b)(b a))(((^y.b)(b a))((^y.b)(b a)))) 4. ==[ alpha ]==> (((^x.b)(b a))(((^y.b)(b a))((^z.b)(b a)))) 5. ==[ beta ]==> (b (((^y.b)(b a))((^z.b)(b a)))) 6. ==[ alpha ]==> (b (((^x.b)(b a))((^y.b)(b a)))) 7. ==[ beta ]==> (b (b ((^y.b)(b a)))) 8. ==[ alpha ]==> (b (b ((^x.b)(b a)))) 9. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 184758/21507129. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 184759/21508269. ------ 1. ==[ start ]==> ((^a.(a b))((^c.a)(b a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.a)(b a))) 3. ==[ beta ]==> (((^y.a)(b a)) b) 4. ==[ alpha ]==> (((^x.a)(b a)) b) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 184760/21509538. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((((^z.a)((^x1.x1) b))((^z.a)((^x1.x1) b)))(^y.y)) 4. ==[ alpha ]==> ((((^x.a)((^y.y) b))((^z.a)((^x1.x1) b)))(^y1.y1)) 5. ==[ beta ]==> ((a ((^z.a)((^x1.x1) b)))(^y1.y1)) 6. ==[ alpha ]==> ((a ((^x.a)((^y.y) b)))(^z.z)) 7. ==[ beta ]==> ((a a)(^z.z)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 184761/21510294. ------ 1. ==[ start ]==> ((^a.(b a))(c (^b.b))) 2. ==[ alpha ]==> ((^x.(b x))(c (^y.y))) 3. ==[ eta ]==> (b (c (^y.y))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 184762/21511053. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(a a)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 184763/21512049. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 184764/21512052. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^b.(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.z))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 184765/21512061. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) b))) 5. ==[ beta ]==> (^y.((^z.z) b)) 6. ==[ alpha ]==> (^x.((^y.y) b)) 7. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 184766/21514128. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184767/21515022. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((b a)(^y.((^z.z)(a a)))) 6. ==[ alpha ]==> ((b a)(^x.((^y.y)(a a)))) 7. ==[ beta ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 184768/21515238. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 184769/21516183. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.((a a) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.((a a) a))) REDUCED to normal form. ------ 184770/21516345. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.a))) REDUCED to normal form. ------ 184771/21516531. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((^z.(^x1.x1))(a a))(((^z.(^x1.x1))(a a))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.(^x1.x1))(a a))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(a a))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(a a))(^x1.x1))) 7. ==[ beta ]==> (((^y.(^z.z))(a a))(^x1.x1)) 8. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184772/21517137. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(y (y y)))) 3. ==[ beta ]==> (b (^y.(y (y y)))) 4. ==[ alpha ]==> (b (^x.(x (x x)))) REDUCED to normal form. ------ 184773/21517404. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a ((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184774/21517407. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 184775/21517479. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.z))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.z))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 184776/21517533. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(a (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(a (^z.z)))) 7. ==[ beta ]==> (b (^y.(a (^z.z)))) 8. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 184777/21517587. ------ 1. ==[ start ]==> (((a b)(b a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 184778/21517641. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 184779/21517695. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.x1))) REDUCED to normal form. ------ 184780/21517722. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 184781/21517752. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 184782/21517779. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 184783/21517806. ------ 1. ==[ start ]==> (((^a.a)(a a))((b a)(a b))) 2. ==[ alpha ]==> (((^x.x)(a a))((b a)(a b))) 3. ==[ beta ]==> ((a a)((b a)(a b))) REDUCED to normal form. ------ 184784/21517833. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 184785/21517887. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a b)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184786/21517914. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 184787/21517941. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x))((^z.z) b)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 9. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 184788/21517968. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 184789/21517995. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a (^x.a))(a (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.a))(a (b (^y.y)))) REDUCED to normal form. ------ 184790/21518040. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 184791/21518067. ------ 1. ==[ start ]==> ((a ((^a.a) a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 184792/21518112. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 184793/21518139. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((a a)((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((a a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 184794/21518166. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 184795/21518193. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 184796/21518310. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 184797/21518337. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.b)(b a))) 3. ==[ beta ]==> ((a (a (a a))) b) REDUCED to normal form. ------ 184798/21518409. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a (a a))(^y.(a a)))) 3. ==[ beta ]==> ((a b)((a (a a))(^y.(a a)))) 4. ==[ alpha ]==> ((a b)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 184799/21518490. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 184800/21518517. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 184801/21518544. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z) b)) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y) b)) 5. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 184802/21518634. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 184803/21518913. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 184804/21518949. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 (^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1))) a)) 5. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1))) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) a)) 7. ==[ beta ]==> ((^y.(y (^z.z))) a) 8. ==[ alpha ]==> ((^x.(x (^y.y))) a) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 184805/21519156. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 7. ==[ beta ]==> ((a a)((^y.y)(a a))) 8. ==[ alpha ]==> ((a a)((^x.x)(a a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 184806/21519210. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a) a)(b a))) 5. ==[ beta ]==> (a (((a a) a)(b a))) REDUCED to normal form. ------ 184807/21519291. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) a)((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 184808/21519318. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 184809/21519381. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 184810/21519408. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184811/21519435. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 184812/21519471. ------ 1. ==[ start ]==> (((a a)((a a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(a (a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(a (a a))) REDUCED to normal form. ------ 184813/21519498. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 184814/21519579. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 184815/21519606. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 184816/21519633. ------ 1. ==[ start ]==> ((a (a b))((^c.a)(b a))) 2. ==[ alpha ]==> ((a (a b))((^x.a)(b a))) 3. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 184817/21519786. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> ((((a a) a) b)((^y.y) a)) 4. ==[ alpha ]==> ((((a a) a) b)((^x.x) a)) 5. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 184818/21519813. ------ 1. ==[ start ]==> (((a b) a)((b (^a.a)) b)) 2. ==[ alpha ]==> (((a b) a)((b (^x.x)) b)) REDUCED to normal form. ------ 184819/21519840. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(a a)) c)) REDUCED to normal form. ------ 184820/21520038. ------ 1. ==[ start ]==> (((a a)(a b))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.a))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 184821/21520065. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 184822/21520092. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.z))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^z.z))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 184823/21520119. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 184824/21520236. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((^y.(a a))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(a a))(a (^y.y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184825/21520263. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> (((^y.y) b)((^z.z) a)) 6. ==[ alpha ]==> (((^x.x) b)((^y.y) a)) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 184826/21520317. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((b a)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((b a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((b a)(^y.y)) 10. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 184827/21520398. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 184828/21520452. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(b a))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(b a))) 7. ==[ beta ]==> ((a a)((^y.y)(b a))) 8. ==[ alpha ]==> ((a a)((^x.x)(b a))) 9. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 184829/21520479. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 184830/21520533. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.y1))((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.y1))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.x1))((a a)(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))((a a)(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((a a)(a a)))) 9. ==[ beta ]==> ((^y.y)((a (^z.z))((a a)(a a)))) 10. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(a a)))) 11. ==[ beta ]==> ((a (^y.y))((a a)(a a))) 12. ==[ alpha ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 184831/21520596. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 184832/21520623. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 184833/21520650. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.a))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.a))) REDUCED to normal form. ------ 184834/21520686. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 184835/21520767. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(a a))(a b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a))(a b))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 184836/21520794. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.b)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 184837/21520839. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(^a.a))(^d.a))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (b ((^y.y)(^z.a))) 6. ==[ alpha ]==> (b ((^x.x)(^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 184838/21520848. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 184839/21520875. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 184840/21520902. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 184841/21521316. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 184842/21521658. ------ 1. ==[ start ]==> ((a (b a))(c (^b.b))) 2. ==[ alpha ]==> ((a (b a))(c (^x.x))) REDUCED to normal form. ------ 184843/21521892. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a b)(^y.b))) REDUCED to normal form. ------ 184844/21522000. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(a a)))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 184845/21522027. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 184846/21522081. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 184847/21522108. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) b) b)) 3. ==[ beta ]==> (((a b)(^x.(x x)))(b b)) REDUCED to normal form. ------ 184848/21522135. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z))) c)) REDUCED to normal form. ------ 184849/21522225. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 184850/21522252. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 184851/21522306. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 184852/21522360. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a) a)(^x.x)) a) REDUCED to normal form. ------ 184853/21522387. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 184854/21522504. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((b a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((b a)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)((^x1.x1) a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184855/21522585. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a b)((a a) a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a b)((a a) a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a b)((a a) a))) 5. ==[ beta ]==> ((a a)((a b)((a a) a))) REDUCED to normal form. ------ 184856/21522666. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((a (a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 184857/21522783. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b (^z.z))) REDUCED to normal form. ------ 184858/21522810. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) REDUCED to normal form. ------ 184859/21522891. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 184860/21522918. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a b)(^z.a))) 5. ==[ beta ]==> ((^y.b)((a b)(^z.a))) 6. ==[ alpha ]==> ((^x.b)((a b)(^y.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 184861/21522972. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(a a))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 184862/21523080. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.x1))) REDUCED to normal form. ------ 184863/21523116. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 184864/21523143. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 184865/21523224. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 184866/21523251. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.b)(^y.a))) 3. ==[ beta ]==> ((((a a) a)((a a) a)) b) REDUCED to normal form. ------ 184867/21523278. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(^z.b))) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 184868/21523305. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 184869/21523386. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 184870/21523413. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)(^z.z))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 184871/21523422. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.z) b))) 3. ==[ beta ]==> ((^y.y)(a ((^z.z) b))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y) b))) 5. ==[ beta ]==> (a ((^y.y) b)) 6. ==[ alpha ]==> (a ((^x.x) b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 184872/21523449. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.(^x2.x2)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (^z1.(^x2.x2)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 184873/21523584. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a) a)((a a) a))) 3. ==[ beta ]==> (b (((a a) a)((a a) a))) REDUCED to normal form. ------ 184874/21523692. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.z1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184875/21523755. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 184876/21523782. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((b a)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 184877/21523863. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))((a b)(^y.(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 184878/21523890. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a) a)(^y.a))) REDUCED to normal form. ------ 184879/21523917. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.b)) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.b)) REDUCED to normal form. ------ 184880/21523944. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 184881/21524025. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 184882/21524052. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((b (^y.y))((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 184883/21524142. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (b a))((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (b a))((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 184884/21524169. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) b) REDUCED to normal form. ------ 184885/21524223. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.x)) REDUCED to normal form. ------ 184886/21524250. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> (((a b)((a a) a))((^y.(a a))(^y.(a a)))) 4. ==[ alpha ]==> (((a b)((a a) a))((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a b)((a a) a))(a a)) REDUCED to normal form. ------ 184887/21524277. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 184888/21524448. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(a (a a)))) 5. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 184889/21524583. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 184890/21524727. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a b)(^y.(y y)))) 3. ==[ beta ]==> ((b b)((a b)(^y.(y y)))) 4. ==[ alpha ]==> ((b b)((a b)(^x.(x x)))) REDUCED to normal form. ------ 184891/21524754. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 184892/21524808. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.b))) REDUCED to normal form. ------ 184893/21524835. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(a a)))) REDUCED to normal form. ------ 184894/21524916. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((b a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((b a) a)) REDUCED to normal form. ------ 184895/21524943. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 184896/21525411. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 184897/21525492. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 184898/21525879. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c (a b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(c (a b))) 3. ==[ beta ]==> ((b (^y.y))(c (a b))) 4. ==[ alpha ]==> ((b (^x.x))(c (a b))) REDUCED to normal form. ------ 184899/21525906. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(b ((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)(b ((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.x)(b ((^y.y)(a a)))) 5. ==[ beta ]==> (b ((^y.y)(a a))) 6. ==[ alpha ]==> (b ((^x.x)(a a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 184900/21525942. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 184901/21525960. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(a a))(a a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(a a))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(a a))(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(a a))) REDUCED to normal form. ------ 184902/21525969. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(a a)) b)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 184903/21526041. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (a a)))) 5. ==[ beta ]==> (b ((^y.y)(a (a a)))) 6. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 184904/21526149. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184905/21526185. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> ((b (^x.a))((a a)(^z.z))) 6. ==[ alpha ]==> ((b (^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 184906/21526212. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 184907/21526275. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 184908/21526302. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(^z.z))) 9. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 10. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 184909/21526329. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)((a a) a))) 5. ==[ beta ]==> ((a b)((^y.a)((a a) a))) 6. ==[ alpha ]==> ((a b)((^x.a)((a a) a))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 184910/21526356. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 184911/21526383. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((b a)((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> ((b a)((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> ((b a)((^y.y)(a a))) 8. ==[ alpha ]==> ((b a)((^x.x)(a a))) 9. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 184912/21526410. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 184913/21526437. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 184914/21526464. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(a b))((^y.a)(^z.a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.a))) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 184915/21526491. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 184916/21526545. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 184917/21526572. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.b))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 184918/21526599. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 184919/21526743. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.z))) 9. ==[ beta ]==> (a ((^y.y)(^z.z))) 10. ==[ alpha ]==> (a ((^x.x)(^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 184920/21527049. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((a a) a) b)) 3. ==[ beta ]==> (((^y.y) a)(((a a) a) b)) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a) b)) 5. ==[ beta ]==> (a (((a a) a) b)) REDUCED to normal form. ------ 184921/21527148. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(c ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(c ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b b)(c ((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b b)(c ((^x.x)(^y.y)))) 9. ==[ beta ]==> ((b b)(c (^y.y))) 10. ==[ alpha ]==> ((b b)(c (^x.x))) REDUCED to normal form. ------ 184922/21527229. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((a a) a)(a a))) 3. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 184923/21527238. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 184924/21527265. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z)) c)) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 184925/21527337. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184926/21527400. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((a a) a)(^y.y))) REDUCED to normal form. ------ 184927/21527454. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.a))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.a))) 7. ==[ beta ]==> ((a (a a))(^y.a)) 8. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 184928/21527490. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 184929/21527517. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 184930/21527544. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.y)((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)((a a) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)((a a) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a a) a)) REDUCED to normal form. ------ 184931/21527571. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)(^y.y))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 184932/21527598. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 184933/21527625. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))(^y.a))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.a)(^y.a))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(^y.a))) 5. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 184934/21527652. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 184935/21527679. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 184936/21527706. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.a)) REDUCED to normal form. ------ 184937/21527886. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 184938/21527895. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 184939/21528291. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (a a))(^z.z))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))(^z.z))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))(^y.y))) 5. ==[ beta ]==> (b ((a (a a))(^y.y))) 6. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 184940/21528318. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.(^z.z)))) REDUCED to normal form. ------ 184941/21528345. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 184942/21528453. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z)) c)) 5. ==[ beta ]==> ((^y.y)((a (^z.z)) c)) 6. ==[ alpha ]==> ((^x.x)((a (^y.y)) c)) 7. ==[ beta ]==> ((a (^y.y)) c) 8. ==[ alpha ]==> ((a (^x.x)) c) REDUCED to normal form. ------ 184943/21528498. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(a (a (a a)))) 3. ==[ beta ]==> (b (a (a (a a)))) REDUCED to normal form. ------ 184944/21528561. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 184945/21528642. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 184946/21528669. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(^y.a))) REDUCED to normal form. ------ 184947/21528723. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184948/21528741. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b (a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (a (^y.y)))) REDUCED to normal form. ------ 184949/21528768. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 184950/21528813. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 184951/21528840. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a (^z.a))) 3. ==[ beta ]==> ((a (b (^y.y)))(a (^z.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.a))) REDUCED to normal form. ------ 184952/21528867. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 184953/21528894. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(a (^z.z)))) 7. ==[ beta ]==> (b ((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 9. ==[ beta ]==> (b (a (^y.y))) 10. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 184954/21528921. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 184955/21528948. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 184956/21528975. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b (^z.z))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b (^z.z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 184957/21529002. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 184958/21529056. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 184959/21529083. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a (^x1.x1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a (^x1.x1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a (^z.z))) 5. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 184960/21534459. ------ 1. ==[ start ]==> ((^a.(^b.b))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((^x.(^y.y))(^x1.x1)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184961/21540129. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184962/21540447. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a))) c) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z))) c) 3. ==[ beta ]==> ((b ((^y.y)(^z.z))) c) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y))) c) 5. ==[ beta ]==> ((b (^y.y)) c) 6. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 184963/21540807. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.a)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 184964/21540966. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 184965/21541680. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(x1 (x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 (x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(z (z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 7. ==[ beta ]==> (^y.(y (y (^z.z)))) 8. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 184966/21542103. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(z (^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 8. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 184967/21542181. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 184968/21542748. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.b)(^x1.(^y1.y1)))((^z.b)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(((^y.b)(^z.(^x1.x1)))((^y1.b)(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^x.(b ((^y1.b)(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (^x.(b ((^y.b)(^z.(^x1.x1))))) 7. ==[ beta ]==> (^x.(b b)) REDUCED to normal form. ------ 184969/21542922. ------ 1. ==[ start ]==> (((^a.b) b)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) b)(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((^x.b) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.b) b)(^y.(^z.z))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 184970/21543630. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((((^z.z) a)(^x1.x1))(((^z.z) a)(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> (((((^x.x) a)(^y.y))(((^z.z) a)(^x1.x1)))(^y1.y1)) 5. ==[ beta ]==> (((a (^y.y))(((^z.z) a)(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.x))(((^y.y) a)(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (((a (^x.x))(a (^z.z)))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 184971/21544083. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 184972/21545826. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184973/21545829. ------ 1. ==[ start ]==> ((a (^b.b))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) y))) 3. ==[ eta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 184974/21546153. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 184975/21546459. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 184976/21546477. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 184977/21548220. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 184978/21548673. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 184979/21549114. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(a a)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(a a)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 184980/21549381. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.b) b)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.b) b)) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.b) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184981/21549555. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 184982/21550104. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.((a a) a))) REDUCED to normal form. ------ 184983/21550200. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 184984/21550623. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((^z.z)(^x1.x1))(^y1.y1))((((^z.z)(^x1.x1))(^y1.y1))(^y.y))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((((^x1.x1)(^y1.y1))(^z1.z1))(^x2.x2))) 5. ==[ beta ]==> (((^y.y)(^z.z))((((^x1.x1)(^y1.y1))(^z1.z1))(^x2.x2))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((((^z.z)(^x1.x1))(^y1.y1))(^z1.z1))) 7. ==[ beta ]==> ((^y.y)((((^z.z)(^x1.x1))(^y1.y1))(^z1.z1))) 8. ==[ alpha ]==> ((^x.x)((((^y.y)(^z.z))(^x1.x1))(^y1.y1))) 9. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.x1))(^y1.y1)) 10. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.x1)) 11. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 12. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 13. ==[ beta ]==> ((^y.y)(^z.z)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184985/21551229. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.(z z)))) 3. ==[ beta ]==> (b (^y.(^z.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 184986/21551337. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 184987/21551496. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 184988/21551499. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.a))) REDUCED to normal form. ------ 184989/21551571. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.c)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.c)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.c)) REDUCED to normal form. ------ 184990/21551625. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 184991/21551679. ------ 1. ==[ start ]==> (((a b)(b a))(^c.b)) 2. ==[ alpha ]==> (((a b)(b a))(^x.b)) REDUCED to normal form. ------ 184992/21551733. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.z)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 184993/21551814. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.a)) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 184994/21551862. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (a (((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (a (((^x.x) b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (a (b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (a (b ((^x.x)(^y.y)))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 184995/21551889. ------ 1. ==[ start ]==> (((a a) a)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 184996/21551916. ------ 1. ==[ start ]==> (((a a)(^a.a))((b a)(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))((b a)(a b))) REDUCED to normal form. ------ 184997/21551943. ------ 1. ==[ start ]==> (((^a.a) b)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (b (((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (b (((a a)(^x.x))(a a))) REDUCED to normal form. ------ 184998/21551970. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 184999/21551997. ------ 1. ==[ start ]==> (((a a) b)((a b)(b a))) REDUCED to normal form. ------ 185000/21552024. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 185001/21552051. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1) b)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) b)) 7. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 185002/21552078. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 185003/21552132. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 185004/21552177. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.a)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 185005/21552204. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 (^z1.z1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 (^z1.z1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 185006/21552339. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 185007/21552357. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((b a)(^y.b))) 3. ==[ beta ]==> (((a a) a)((b a)(^y.b))) 4. ==[ alpha ]==> (((a a) a)((b a)(^x.b))) REDUCED to normal form. ------ 185008/21552384. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 185009/21552447. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b)(b a))) 3. ==[ beta ]==> ((^y.(y y))((^z.b)(b a))) 4. ==[ alpha ]==> ((^x.(x x))((^y.b)(b a))) 5. ==[ beta ]==> (((^y.b)(b a))((^y.b)(b a))) 6. ==[ alpha ]==> (((^x.b)(b a))((^y.b)(b a))) 7. ==[ beta ]==> (b ((^y.b)(b a))) 8. ==[ alpha ]==> (b ((^x.b)(b a))) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 185010/21552474. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.a)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)(a (^y.(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185011/21552528. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 7. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 8. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 9. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 185012/21552555. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((a (a a))((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 185013/21552582. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185014/21552636. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> (((a a)(a a))((^z.z)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 185015/21552681. ------ 1. ==[ start ]==> (((a a)(a (a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(a (a a)))((b (^x.x)) c)) REDUCED to normal form. ------ 185016/21552933. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185017/21552996. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(c (b (^z.z)))) 3. ==[ beta ]==> ((a (^y.a))(c (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.a))(c (b (^y.y)))) REDUCED to normal form. ------ 185018/21553023. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 185019/21553050. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)(a (a (a (^z.z))))) 6. ==[ alpha ]==> ((^x.x)(a (a (a (^y.y))))) 7. ==[ beta ]==> (a (a (a (^y.y)))) 8. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 185020/21553347. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (b ((^y.y)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (b ((^x.x)(a (^y.(^z.z))))) 9. ==[ beta ]==> (b (a (^y.(^z.z)))) 10. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 185021/21553374. ------ 1. ==[ start ]==> ((((a a) a) a)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a) a)((a (a a))((^x.x) b))) 3. ==[ beta ]==> ((((a a) a) a)((a (a a)) b)) REDUCED to normal form. ------ 185022/21553428. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(b (^y1.y1)))) REDUCED to normal form. ------ 185023/21553455. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.(y y)))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (^x.(x x)))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 185024/21553473. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a (^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a ((^y.y) a))(a (^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(a (^y.(y (^z.z))))) 7. ==[ beta ]==> ((a a)(a (^y.(y (^z.z))))) 8. ==[ alpha ]==> ((a a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 185025/21553554. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 185026/21553572. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> (((a a)((a a) a))(b (^y.(y y)))) 4. ==[ alpha ]==> (((a a)((a a) a))(b (^x.(x x)))) REDUCED to normal form. ------ 185027/21553599. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 185028/21553626. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((b a)(^y.a))) 3. ==[ beta ]==> ((a (a (a a)))((b a)(^y.a))) 4. ==[ alpha ]==> ((a (a (a a)))((b a)(^x.a))) REDUCED to normal form. ------ 185029/21553653. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> (((a (a a)) a)(((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> (((a (a a)) a)(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 185030/21553680. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a a)(^z.(a a)))) 8. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 185031/21553707. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 185032/21553743. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(b a))) 3. ==[ beta ]==> ((^y.b)((^z.a)(b a))) 4. ==[ alpha ]==> ((^x.b)((^y.a)(b a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 185033/21553824. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.a)((a a)(a a)))) IRREDUCIBLE: cycle. ------ 185034/21554013. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 185035/21554094. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 185036/21554121. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 185037/21554292. ------ 1. ==[ start ]==> (((^a.b) b)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) b)(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (b (a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (b (a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 185038/21554508. ------ 1. ==[ start ]==> (((a b) b)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) b)((a b)((^x.x)(a a)))) 3. ==[ beta ]==> (((a b) b)((a b)(a a))) REDUCED to normal form. ------ 185039/21554535. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a a) a)(((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a) a)(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 185040/21554562. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(b a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(b a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(b a)) REDUCED to normal form. ------ 185041/21554589. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (a a))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 185042/21554643. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.z))((a a)(a a)))) REDUCED to normal form. ------ 185043/21554670. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(b (^z.z)))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(b (^y.y)))) 7. ==[ beta ]==> (((a a)(b (^y.y)))((a a)(b (^y.y)))) 8. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 185044/21554787. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 185045/21554814. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 185046/21554868. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((a (a a))(^x.x))((a a)(^z.b))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 185047/21554895. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a b)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))((a b)(^y.(a a)))) 6. ==[ alpha ]==> ((a (a a))((a b)(^x.(a a)))) REDUCED to normal form. ------ 185048/21554976. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a (a a))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 185049/21555003. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(a (^z.z))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 185050/21555039. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185051/21555174. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 185052/21555255. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 185053/21555282. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(a a)))) 5. ==[ beta ]==> ((^y.b)(^z.(a a))) 6. ==[ alpha ]==> ((^x.b)(^y.(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 185054/21555417. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185055/21555426. ------ 1. ==[ start ]==> (((a b)(^b.a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(b ((a a)(a a)))) REDUCED to normal form. ------ 185056/21555453. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(a (b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 185057/21555480. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(a a))(a a))) REDUCED to normal form. ------ 185058/21555516. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y) c)) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) c) REDUCED to normal form. ------ 185059/21555849. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a))(a a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a))(a a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))(a a))) 5. ==[ beta ]==> (b ((^z.(a a))(a a))) 6. ==[ alpha ]==> (b ((^x.(a a))(a a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 185060/21556038. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b a)((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b a)((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 185061/21556065. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185062/21556119. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 185063/21556200. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.z))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 185064/21556587. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a (^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185065/21556902. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 185066/21556929. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185067/21557064. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.a)(a b))) 3. ==[ beta ]==> (b ((^x1.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 185068/21557172. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185069/21557199. ------ 1. ==[ start ]==> ((a (^b.b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) b))) 3. ==[ beta ]==> ((a (^x.x))((^z.z) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 185070/21557217. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z) b) a)) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(b a)) REDUCED to normal form. ------ 185071/21557244. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 185072/21557271. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((b a) c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((b a) c)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((b a) c)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a) c)) REDUCED to normal form. ------ 185073/21557478. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(c (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(c (b a))) 3. ==[ beta ]==> ((^y.(^z.z))(c (b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185074/21557523. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185075/21557802. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.z))(b a))) REDUCED to normal form. ------ 185076/21557829. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((b a)((a a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((b a)((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 185077/21557847. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(a (^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (^z.z))) 3. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 4. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 185078/21557874. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(a a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185079/21558009. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.a)((a a) a))) 3. ==[ beta ]==> (b ((^y.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 185080/21558117. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.z1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185081/21558189. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((b a) b)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((b a) b)) 3. ==[ beta ]==> (((a a) b)((b a) b)) REDUCED to normal form. ------ 185082/21558459. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 185083/21558684. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 185084/21558792. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185085/21558900. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185086/21558954. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 185087/21559323. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y)) b)) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 185088/21559350. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(a a)) c)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a)) c)) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a)) c)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a)) c)) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 185089/21559566. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 185090/21559593. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 185091/21559683. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))((^z2.z2)(^x3.x3)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))((^z2.z2)(^x3.x3)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185092/21559764. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185093/21559872. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.b)(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185094/21559980. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(^x1.b))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.b))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 185095/21560007. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185096/21560043. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a ((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.y))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 185097/21560070. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(a a))(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 185098/21560151. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(a (a a)))) 5. ==[ beta ]==> (((a b)(^x.(a a)))(a (a a))) REDUCED to normal form. ------ 185099/21560178. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.b))((a (a a))(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(^y.y))) REDUCED to normal form. ------ 185100/21560250. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(b (^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185101/21560259. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(a a))) REDUCED to normal form. ------ 185102/21560376. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 185103/21560403. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 185104/21560430. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((a b)(((^y.y) a)(^z.a))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)(^y.a))) 7. ==[ beta ]==> ((a b)(a (^y.a))) 8. ==[ alpha ]==> ((a b)(a (^x.a))) REDUCED to normal form. ------ 185105/21560457. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 185106/21560484. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a a)(^y.(a a)))) 5. ==[ beta ]==> ((b a)((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((b a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 185107/21560511. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 185108/21560538. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a b) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b) b)) 3. ==[ beta ]==> (((a b)(a a))((a b) b)) REDUCED to normal form. ------ 185109/21560565. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((a a) a) c)) 3. ==[ beta ]==> (((a a)(a b))(((a a) a) c)) REDUCED to normal form. ------ 185110/21560754. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.b) b)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.b) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.b) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.b) b)) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 185111/21560925. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a (^x1.(a a)))) 3. ==[ beta ]==> (b (a (^x1.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 185112/21561033. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(z1 z1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185113/21561195. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185114/21561249. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)((^y.a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.a)(^y.(^z.z)))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 185115/21561258. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(c (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(c (^y.y))) REDUCED to normal form. ------ 185116/21561285. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(b ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b ((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b ((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((a a) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185117/21561339. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 185118/21561366. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(a (^z.z))) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 185119/21561393. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (a a))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a (a a)) a)) REDUCED to normal form. ------ 185120/21561447. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1))) REDUCED to normal form. ------ 185121/21561474. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)((a a) a))) REDUCED to normal form. ------ 185122/21561573. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(((^x1.x1) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(a ((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a ((^z.z) a))) 7. ==[ beta ]==> ((a (^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 185123/21561591. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 185124/21561618. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 185125/21561672. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((a a) a) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((a a) a) a)) 3. ==[ beta ]==> (((a (a a)) b)(((a a) a) a)) REDUCED to normal form. ------ 185126/21561699. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1)) b)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1)) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1)) b)) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) b)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 9. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 185127/21561726. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a)) c)) REDUCED to normal form. ------ 185128/21561861. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1)) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 185129/21561888. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y)) c)) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y)) c)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x)) c)) 5. ==[ beta ]==> ((b (a (a a)))(c c)) REDUCED to normal form. ------ 185130/21561996. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 6. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 185131/21562005. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> (((^z.(^x1.x1))(a a))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185132/21562410. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a a))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a a))) 7. ==[ beta ]==> ((^y.(y y))(a a)) 8. ==[ alpha ]==> ((^x.(x x))(a a)) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 185133/21562437. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 185134/21562464. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185135/21562518. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(y y))(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(x x))(^y.y))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)(^y.y))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 185136/21562554. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(c (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c (a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(c (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(c (a (^y.y)))) 7. ==[ beta ]==> (c (a (^y.y))) 8. ==[ alpha ]==> (c (a (^x.x))) REDUCED to normal form. ------ 185137/21562581. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b ((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 185138/21562599. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 185139/21562662. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 185140/21562707. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185141/21562743. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c b)) REDUCED to normal form. ------ 185142/21562770. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b c)) REDUCED to normal form. ------ 185143/21562842. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 185144/21562851. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b (a (^z.z)))) REDUCED to normal form. ------ 185145/21562869. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.a)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 185146/21562887. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^b.a) a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.a) a)) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 185147/21562914. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 185148/21562941. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z) c)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z) c)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y) c)) 5. ==[ beta ]==> ((a (b (^x.x))) c) REDUCED to normal form. ------ 185149/21562968. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 185150/21562995. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)((a a)(^y.(^z.z)))) 7. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 8. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 185151/21563022. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a (^z.z)) a)) REDUCED to normal form. ------ 185152/21563049. ------ 1. ==[ start ]==> (((a b)(b a))((a a) b)) REDUCED to normal form. ------ 185153/21563076. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 185154/21563103. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a)) b) REDUCED to normal form. ------ 185155/21563157. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a a) a)) REDUCED to normal form. ------ 185156/21563184. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1) a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1) a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z) a)) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 185157/21563210. ------ 1. ==[ start ]==> (^a.(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (^x.(((x x)(x x))(x (x x)))) REDUCED to normal form. ------ 185158/21563211. ------ 1. ==[ start ]==> (a (((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 185159/21568569. ------ 1. ==[ start ]==> ((^a.(^b.b))(^c.(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185160/21574239. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 185161/21574584. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a))) a) REDUCED to normal form. ------ 185162/21574590. ------ 1. ==[ start ]==> ((^a.a)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 185163/21574617. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^z.z)(^x1.x1)))(((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((b ((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((b (^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((b (^x.x))(((^y.y) b)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((b (^x.x))(b ((^z.z)(^x1.x1)))) 10. ==[ alpha ]==> ((b (^x.x))(b ((^y.y)(^z.z)))) 11. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 12. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 185164/21574644. ------ 1. ==[ start ]==> ((^a.b)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 185165/21574725. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((^z.z)(a a))((a a)(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.z)) 5. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 185166/21574914. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a a)(a (a (^z.z))))) 3. ==[ eta ]==> ((^y.y)((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 185167/21575367. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 185168/21575409. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185169/21575799. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 7. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 8. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 185170/21575967. ------ 1. ==[ start ]==> ((^a.((a a) a))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.((x x) x))((b a)((a a) a))) 3. ==[ beta ]==> ((((b a)((a a) a))((b a)((a a) a)))((b a)((a a) a))) REDUCED to normal form. ------ 185171/21576231. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 185172/21576300. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 185173/21576636. ------ 1. ==[ start ]==> ((((a a) a) b)(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a) b)(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 185174/21577050. ------ 1. ==[ start ]==> (((a b)(a a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(a a))(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> (((a b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 185175/21577074. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b (^z.z))(a a))) 3. ==[ beta ]==> ((^y.y)(((b (^z.z))(a a))((b (^z.z))(a a)))) 4. ==[ alpha ]==> ((^x.x)(((b (^y.y))(a a))((b (^z.z))(a a)))) 5. ==[ beta ]==> (((b (^y.y))(a a))((b (^z.z))(a a))) 6. ==[ alpha ]==> (((b (^x.x))(a a))((b (^y.y))(a a))) REDUCED to normal form. ------ 185176/21578505. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ eta ]==> (b (((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (a (^y.(^z.z))))) 6. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 185177/21578931. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.((a a)(a a)))) REDUCED to normal form. ------ 185178/21579291. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.((z z)(z z)))) REDUCED to normal form. ------ 185179/21579342. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x1.(^y1.y1)))(a (^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 185180/21579945. ------ 1. ==[ start ]==> ((^a.(^b.b))((a a)(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185181/21579948. ------ 1. ==[ start ]==> ((a (^b.b))(^c.(^b.b))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 185182/21580260. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 185183/21580605. ------ 1. ==[ start ]==> (((a a)(^b.b))(^a.(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 185184/21580902. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (^y.y))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 185185/21581208. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(x1 (^y1.(^z1.z1))))) REDUCED to normal form. ------ 185186/21581259. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((((a a)(^y.y))(a (^z.z)))(((a a)(^y.y))(a (^z.z))))((((a a)(^y.y))(a (^z.z)))(((a a)(^y.y))(a (^z.z))))) 4. ==[ alpha ]==> (((((a a)(^x.x))(a (^y.y)))(((a a)(^z.z))(a (^x1.x1))))((((a a)(^y1.y1))(a (^z1.z1)))(((a a)(^x2.x2))(a (^y2.y2))))) REDUCED to normal form. ------ 185187/21581766. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^b.(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(y a))) REDUCED to normal form. ------ 185188/21582045. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(^x1.(b x1))) 3. ==[ eta ]==> ((((^x.x) a)(a (^y.(^z.z)))) b) 4. ==[ beta ]==> ((a (a (^y.(^z.z)))) b) 5. ==[ alpha ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 185189/21582288. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 185190/21582792. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 185191/21583035. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 185192/21583500. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a b)(a a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a b)(a a))) 3. ==[ eta ]==> ((^y.(^z.z))((a b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185193/21584250. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.b))) REDUCED to normal form. ------ 185194/21584319. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (a a))(^x1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 185195/21585141. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 185196/21585348. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.d)) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.d)) 3. ==[ beta ]==> (b (^y.d)) 4. ==[ alpha ]==> (b (^x.d)) REDUCED to normal form. ------ 185197/21585615. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a) c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 185198/21585618. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 185199/21585636. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 185200/21585690. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 185201/21585825. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 185202/21585906. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.b)) REDUCED to normal form. ------ 185203/21585933. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(x1 x1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(z z))) 5. ==[ beta ]==> ((b (^y.y))(^z.(z z))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(y y))) REDUCED to normal form. ------ 185204/21585960. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 185205/21585972. ------ 1. ==[ start ]==> ((a a)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 185206/21585999. ------ 1. ==[ start ]==> ((a (a a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a a))(((^x.x) b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a a))(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a (a a))(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a (a a))(b (^y.y))) 6. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 185207/21586026. ------ 1. ==[ start ]==> ((a b)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 185208/21586080. ------ 1. ==[ start ]==> (((a a)(a a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 185209/21586107. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (a (^x.x)))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 185210/21586242. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 185211/21586269. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 185212/21586296. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((a a)((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> ((a a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 185213/21586332. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((a (a (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 185214/21586341. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.y))) REDUCED to normal form. ------ 185215/21586386. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.y) a)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x) a)((b (^y.y))(^z.a))) 5. ==[ beta ]==> (a ((b (^y.y))(^z.a))) 6. ==[ alpha ]==> (a ((b (^x.x))(^y.a))) REDUCED to normal form. ------ 185216/21586413. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 185217/21586449. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 185218/21586557. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 185219/21586602. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 185220/21586638. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 185221/21586665. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a)) a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 185222/21586692. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(x x))) a) REDUCED to normal form. ------ 185223/21586719. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 185224/21586746. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (a (^x1.x1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 185225/21586764. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a (a (^y.y))) a)) 3. ==[ beta ]==> (((a a)(a a))((a (a (^y.y))) a)) 4. ==[ alpha ]==> (((a a)(a a))((a (a (^x.x))) a)) REDUCED to normal form. ------ 185226/21586773. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 185227/21586791. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 185228/21586881. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 185229/21587070. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 185230/21587178. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z (^x1.x1))))) 7. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 9. ==[ beta ]==> (^y.(y (^z.z))) 10. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 185231/21587214. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 185232/21587241. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 185233/21587268. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a ((^y.y) a))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a a)(((a a)(a a))((^y.y) a))) 6. ==[ alpha ]==> ((a a)(((a a)(a a))((^x.x) a))) 7. ==[ beta ]==> ((a a)(((a a)(a a)) a)) REDUCED to normal form. ------ 185234/21587295. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(b (a (a a)))) REDUCED to normal form. ------ 185235/21587322. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a a)((a (^x.(^y.y)))(^x1.x1))) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 185236/21587349. ------ 1. ==[ start ]==> ((a ((a a) a))((b a)((a a) a))) REDUCED to normal form. ------ 185237/21587556. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(c (^x1.(^y1.y1)))) REDUCED to normal form. ------ 185238/21587610. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 185239/21587682. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 185240/21587853. ------ 1. ==[ start ]==> (((^a.b) a)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (b ((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 185241/21588015. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a) b)((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y)) a)) 5. ==[ beta ]==> ((((a a) a) b)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 185242/21588033. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (b (((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 185243/21588060. ------ 1. ==[ start ]==> (((^a.a)(a b))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(a b))((b (^y.y)) b)) 3. ==[ beta ]==> ((a b)((b (^y.y)) b)) 4. ==[ alpha ]==> ((a b)((b (^x.x)) b)) REDUCED to normal form. ------ 185244/21588123. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 185245/21588150. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 185246/21588231. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 185247/21588402. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b (b (^y.y)))) REDUCED to normal form. ------ 185248/21588429. ------ 1. ==[ start ]==> (((a b)(a a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(a a))(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a b)(a a))(a (^y.y))) 4. ==[ alpha ]==> (((a b)(a a))(a (^x.x))) REDUCED to normal form. ------ 185249/21588456. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((b (^y.y))(a a))) 3. ==[ beta ]==> ((a (a a))((b (^y.y))(a a))) 4. ==[ alpha ]==> ((a (a a))((b (^x.x))(a a))) REDUCED to normal form. ------ 185250/21588492. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(a a)) c)) 3. ==[ beta ]==> ((^y.y)((^x1.(a a)) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(a a)) c)) 5. ==[ beta ]==> ((^y.(a a)) c) 6. ==[ alpha ]==> ((^x.(a a)) c) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185251/21588771. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(c (^z.(a a)))) REDUCED to normal form. ------ 185252/21588843. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (b ((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 185253/21589068. ------ 1. ==[ start ]==> (((^a.b) c)((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (b ((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 185254/21589167. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(a a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 185255/21589311. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 185256/21589419. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) b) REDUCED to normal form. ------ 185257/21589446. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 185258/21589500. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185259/21589527. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) a) REDUCED to normal form. ------ 185260/21589554. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 185261/21589644. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(b (a (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (a (^y.y)))) REDUCED to normal form. ------ 185262/21589671. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(a a))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 185263/21589698. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((b a)(a (a a)))) 3. ==[ beta ]==> ((a (a b))((b a)(a (a a)))) REDUCED to normal form. ------ 185264/21589725. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((a a)(^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(((a a)(^x.x))(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 185265/21589752. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))((a a) a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((a a) a))) 7. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a) a))) 8. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a) a))) 9. ==[ beta ]==> (((^y.y)(a a))((a a) a)) 10. ==[ alpha ]==> (((^x.x)(a a))((a a) a)) 11. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 185266/21589779. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a b)(a b))) REDUCED to normal form. ------ 185267/21589806. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b) a)(((a a) a)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b) a)(((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> (((a b) a)(((a a) a)(a a))) REDUCED to normal form. ------ 185268/21589833. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)((a a)(^z.z)))) 7. ==[ beta ]==> (((a a)(a (^x.x)))((a a)(^z.z))) 8. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 185269/21589860. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (a a))(b a))) REDUCED to normal form. ------ 185270/21589887. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (b a))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (b a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 185271/21589977. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(a a))(^z.z))) 5. ==[ beta ]==> (b (((a a)(a a))(^z.z))) 6. ==[ alpha ]==> (b (((a a)(a a))(^x.x))) REDUCED to normal form. ------ 185272/21590058. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((b a)(^z.(z z)))) 3. ==[ beta ]==> (b ((b a)(^z.(z z)))) 4. ==[ alpha ]==> (b ((b a)(^x.(x x)))) REDUCED to normal form. ------ 185273/21590121. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 185274/21590166. ------ 1. ==[ start ]==> (((^a.a)(b a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((a a) a)(^y.(a a)))) 3. ==[ beta ]==> ((b a)(((a a) a)(^y.(a a)))) 4. ==[ alpha ]==> ((b a)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 185275/21590229. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(z z))(b a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(z z))(b a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))(b a))) 5. ==[ beta ]==> ((a (^x.(a a)))((b a)(b a))) REDUCED to normal form. ------ 185276/21590247. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b)(a b))(a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a b)(a b))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 185277/21590256. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 185278/21590310. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 185279/21590328. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((a a)(a a)) a)) 3. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 185280/21590337. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 185281/21590364. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 185282/21590391. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 185283/21590616. ------ 1. ==[ start ]==> (((a b)(a (a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 185284/21590643. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(b ((^z.z) b))) 3. ==[ beta ]==> (((a a)((^y.y) a))(b ((^z.z) b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(b ((^y.y) b))) 5. ==[ beta ]==> (((a a) a)(b ((^y.y) b))) 6. ==[ alpha ]==> (((a a) a)(b ((^x.x) b))) 7. ==[ beta ]==> (((a a) a)(b b)) REDUCED to normal form. ------ 185285/21590670. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 185286/21590724. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 185287/21591030. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 185288/21591039. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.b)(a a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)(a a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 185289/21591057. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 185290/21591111. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a)(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(^y.y))(^z.(z z)))) 7. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))(^z.(z z)))) 8. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 185291/21591120. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 185292/21591147. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)((^z.(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(a a))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 185293/21591192. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((a a) a)(^x1.b))) 3. ==[ beta ]==> (b (((a a) a)(^x1.b))) 4. ==[ alpha ]==> (b (((a a) a)(^x.b))) REDUCED to normal form. ------ 185294/21591201. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 185295/21591228. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 185296/21591255. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(((a a)(^x1.x1))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 185297/21591300. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185298/21591309. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 185299/21591327. ------ 1. ==[ start ]==> ((a (^b.b))((a a)(^b.b))) 2. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 185300/21591642. ------ 1. ==[ start ]==> ((a ((^a.a) b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))(b (a (^y.(^z.z))))) 3. ==[ beta ]==> ((a b)(b (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a b)(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 185301/21591678. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1) a)) 3. ==[ beta ]==> ((^y.y)((^z1.z1) a)) 4. ==[ alpha ]==> ((^x.x)((^y.y) a)) 5. ==[ beta ]==> ((^y.y) a) 6. ==[ alpha ]==> ((^x.x) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185302/21591930. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(c (^d.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(c (^z.a))) REDUCED to normal form. ------ 185303/21591957. ------ 1. ==[ start ]==> ((((^a.a) b) a)(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)(b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 185304/21591984. ------ 1. ==[ start ]==> (((a a)(^b.b))(a (^b.b))) 2. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 185305/21592002. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 185306/21592011. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) REDUCED to normal form. ------ 185307/21592056. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 185308/21592092. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(a (a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185309/21592119. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) b) REDUCED to normal form. ------ 185310/21592137. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((a a) a)(^y.a))) 3. ==[ beta ]==> (b (((a a) a)(^y.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 185311/21592146. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 185312/21592173. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 185313/21592200. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(((^x1.x1)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(a a))) REDUCED to normal form. ------ 185314/21592254. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 185315/21592281. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((b (^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 185316/21592587. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 185317/21592614. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((b a)(a a))) 3. ==[ beta ]==> ((b (a a))((b a)(a a))) REDUCED to normal form. ------ 185318/21592641. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 185319/21592920. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185320/21592956. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((b b)((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((b b)((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 185321/21592983. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 185322/21593001. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 185323/21593028. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 7. ==[ beta ]==> ((^y.y)(^z.a)) 8. ==[ alpha ]==> ((^x.x)(^y.a)) 9. ==[ beta ]==> (^y.a) 10. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 185324/21593037. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 185325/21593064. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(a b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(y1 y1))(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))(a b))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a b)(a b))) REDUCED to normal form. ------ 185326/21593082. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (((b a)(b a))(a (^y.(a a)))) 6. ==[ alpha ]==> (((b a)(b a))(a (^x.(a a)))) REDUCED to normal form. ------ 185327/21593145. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(b a)) REDUCED to normal form. ------ 185328/21593163. ------ 1. ==[ start ]==> (((^a.b)(a b))((b a) a)) 2. ==[ alpha ]==> (((^x.b)(a b))((b a) a)) 3. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 185329/21593226. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 185330/21593280. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 185331/21593307. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 185332/21593334. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((^z.b)(^z.b))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.b)(^z.b))) 5. ==[ beta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 185333/21593397. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(b ((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b ((a a)(^y.y)))) REDUCED to normal form. ------ 185334/21593424. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(a (b a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(a (b a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (b a))) REDUCED to normal form. ------ 185335/21593451. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(b a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 185336/21593478. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(a (^z.z)))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(a (^y.y)))) REDUCED to normal form. ------ 185337/21593505. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a b)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((a b)((^y.y) a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a b)((^x.x) a))) 5. ==[ beta ]==> ((((a a) a)(a a))((a b) a)) REDUCED to normal form. ------ 185338/21593532. ------ 1. ==[ start ]==> (((a b)(a b))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 185339/21593559. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((a a) a))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)((a a) a))((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)((a a) a))((^y.y)(^z.z))) 8. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.y))) 9. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 10. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 185340/21593586. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a (a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a))((a a) a))) REDUCED to normal form. ------ 185341/21593640. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (^z.z))(a a))) REDUCED to normal form. ------ 185342/21593667. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 185343/21593811. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(^z2.(^x3.x3)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(^y2.y2))(^z2.(^x3.x3)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185344/21593892. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 185345/21594000. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a b) c)) 3. ==[ beta ]==> ((^y.(^z.z))((a b) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185346/21594036. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((b c)((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> ((b c)((^x.a)(^y.(y y)))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 185347/21594063. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 185348/21594171. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 185349/21594270. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a) d)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a) d)) 3. ==[ beta ]==> (b ((^z.a) d)) 4. ==[ alpha ]==> (b ((^x.a) d)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 185350/21594387. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(b (^x1.(a a)))) REDUCED to normal form. ------ 185351/21594414. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 185352/21594441. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 185353/21594801. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(c ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(c ((a a) a))) 3. ==[ beta ]==> ((b ((^y.y) a))(c ((a a) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(c ((a a) a))) 5. ==[ beta ]==> ((b a)(c ((a a) a))) REDUCED to normal form. ------ 185354/21594828. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(b (a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(b (a b))) REDUCED to normal form. ------ 185355/21594882. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a b)(a a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a b)(a a))) 3. ==[ beta ]==> ((a (^y.y))((a b)(a a))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(a a))) REDUCED to normal form. ------ 185356/21595161. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185357/21595278. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)(^z.z))) 5. ==[ beta ]==> (a ((^y.b)(^z.z))) 6. ==[ alpha ]==> (a ((^x.b)(^y.y))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 185358/21595296. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((a a) a) b)) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((a a) a) b)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a) a) b)) 5. ==[ beta ]==> ((^y.y)(((a a) a) b)) 6. ==[ alpha ]==> ((^x.x)(((a a) a) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 185359/21595323. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1)(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> (((^y.y)(^z.z)) c) 6. ==[ alpha ]==> (((^x.x)(^y.y)) c) 7. ==[ beta ]==> ((^y.y) c) 8. ==[ alpha ]==> ((^x.x) c) 9. ==[ beta ]==> c REDUCED to normal form. ------ 185360/21595386. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 185361/21595458. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.b) a)) 3. ==[ beta ]==> (b ((^z.b) a)) 4. ==[ alpha ]==> (b ((^x.b) a)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 185362/21595575. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (^y1.(^z1.z1)))) REDUCED to normal form. ------ 185363/21595602. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b (^z.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(b (^z.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b (^y.a))) REDUCED to normal form. ------ 185364/21595629. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.b))) REDUCED to normal form. ------ 185365/21595683. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185366/21595701. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (a a))(^z.a))) REDUCED to normal form. ------ 185367/21595935. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (^y.y))) REDUCED to normal form. ------ 185368/21595989. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1)(^z1.z1))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(^y1.y1))(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(a a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(a a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 185369/21596016. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (a a))(a (^y.y)))) 3. ==[ beta ]==> ((b (a (a a)))((a (a a))(a (^y.y)))) 4. ==[ alpha ]==> ((b (a (a a)))((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 185370/21596043. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a ((^y.y) a))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(a ((^x.x) a))) 7. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 185371/21596097. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 185372/21596133. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((((^z.z)(^x1.x1))(^y1.y1))(^y.y)) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.x1)) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185373/21596520. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(a (^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 185374/21596538. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.z))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.z))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 185375/21596547. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(y y))(a a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((a a)(a a))) REDUCED to normal form. ------ 185376/21596565. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 185377/21596574. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 185378/21596592. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.a))) 5. ==[ beta ]==> ((a (^y.y))(^z.a)) 6. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 185379/21596646. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (a a)) a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (a a)) a)) REDUCED to normal form. ------ 185380/21596682. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 185381/21596709. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 185382/21596790. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 185383/21596871. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 185384/21596898. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 185385/21596952. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185386/21596970. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (^z.z)) b)) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y)) b)) REDUCED to normal form. ------ 185387/21596979. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 185388/21596997. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a) c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a) c)) REDUCED to normal form. ------ 185389/21597015. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a ((^y.y) a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a a)) REDUCED to normal form. ------ 185390/21597042. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(a a))) REDUCED to normal form. ------ 185391/21597069. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a)(a (^z.z)))) 3. ==[ beta ]==> ((a (b (^y.y)))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 185392/21597123. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b b)) 5. ==[ beta ]==> (((^y.y) b)(b b)) 6. ==[ alpha ]==> (((^x.x) b)(b b)) 7. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 185393/21597177. ------ 1. ==[ start ]==> (((a b)(b a))(b (a a))) REDUCED to normal form. ------ 185394/21597204. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a (a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 185395/21597231. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)(a a))) REDUCED to normal form. ------ 185396/21597285. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a b)) REDUCED to normal form. ------ 185397/21597312. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a (a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a (a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a (a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a (a a))) 5. ==[ beta ]==> ((b (^y.y))(a (a a))) 6. ==[ alpha ]==> ((b (^x.x))(a (a a))) REDUCED to normal form. ------ 185398/21597339. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a a)) REDUCED to normal form. ------ 185399/21608721. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a))) b) REDUCED to normal form. ------ 185400/21608745. ------ 1. ==[ start ]==> ((^a.(^a.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185401/21608826. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((b a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)(a b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185402/21608988. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (^y.((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> (^x.((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 185403/21609060. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(b (^z.(z (^x1.x1))))) 3. ==[ eta ]==> ((^y.y)(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 185404/21609072. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.a)(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.a)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 185405/21609330. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.(a a))((a a)(^z.z)))(((^y.(a a))((a a)(^z.z)))((^y.(a a))((a a)(^z.z))))) 4. ==[ alpha ]==> (((^x.(a a))((a a)(^y.y)))(((^z.(a a))((a a)(^x1.x1)))((^y1.(a a))((a a)(^z1.z1))))) 5. ==[ beta ]==> ((a a)(((^z.(a a))((a a)(^x1.x1)))((^y1.(a a))((a a)(^z1.z1))))) 6. ==[ alpha ]==> ((a a)(((^x.(a a))((a a)(^y.y)))((^z.(a a))((a a)(^x1.x1))))) 7. ==[ beta ]==> ((a a)((a a)((^z.(a a))((a a)(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((a a)((^x.(a a))((a a)(^y.y))))) 9. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 185406/21610626. ------ 1. ==[ start ]==> ((^a.(a b))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.b)((a a)(^z.z))) b) 4. ==[ alpha ]==> (((^x.b)((a a)(^y.y))) b) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 185407/21611895. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^z.(z z))(a (^x1.(^y1.y1))))((^z.(z z))(a (^x1.(^y1.y1)))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(x x))(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.(^z1.z1)))))(^x2.x2)) 5. ==[ beta ]==> ((((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))(a (^y1.(^z1.z1)))))(^x2.x2)) 6. ==[ alpha ]==> ((((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))(a (^z1.(^x2.x2)))))(^y2.y2)) 7. ==[ beta ]==> ((((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^z1.(^x2.x2)))(a (^z1.(^x2.x2)))))(^y2.y2)) 8. ==[ alpha ]==> ((((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a (^x2.(^y2.y2)))))(^z2.z2)) REDUCED to normal form. ------ 185408/21613077. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 185409/21613437. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 185410/21614112. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 185411/21614406. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 185412/21614445. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.((^x2.x2) b))) 3. ==[ beta ]==> ((^y.y)(^z1.((^x2.x2) b))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) b))) 5. ==[ beta ]==> (^y.((^z.z) b)) 6. ==[ alpha ]==> (^x.((^y.y) b)) 7. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 185413/21614742. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 185414/21615048. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 185415/21615354. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 185416/21615912. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^c.(^d.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.a))) REDUCED to normal form. ------ 185417/21616485. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185418/21616956. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.((x1 x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.((x1 x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.((y1 y1)(^z1.z1)))) REDUCED to normal form. ------ 185419/21617406. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^y.(a a))) REDUCED to normal form. ------ 185420/21617820. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^c.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(a b))) 3. ==[ beta ]==> (b (^x1.(a b))) 4. ==[ alpha ]==> (b (^x.(a b))) REDUCED to normal form. ------ 185421/21618225. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(z b))) 3. ==[ beta ]==> (b (^z.(z b))) 4. ==[ alpha ]==> (b (^x.(x b))) REDUCED to normal form. ------ 185422/21618567. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.((a a) a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.((a a) a))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.((a a) a))) REDUCED to normal form. ------ 185423/21619761. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 185424/21619782. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.a))) REDUCED to normal form. ------ 185425/21619863. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.x))) REDUCED to normal form. ------ 185426/21619917. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 185427/21619971. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 185428/21620052. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(a a))) REDUCED to normal form. ------ 185429/21620079. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 185430/21620106. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 185431/21620136. ------ 1. ==[ start ]==> ((a (^a.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 185432/21620163. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185433/21620190. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 185434/21620217. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b a)(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(a b))) REDUCED to normal form. ------ 185435/21620271. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185436/21620298. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 185437/21620325. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 185438/21620352. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 185439/21620379. ------ 1. ==[ start ]==> ((a (^b.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 185440/21620451. ------ 1. ==[ start ]==> ((a ((^a.a) a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a a)(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 185441/21620460. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((^y.a)((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.a)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 185442/21620496. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 185443/21620523. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 185444/21620550. ------ 1. ==[ start ]==> (((a a)(^b.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 185445/21620577. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) REDUCED to normal form. ------ 185446/21620604. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 185447/21620640. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 185448/21620721. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 185449/21620793. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 185450/21620901. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 185451/21620928. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a (^y.y))) a)) REDUCED to normal form. ------ 185452/21621045. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 185453/21621540. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))(a b)) 6. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 185454/21621594. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a b)((a a)(^z.z)))) 5. ==[ beta ]==> (a ((a b)((a a)(^z.z)))) 6. ==[ alpha ]==> (a ((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 185455/21621675. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a a) a)((a (a a))((^y.y) b))) 4. ==[ alpha ]==> (((a a) a)((a (a a))((^x.x) b))) 5. ==[ beta ]==> (((a a) a)((a (a a)) b)) REDUCED to normal form. ------ 185456/21621702. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((a a)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((a a)(a a))) 7. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 185457/21621756. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a ((^y.y) a))((a a)((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a a)((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a a)((a a)((^y.(^z.z)) a))) 8. ==[ alpha ]==> ((a a)((a a)((^x.(^y.y)) a))) 9. ==[ beta ]==> ((a a)((a a)(^y.y))) 10. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 185458/21621792. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185459/21621819. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 185460/21621882. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 185461/21621909. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 185462/21621990. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 185463/21622008. ------ 1. ==[ start ]==> (((^a.b) a)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 185464/21622017. ------ 1. ==[ start ]==> ((a (a b))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 185465/21622197. ------ 1. ==[ start ]==> (((a b) a)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a b) a)(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> (((a b) a)((^y.y) a)) 4. ==[ alpha ]==> (((a b) a)((^x.x) a)) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 185466/21622224. ------ 1. ==[ start ]==> (((a a)(^a.b))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.b))((b (^y.y)) b)) REDUCED to normal form. ------ 185467/21622422. ------ 1. ==[ start ]==> (((a a)(a b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 185468/21622476. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 185469/21622503. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 185470/21622530. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.(a a)))) 7. ==[ beta ]==> (a ((^y.a)(^z.(a a)))) 8. ==[ alpha ]==> (a ((^x.a)(^y.(a a)))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185471/21622620. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b (^z.z))(a a))) 3. ==[ beta ]==> ((^y.(a a))((b (^z.z))(a a))) 4. ==[ alpha ]==> ((^x.(a a))((b (^y.y))(a a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185472/21622647. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 185473/21622701. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(a (a a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 185474/21622782. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a b))) 5. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 185475/21622836. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a) a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)(((a a) a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a a)(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 185476/21622863. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b a)) 7. ==[ beta ]==> ((^y.y)(b a)) 8. ==[ alpha ]==> ((^x.x)(b a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 185477/21622917. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1) b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) a)((^z1.z1) b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) a)((^y1.y1) b))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)((^y1.y1) b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((^x1.x1) b))) 9. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1) b))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) b))) 11. ==[ beta ]==> (((^y.y) a)((^z.z) b)) 12. ==[ alpha ]==> (((^x.x) a)((^y.y) b)) 13. ==[ beta ]==> (a ((^y.y) b)) 14. ==[ alpha ]==> (a ((^x.x) b)) 15. ==[ beta ]==> (a b) REDUCED to normal form. ------ 185478/21623007. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 185479/21623034. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 185480/21623070. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 185481/21623097. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 185482/21623178. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(a a))(a b))) 5. ==[ beta ]==> ((a (a a))((^y.(a a))(a b))) 6. ==[ alpha ]==> ((a (a a))((^x.(a a))(a b))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 185483/21623205. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a) a) b) REDUCED to normal form. ------ 185484/21623223. ------ 1. ==[ start ]==> (((^a.b) c)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (b (((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 185485/21623232. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 185486/21623259. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(b a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 185487/21623286. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 185488/21623466. ------ 1. ==[ start ]==> (((a b) c)((a (^a.(^a.a))) d)) 2. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y))) d)) REDUCED to normal form. ------ 185489/21623700. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(c ((^z.z) b))) 3. ==[ beta ]==> (b (c ((^z.z) b))) 4. ==[ alpha ]==> (b (c ((^x.x) b))) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 185490/21624276. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((a a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((a a)(^y.a))) REDUCED to normal form. ------ 185491/21624411. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 185492/21624465. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 185493/21624492. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 185494/21624519. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) b) b)) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) b) b)) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b) b)) 5. ==[ beta ]==> (((a a)(^x.a))(b b)) REDUCED to normal form. ------ 185495/21624609. ------ 1. ==[ start ]==> (((a a)(b a))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 185496/21624636. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 185497/21624663. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.b)(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.b)(^z.b))) 5. ==[ beta ]==> ((a (a a))((^y.b)(^z.b))) 6. ==[ alpha ]==> ((a (a a))((^x.b)(^y.b))) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 185498/21624690. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a (a a))(a b)) a) REDUCED to normal form. ------ 185499/21624717. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 185500/21624771. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 185501/21624798. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 185502/21624870. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.x1) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185503/21624888. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185504/21624969. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((a a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a a)((a a)((^x.x)(^y.y)))) 9. ==[ beta ]==> ((a a)((a a)(^y.y))) 10. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 185505/21625050. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> (b ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 185506/21625158. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a a)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185507/21625194. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(b (^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(b (^x1.x1))) REDUCED to normal form. ------ 185508/21625275. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 185509/21625302. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 185510/21625356. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(^z.b))) REDUCED to normal form. ------ 185511/21625383. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(a a))) 8. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(a a))) REDUCED to normal form. ------ 185512/21625410. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 185513/21625464. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 185514/21625500. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((^x1.x1) b)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z) b)) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 185515/21625527. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 185516/21625554. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 185517/21625608. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 185518/21625635. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 185519/21625662. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.b)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 185520/21625716. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 185521/21625797. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 185522/21625806. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(b (a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 185523/21625833. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(a ((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(a ((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y) b))) 5. ==[ beta ]==> (a ((^y.y) b)) 6. ==[ alpha ]==> (a ((^x.x) b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 185524/21625968. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((a b)(^y.y))) 6. ==[ alpha ]==> (b ((a b)(^x.x))) REDUCED to normal form. ------ 185525/21626076. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) a)((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185526/21626130. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y) b)((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b ((a a)(a (^y.(^z.z))))) 6. ==[ alpha ]==> (b ((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 185527/21626166. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1)))(^x2.x2))) REDUCED to normal form. ------ 185528/21626247. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a))(^z.(z z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185529/21626274. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 185530/21626301. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a) a)(^y.a))) REDUCED to normal form. ------ 185531/21626328. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.b))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.b))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.b)) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 185532/21626355. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 185533/21626436. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (^y.y))((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 185534/21626472. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 185535/21626526. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 185536/21626553. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 185537/21626580. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.b)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.b)(^y.(^z.z)))) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 185538/21626607. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.a)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(a b)) a) REDUCED to normal form. ------ 185539/21626634. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 185540/21626661. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.(a a))(^z.(a a)))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(a a)))) 9. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 185541/21626688. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) a) REDUCED to normal form. ------ 185542/21626742. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 185543/21626832. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y) a)) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 185544/21626967. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y)(a a)))) 5. ==[ beta ]==> (b (a ((^y.y)(a a)))) 6. ==[ alpha ]==> (b (a ((^x.x)(a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 185545/21627111. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((b b)(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> ((b b)((a a)(^y.a))) 6. ==[ alpha ]==> ((b b)((a a)(^x.a))) REDUCED to normal form. ------ 185546/21627138. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((a b)(^x.(x x)))) REDUCED to normal form. ------ 185547/21627192. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.a)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.a)) REDUCED to normal form. ------ 185548/21627219. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a (a a))(^y1.b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (a a))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))(^x1.b))) REDUCED to normal form. ------ 185549/21627327. ------ 1. ==[ start ]==> (((a b)(^a.b))((b a) a)) 2. ==[ alpha ]==> (((a b)(^x.b))((b a) a)) REDUCED to normal form. ------ 185550/21627381. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(a a)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a) c)) REDUCED to normal form. ------ 185551/21627525. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a a)((a a)(a a))) a) REDUCED to normal form. ------ 185552/21627552. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 185553/21627822. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 185554/21627876. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 185555/21628191. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a) d)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a) a) d)) 3. ==[ beta ]==> ((b c)(((a a) a) d)) REDUCED to normal form. ------ 185556/21628344. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(a ((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a ((a a)(^y1.y1)))) REDUCED to normal form. ------ 185557/21628425. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (b (((a a) a)((^z.z) a))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x) a))) 5. ==[ beta ]==> (b (((a a) a) a)) REDUCED to normal form. ------ 185558/21628434. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a) d)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a) d)) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 185559/21628533. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a (^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185560/21628596. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 185561/21628659. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 185562/21628686. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 185563/21628713. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.(y y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.(x x))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a b)(((^y.y)(^z.z))((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((a b)((^y.y)((^z.z)(^x1.x1)))) 10. ==[ alpha ]==> ((a b)((^x.x)((^y.y)(^z.z)))) 11. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 12. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 13. ==[ beta ]==> ((a b)(^y.y)) 14. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 185564/21628740. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.a)((a a) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 185565/21628767. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(a b))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(a b))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 185566/21628794. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 185567/21628821. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(a a))((^y.(a a))(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(a a))(^y.y))) 5. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 185568/21628848. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a b))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 185569/21628929. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 185570/21628956. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.a))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.a))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 185571/21628983. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 185572/21629127. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a (a a)))) 7. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 185573/21629208. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(a b))) 3. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 185574/21629433. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a b) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a b) a)) 3. ==[ beta ]==> (((^y.y) a)((a b) a)) 4. ==[ alpha ]==> (((^x.x) a)((a b) a)) 5. ==[ beta ]==> (a ((a b) a)) REDUCED to normal form. ------ 185575/21629613. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(a (a b))) 3. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 185576/21629622. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 185577/21629649. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a) b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a) b)) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 185578/21629676. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 185579/21629721. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1) a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185580/21629838. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185581/21629874. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))(((^z.z) a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.x))(a ((^z.z) a))) 8. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) a))) 9. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 185582/21629901. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 185583/21629928. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 185584/21629955. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.y)((a a) a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)((a a) a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)((a a) a))) 5. ==[ beta ]==> (((a (a a)) b)((a a) a)) REDUCED to normal form. ------ 185585/21630009. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 185586/21630036. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.a)(^z.a))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 185587/21630063. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(y y)))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 185588/21630090. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 185589/21630252. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 185590/21630702. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (a a))(^y.y))) REDUCED to normal form. ------ 185591/21630729. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 185592/21630837. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a) b)) 5. ==[ beta ]==> ((^y.y)(((^z.z) a) b)) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a) b)) 7. ==[ beta ]==> (((^y.y) a) b) 8. ==[ alpha ]==> (((^x.x) a) b) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 185593/21630882. ------ 1. ==[ start ]==> (((^a.b)(b a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))(b ((^y.y) a))) 3. ==[ beta ]==> (b (b ((^y.y) a))) 4. ==[ alpha ]==> (b (b ((^x.x) a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 185594/21630945. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 185595/21630990. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185596/21631026. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 185597/21631053. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 185598/21631107. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.y1) a) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a) a)) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185599/21631134. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (^z.z)) b)) REDUCED to normal form. ------ 185600/21631152. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (a (^x1.x1)))) REDUCED to normal form. ------ 185601/21631170. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.a)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.a)) REDUCED to normal form. ------ 185602/21631224. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 185603/21631251. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a (^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (^x.a))) REDUCED to normal form. ------ 185604/21631278. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a a))) 7. ==[ beta ]==> (b ((^y.(^z.z))(a a))) 8. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185605/21631305. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (^z.z))) REDUCED to normal form. ------ 185606/21631332. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 185607/21631359. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 185608/21631386. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b (^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b (^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (^y.y))) REDUCED to normal form. ------ 185609/21631440. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(a a)) REDUCED to normal form. ------ 185610/21631467. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 185611/21631494. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a (^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 185612/21643272. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 185613/21643404. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 185614/21643704. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(a (a (^z.z))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 185615/21643728. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185616/21644550. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 185617/21644799. ------ 1. ==[ start ]==> ((^a.(a b))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(^y.(^z.z))) b) 4. ==[ alpha ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 185618/21644973. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (b (^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (b (^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 185619/21645186. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (^y.(((^z.(a a))(^x1.(a a)))((^z.(a a))(^x1.(a a))))) 4. ==[ alpha ]==> (^x.(((^y.(a a))(^z.(a a)))((^x1.(a a))(^y1.(a a))))) 5. ==[ beta ]==> (^x.((a a)((^x1.(a a))(^y1.(a a))))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a))(^z.(a a))))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 185620/21645765. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(b (^z.z)))) REDUCED to normal form. ------ 185621/21646068. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a (a a))(^z.(^x1.(^y1.y1))))((a (a a))(^z.(^x1.(^y1.y1)))))(^y.y)) 4. ==[ alpha ]==> ((((a (a a))(^x.(^y.(^z.z))))((a (a a))(^x1.(^y1.(^z1.z1)))))(^x2.x2)) REDUCED to normal form. ------ 185622/21646548. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 185623/21647268. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.((a a)(a a)))) 3. ==[ beta ]==> (b (^y.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 185624/21647661. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.b) b)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1) b)) 3. ==[ beta ]==> (((^x1.x1) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 185625/21648264. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185626/21648618. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(^z1.(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185627/21648924. ------ 1. ==[ start ]==> (((a a)(^b.b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 185628/21648942. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185629/21650103. ------ 1. ==[ start ]==> (((^a.b)(a b))(^b.(b a))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(y a))) 3. ==[ beta ]==> (b (^y.(y a))) 4. ==[ alpha ]==> (b (^x.(x a))) REDUCED to normal form. ------ 185630/21650658. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185631/21651129. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) REDUCED to normal form. ------ 185632/21651138. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.((x1 x1)(^y1.y1)))) REDUCED to normal form. ------ 185633/21651354. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.a))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.a))(^y.(a a))) REDUCED to normal form. ------ 185634/21651819. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(a a)) a)) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185635/21651993. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> (b (^x1.(^y1.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 185636/21652398. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.z))) 3. ==[ beta ]==> (b (^z.(^x1.z))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 185637/21652407. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(z b))) REDUCED to normal form. ------ 185638/21652569. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.((a a) a))) REDUCED to normal form. ------ 185639/21652638. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 185640/21652740. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.a))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.a))) REDUCED to normal form. ------ 185641/21653460. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(a (a a)))) 5. ==[ beta ]==> (b (^y.(a (a a)))) 6. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 185642/21653478. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 185643/21653586. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(a (a a)))) REDUCED to normal form. ------ 185644/21653934. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 185645/21654036. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.c)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.c)) REDUCED to normal form. ------ 185646/21654252. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.a)) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 185647/21654279. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.a)) REDUCED to normal form. ------ 185648/21654327. ------ 1. ==[ start ]==> (((^a.a) a)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x) a)(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (a (((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 185649/21654354. ------ 1. ==[ start ]==> (((a a) a)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.x) b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) a)(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a) a)(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 185650/21654381. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 185651/21654408. ------ 1. ==[ start ]==> (((^a.a) b)((b a)(a b))) 2. ==[ alpha ]==> (((^x.x) b)((b a)(a b))) 3. ==[ beta ]==> (b ((b a)(a b))) REDUCED to normal form. ------ 185652/21654435. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 185653/21654462. ------ 1. ==[ start ]==> (((a a) b)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a a) b)((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a) b)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 185654/21654489. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a b)(b a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a b)(b a))) REDUCED to normal form. ------ 185655/21654516. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 185656/21654543. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1) b)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) b)) 7. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 185657/21654597. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 185658/21654642. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.a)(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.a)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 185659/21654669. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(a (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 185660/21654804. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 185661/21654849. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a)(^z.b))) REDUCED to normal form. ------ 185662/21654876. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 185663/21654912. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.(a a))((a a)(^z.z)))((^y.(a a))((a a)(^z.z)))) 6. ==[ alpha ]==> (((^x.(a a))((a a)(^y.y)))((^z.(a a))((a a)(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^z.(a a))((a a)(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))((a a)(^y.y)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 185664/21654939. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 185665/21654993. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185666/21655020. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 185667/21655047. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185668/21655101. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> (((a a)(a a))(a (a (^y.y)))) 6. ==[ alpha ]==> (((a a)(a a))(a (a (^x.x)))) REDUCED to normal form. ------ 185669/21655128. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^y1.y1)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 185670/21655146. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y) b)) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x) b)) 5. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 185671/21655173. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((b (^z.z)) c)) 3. ==[ beta ]==> (((a (^x.x)) a)((b (^z.z)) c)) 4. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y)) c)) REDUCED to normal form. ------ 185672/21655263. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185673/21655344. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185674/21655425. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185675/21655515. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.y)(b ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((^x.x)(b ((^y.(^z.z)) a))) 7. ==[ beta ]==> (b ((^y.(^z.z)) a)) 8. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185676/21655551. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 185677/21655812. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y) b)(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x) b)(((a a) a)(b a))) 5. ==[ beta ]==> (b (((a a) a)(b a))) REDUCED to normal form. ------ 185678/21655839. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((((a a) a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 185679/21655893. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a ((a a)(a a)))) REDUCED to normal form. ------ 185680/21655920. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 185681/21655947. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 185682/21656037. ------ 1. ==[ start ]==> (((a a)((a a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 185683/21656064. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(b (^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(z z)))) REDUCED to normal form. ------ 185684/21656091. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (a a)))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 185685/21656118. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((b a)(^y.a))) 3. ==[ beta ]==> (((a (a a)) a)((b a)(^y.a))) 4. ==[ alpha ]==> (((a (a a)) a)((b a)(^x.a))) REDUCED to normal form. ------ 185686/21656145. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 185687/21656172. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a a)(^x.(a a)))) REDUCED to normal form. ------ 185688/21656199. ------ 1. ==[ start ]==> ((a (a b))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 185689/21656208. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 185690/21656289. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(z z))((^x1.x1) b))) IRREDUCIBLE: cycle. ------ 185691/21656370. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (b ((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185692/21656478. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(y y))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(x x))) REDUCED to normal form. ------ 185693/21656559. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185694/21656586. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 185695/21656757. ------ 1. ==[ start ]==> (((^a.b) b)(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)(b (b (^y.y)))) 3. ==[ beta ]==> (b (b (b (^y.y)))) 4. ==[ alpha ]==> (b (b (b (^x.x)))) REDUCED to normal form. ------ 185696/21656973. ------ 1. ==[ start ]==> (((a b) b)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a b) b)(((^x.x)(a a))(a b))) 3. ==[ beta ]==> (((a b) b)((a a)(a b))) REDUCED to normal form. ------ 185697/21657000. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) a)((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a) a)((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (((a a) a)((a b)(a a))) REDUCED to normal form. ------ 185698/21657027. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 185699/21657054. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.x1)(b a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(b a))) 5. ==[ beta ]==> (((a (^x.x))(^y.b))(b a)) REDUCED to normal form. ------ 185700/21657108. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a ((^x1.x1) b))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a ((^z.z) b))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 185701/21657135. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a (^z.z))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.y))((a a)(a a)))) 7. ==[ beta ]==> (((a (^y.y))((a a)(a a)))((a (^y.y))((a a)(a a)))) 8. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 185702/21657162. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a a)(b (^y.y)))) REDUCED to normal form. ------ 185703/21657252. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) b)(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.a))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.a))) REDUCED to normal form. ------ 185704/21657279. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 185705/21657306. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 185706/21657360. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(a a))(^z.b))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))(^y.b))) 7. ==[ beta ]==> ((a (a a))((a a)(^y.b))) 8. ==[ alpha ]==> ((a (a a))((a a)(^x.b))) REDUCED to normal form. ------ 185707/21657387. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a b)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((a b)(^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((a b)(^x.(a a)))) REDUCED to normal form. ------ 185708/21657414. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 185709/21657468. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 185710/21657504. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) b))) 5. ==[ beta ]==> ((^y.a)((^z.z) b)) 6. ==[ alpha ]==> ((^x.a)((^y.y) b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185711/21657639. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z)(^x1.a))) 3. ==[ beta ]==> (b ((^z.z)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 185712/21657747. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.b))) 5. ==[ beta ]==> ((^y.(a a))(^z.b)) 6. ==[ alpha ]==> ((^x.(a a))(^y.b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185713/21657882. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 185714/21657891. ------ 1. ==[ start ]==> (((a b)(^b.a))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))(c ((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.a))(c b)) REDUCED to normal form. ------ 185715/21657918. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b ((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b ((a a)(a a)))) REDUCED to normal form. ------ 185716/21657945. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (b (^z.z)))) REDUCED to normal form. ------ 185717/21658008. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z) c)) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z) c)) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) c)) 5. ==[ beta ]==> (((a (^x.x))(a a)) c) REDUCED to normal form. ------ 185718/21658395. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 185719/21658503. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.b)(a b))) 3. ==[ beta ]==> ((b a)((^y.b)(a b))) 4. ==[ alpha ]==> ((b a)((^x.b)(a b))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 185720/21658584. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a b)(a b))((^y.(y y))(b a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(x x))(b a))) 5. ==[ beta ]==> (((a b)(a b))((b a)(b a))) REDUCED to normal form. ------ 185721/21658665. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (b ((^y.y)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 185722/21659052. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185723/21659061. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.b) b)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z) b)) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 185724/21659340. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(b (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185725/21659349. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a) b)) REDUCED to normal form. ------ 185726/21659394. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.z)(a a))) 3. ==[ beta ]==> ((^y.y)((^z.z)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a a))) 5. ==[ beta ]==> ((^y.y)(a a)) 6. ==[ alpha ]==> ((^x.x)(a a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185727/21659529. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.b)((a a) a))) 3. ==[ beta ]==> (b ((^x1.b)((a a) a))) 4. ==[ alpha ]==> (b ((^x.b)((a a) a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 185728/21659637. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185729/21659664. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 185730/21659682. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a a)(^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 185731/21659709. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y) b) a)) 3. ==[ beta ]==> (((a (^x.x))(b a))(b a)) REDUCED to normal form. ------ 185732/21659736. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 185733/21659763. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((b a) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((b a) c)) 3. ==[ beta ]==> (((a (a a))(a a))((b a) c)) REDUCED to normal form. ------ 185734/21659988. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185735/21660015. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1)(^x2.x2))) 3. ==[ beta ]==> ((^y.y)((^z1.z1)(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185736/21660267. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a ((a a)(^z.z)))) REDUCED to normal form. ------ 185737/21660294. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (^y.y))(b a))) 3. ==[ beta ]==> ((b a)((a (^y.y))(b a))) 4. ==[ alpha ]==> ((b a)((a (^x.x))(b a))) REDUCED to normal form. ------ 185738/21660312. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)(b (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (b (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 185739/21660321. ------ 1. ==[ start ]==> (((a a)(^b.b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 185740/21660339. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> ((^y.y)(a (^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(a (^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 185741/21660474. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 185742/21660582. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.a)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185743/21660654. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (^y.(^z.z))) a)) 3. ==[ beta ]==> (((a a) b)((a (^y.(^z.z))) a)) 4. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 185744/21660681. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((b a) b)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((b a) b)) REDUCED to normal form. ------ 185745/21660708. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((a a)(^y.y)) c)) 3. ==[ beta ]==> ((a (b a))(((a a)(^y.y)) c)) 4. ==[ alpha ]==> ((a (b a))(((a a)(^x.x)) c)) REDUCED to normal form. ------ 185746/21660951. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((b (a a))((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> ((b (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((b (a a))(^x.(^y.y))) REDUCED to normal form. ------ 185747/21661338. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(a (a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(a (a a)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 185748/21661365. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185749/21661419. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(y y))(a b))) 3. ==[ beta ]==> (((b a)(b a))((^y.(y y))(a b))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(x x))(a b))) 5. ==[ beta ]==> (((b a)(b a))((a b)(a b))) REDUCED to normal form. ------ 185750/21661500. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.y)(b a))) 3. ==[ beta ]==> (b ((^y.y)(b a))) 4. ==[ alpha ]==> (b ((^x.x)(b a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 185751/21661608. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.b)(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185752/21661842. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(a a)) c)) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(a a)) c)) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a)) c)) 5. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 185753/21662058. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 185754/21662229. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a)(a b))) 3. ==[ beta ]==> (b ((^z.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 185755/21662337. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185756/21662445. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((b (^x.x))((^z.a)(^z.a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.a))) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 185757/21662472. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.b))) 5. ==[ beta ]==> ((^y.a)(^z.b)) 6. ==[ alpha ]==> ((^x.a)(^y.b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185758/21662508. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b ((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(b ((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(b (a a))) REDUCED to normal form. ------ 185759/21662535. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 185760/21662616. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(((a a) a) a)) REDUCED to normal form. ------ 185761/21662643. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z)(a (a a)))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(a (a a)))) 7. ==[ beta ]==> (((a a)(^x.b))(a (a a))) REDUCED to normal form. ------ 185762/21662724. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.x1))(a b))) REDUCED to normal form. ------ 185763/21662751. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b (^y.a))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (^x.a))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b (^x.a))((a a)(a a))) REDUCED to normal form. ------ 185764/21662841. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a)(^y.a))) REDUCED to normal form. ------ 185765/21662868. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.(z z))) 6. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(y y))) REDUCED to normal form. ------ 185766/21662895. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)((a (a a))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 185767/21662949. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(b a))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((b a)((a (^y.y))(^z.b))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 185768/21662976. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 185769/21663003. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(a a)) a)) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(a a)) a)) 5. ==[ beta ]==> (((a b)(a a))((a a) a)) REDUCED to normal form. ------ 185770/21663030. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a b) b)) 3. ==[ beta ]==> (((a a)(a b))((a b) b)) REDUCED to normal form. ------ 185771/21663219. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(a a)) a)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(a a)) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a)) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a)) a)) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 185772/21663390. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (^x1.b))) 3. ==[ beta ]==> (b (b (^x1.b))) 4. ==[ alpha ]==> (b (b (^x.b))) REDUCED to normal form. ------ 185773/21663498. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))((^y2.y2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))((^y2.y2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185774/21663633. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.b)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.b)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.b)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(^z.z))) 7. ==[ beta ]==> ((^y.b)(^z.z)) 8. ==[ alpha ]==> ((^x.b)(^y.y)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 185775/21663660. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185776/21663714. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))(^z.(z z)))) 7. ==[ beta ]==> ((b b)((^y.(y y))(^z.(z z)))) 8. ==[ alpha ]==> ((b b)((^x.(x x))(^y.(y y)))) 9. ==[ beta ]==> ((b b)((^y.(y y))(^y.(y y)))) 10. ==[ alpha ]==> ((b b)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 185777/21663795. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (b ((^z.z)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.x)(^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 185778/21663804. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 185779/21663831. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((a a) a)(a a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((a a) a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 185780/21663858. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.z))) REDUCED to normal form. ------ 185781/21663912. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1) a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a (a a)))) REDUCED to normal form. ------ 185782/21663939. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 185783/21663966. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)((a a) a))) REDUCED to normal form. ------ 185784/21664038. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 185785/21664056. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a (a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.a))) REDUCED to normal form. ------ 185786/21664083. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 185787/21664110. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 185788/21664137. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a a)(^y.a))) 3. ==[ beta ]==> (((a (a a)) b)((a a)(^y.a))) 4. ==[ alpha ]==> (((a (a a)) b)((a a)(^x.a))) REDUCED to normal form. ------ 185789/21664164. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((a a) a) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((a a) a) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a) a) a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a) a)) REDUCED to normal form. ------ 185790/21664191. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x)(^y.y)) b)) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y) b)) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x) b)) 5. ==[ beta ]==> ((((a a) a)(b a)) b) REDUCED to normal form. ------ 185791/21664218. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (a a)) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (a a)) c)) REDUCED to normal form. ------ 185792/21664353. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z)) b)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y)) b)) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 185793/21664452. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 185794/21664857. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a)(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((a a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(a (a a)))) 5. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 185795/21664875. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 185796/21664902. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(z z))(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))(a a))) 5. ==[ beta ]==> ((a (a (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 185797/21664929. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.a)(a (^z.z))) 6. ==[ alpha ]==> ((^x.a)(a (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185798/21664983. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 185799/21665064. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185800/21665127. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (a a))) REDUCED to normal form. ------ 185801/21665172. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b (^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185802/21665307. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 185803/21665334. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 185804/21665379. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^b.a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.a) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 185805/21665406. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 185806/21665460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y) b)((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.z))) 7. ==[ beta ]==> (b ((a (^y.y))(^z.z))) 8. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 185807/21665487. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 185808/21665514. ------ 1. ==[ start ]==> (((a b)(b a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(b a))((a (^x.x)) a)) REDUCED to normal form. ------ 185809/21665541. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a) b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a) b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a) b)) REDUCED to normal form. ------ 185810/21665568. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 185811/21665622. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a a)(^z.z))) REDUCED to normal form. ------ 185812/21665649. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a) a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a) a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a) a)) 5. ==[ beta ]==> ((b (^y.y))((a a) a)) 6. ==[ alpha ]==> ((b (^x.x))((a a) a)) REDUCED to normal form. ------ 185813/21665676. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (a a))) a) REDUCED to normal form. ------ 185814/21665702. ------ 1. ==[ start ]==> (^a.((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (^x.((b (^y.y))((^z.z) x))) 3. ==[ beta ]==> (^x.((b (^y.y)) x)) 4. ==[ eta ]==> (b (^y.y)) 5. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185815/21665703. ------ 1. ==[ start ]==> (a ((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (a ((b (^x.x))((^y.y) a))) 3. ==[ beta ]==> (a ((b (^x.x)) a)) REDUCED to normal form. ------ 185816/21668190. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((^x.((^y.y)(x x)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185817/21674616. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ eta ]==> ((^y.(^z.z))(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185818/21677109. ------ 1. ==[ start ]==> ((^a.a)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 185819/21677136. ------ 1. ==[ start ]==> ((^a.(a a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 185820/21677163. ------ 1. ==[ start ]==> ((^a.b)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 185821/21677244. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^z.z))((^x1.x1)(a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.z)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 185822/21677433. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ eta ]==> ((^y.y)((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 185823/21677481. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 185824/21677604. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 185825/21677913. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 185826/21677928. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185827/21678354. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 185828/21678486. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1))))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2))))((a (^z2.(^x3.x3)))((^y3.y3)(^z3.z3)))) 5. ==[ beta ]==> ((((a (^x.(^y.y)))(^x1.x1))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2))))((a (^z2.(^x3.x3)))((^y3.y3)(^z3.z3)))) 6. ==[ alpha ]==> ((((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2))))((a (^y2.(^z2.z2)))((^x3.x3)(^y3.y3)))) 7. ==[ beta ]==> ((((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^x2.x2)))((a (^y2.(^z2.z2)))((^x3.x3)(^y3.y3)))) 8. ==[ alpha ]==> ((((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^z1.z1)))((a (^x2.(^y2.y2)))((^z2.z2)(^x3.x3)))) 9. ==[ beta ]==> ((((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^z1.z1)))((a (^x2.(^y2.y2)))(^x3.x3))) 10. ==[ alpha ]==> ((((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^z1.z1)))((a (^x2.(^y2.y2)))(^z2.z2))) REDUCED to normal form. ------ 185829/21678777. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185830/21678819. ------ 1. ==[ start ]==> ((^a.(^a.b))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 185831/21679182. ------ 1. ==[ start ]==> (((a b) a)(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) a)(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a b) a)(^x.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 185832/21679593. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.y)((a ((^z.(^x1.x1)) a))(a ((^z.(^x1.x1)) a)))) 4. ==[ alpha ]==> ((^x.x)((a ((^y.(^z.z)) a))(a ((^x1.(^y1.y1)) a)))) 5. ==[ beta ]==> ((a ((^y.(^z.z)) a))(a ((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(a ((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a (^y.y))(a ((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> ((a (^x.x))(a ((^y.(^z.z)) a))) 9. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 185833/21679596. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((a ((^x.x)(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.(^z.z))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 185834/21681024. ------ 1. ==[ start ]==> ((^a.(b a))((a (a a))(b a))) 2. ==[ alpha ]==> ((^x.(b x))((a (a a))(b a))) 3. ==[ eta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 185835/21681468. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.(^z.(a a)))) 3. ==[ beta ]==> (b (^y.(^z.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 185836/21681477. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 185837/21681861. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((((^x1.x1) b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(^z.z))) 5. ==[ beta ]==> ((b (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((b (a a))(^x.(^y.y))) REDUCED to normal form. ------ 185838/21682464. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185839/21682779. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(c (b a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(c (b a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 185840/21683151. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) REDUCED to normal form. ------ 185841/21683754. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b (a a))(^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b (a a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 185842/21683778. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((b a)(a a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((b a)(a a))) 3. ==[ beta ]==> ((((b a)(a a))((b a)(a a)))(((b a)(a a))((b a)(a a)))) REDUCED to normal form. ------ 185843/21684303. ------ 1. ==[ start ]==> (((^a.b)(a b))(^c.(^d.a))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.a))) 3. ==[ beta ]==> (b (^y.(^z.a))) 4. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 185844/21684312. ------ 1. ==[ start ]==> (((a b)(^a.b))(^b.(b a))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(y a))) REDUCED to normal form. ------ 185845/21684591. ------ 1. ==[ start ]==> (((a (a a))(b a))(^a.(b a))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(b x))) 3. ==[ eta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 185846/21685338. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 185847/21686019. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(a ((^x1.x1)(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185848/21686022. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(y y)))) 5. ==[ beta ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 185849/21686418. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^b.(a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(a z))) 3. ==[ eta ]==> ((((^x.(^y.y)) a) a) a) 4. ==[ beta ]==> (((^y.y) a) a) 5. ==[ alpha ]==> (((^x.x) a) a) 6. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185850/21686607. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 185851/21686838. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 185852/21687129. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.((y1 y1) y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.((y1 y1) y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((x1 x1) x1))) REDUCED to normal form. ------ 185853/21687261. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((^z.z)(^x1.x1)))(((a a)((^z.z)(^x1.x1)))(^y.y))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)((^z.z)(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)((^z.z)(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)((^y.y)(^z.z)))(^x1.x1))) 7. ==[ beta ]==> (((a a)(^x.x))(((a a)(^z.z))(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 185854/21687687. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 185855/21688011. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 185856/21688092. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185857/21688134. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1)) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 185858/21688182. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((a (^x.x))((^y.(^z.z)) a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.x1)) 5. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 185859/21688317. ------ 1. ==[ start ]==> (((a b)(b a))(^a.c)) 2. ==[ alpha ]==> (((a b)(b a))(^x.c)) REDUCED to normal form. ------ 185860/21688371. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 185861/21688452. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.b)) 5. ==[ beta ]==> ((b (^y.y))(^z.b)) 6. ==[ alpha ]==> ((b (^x.x))(^y.b)) REDUCED to normal form. ------ 185862/21688479. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(x x))) REDUCED to normal form. ------ 185863/21688518. ------ 1. ==[ start ]==> ((a a)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a a)((b (^x.x))((^y.y) a))) 3. ==[ beta ]==> ((a a)((b (^x.x)) a)) REDUCED to normal form. ------ 185864/21688545. ------ 1. ==[ start ]==> ((a (a a))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 185865/21688572. ------ 1. ==[ start ]==> ((a b)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.x) b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a b)(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a b)(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a b)(b (^y.y))) 6. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 185866/21688626. ------ 1. ==[ start ]==> (((a a)(a a))((b a)(a b))) REDUCED to normal form. ------ 185867/21688653. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (a (^x.x)))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 185868/21688788. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 185869/21688815. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(a (b (^y.y)))) REDUCED to normal form. ------ 185870/21688842. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a a)((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a a)((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 185871/21688887. ------ 1. ==[ start ]==> (((a (^a.a)) b)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 185872/21688914. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((a a)((a a)(^y.y))) 6. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 185873/21688932. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a (((^y.(^z.z)) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 185874/21688959. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 185875/21689013. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 185876/21689184. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)((^y.a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a b)((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 185877/21689202. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185878/21689211. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a)) a)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 185879/21689238. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 185880/21689265. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 185881/21689292. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 185882/21689310. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a)(a a))((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 185883/21689319. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 185884/21689337. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 185885/21689427. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((b b)((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b b)((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 185886/21689562. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 185887/21689616. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 185888/21689643. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 185889/21689670. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.a))((^z.(a a))(^z.(a a)))) 6. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 185890/21689760. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(a (a (a (^z.z))))) 3. ==[ beta ]==> (((a a)(^y.y))(a (a (a (^z.z))))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (a (a (^y.y))))) REDUCED to normal form. ------ 185891/21689787. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(a a))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 185892/21689814. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a a)((b (^y.y))(a (^z.z)))) 6. ==[ alpha ]==> ((a a)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 185893/21689841. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 185894/21689868. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> ((a a)(((^y.y) b)(a (a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)(a (a a)))) 7. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 185895/21689895. ------ 1. ==[ start ]==> ((a ((a a) a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a) a))((a (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 185896/21690183. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(a (^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(z (^x1.x1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185897/21690228. ------ 1. ==[ start ]==> ((a (^a.b))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 185898/21690399. ------ 1. ==[ start ]==> (((^a.b) a)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (b ((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 185899/21690417. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 185900/21690498. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(^z.z))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (a a))(^z.z))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))(^z.z))) IRREDUCIBLE: cycle. ------ 185901/21690561. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 185902/21690588. ------ 1. ==[ start ]==> (((a b) a)((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) a)((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 185903/21690606. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((a b)(((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a) a)) 5. ==[ beta ]==> ((a b)((^y.y) a)) 6. ==[ alpha ]==> ((a b)((^x.x) a)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 185904/21690633. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((b (^z.z)) b)) 3. ==[ beta ]==> ((^y.y)((b (^z.z)) b)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) b)) 5. ==[ beta ]==> ((b (^y.y)) b) 6. ==[ alpha ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 185905/21690669. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 185906/21690696. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.(z z))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 185907/21690723. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 185908/21690777. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 185909/21690975. ------ 1. ==[ start ]==> (((a b)(a a))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))(b (b (^x.x)))) REDUCED to normal form. ------ 185910/21691002. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a a))(a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((a (a a))(a ((^x.(^y.y)) a))) 5. ==[ beta ]==> ((a (a a))(a (^y.y))) 6. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 185911/21691614. ------ 1. ==[ start ]==> (((^a.b) c)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (b ((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 185912/21691713. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((^y.y) a)(^z.z)) 6. ==[ alpha ]==> (((^x.x) a)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 185913/21691848. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) b) c)) 3. ==[ beta ]==> (b (((^z.z) b) c)) 4. ==[ alpha ]==> (b (((^x.x) b) c)) 5. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 185914/21691857. ------ 1. ==[ start ]==> (((a b) c)((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a b) c)((^x.x)(^y.a))) 3. ==[ beta ]==> (((a b) c)(^y.a)) 4. ==[ alpha ]==> (((a b) c)(^x.a)) REDUCED to normal form. ------ 185915/21691884. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 185916/21691965. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 185917/21691992. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 185918/21692073. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 185919/21692100. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 185920/21692190. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 185921/21692217. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(b (a (^z.z)))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(b (a (^y.y)))) REDUCED to normal form. ------ 185922/21692244. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((a (a b))((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> ((a (a b))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 185923/21692271. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((b a)(a (a a)))) REDUCED to normal form. ------ 185924/21692298. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 11. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 12. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 185925/21692325. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((^x.x)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((a a)((a a) a))) REDUCED to normal form. ------ 185926/21692352. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a b)(a b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a b)(a b))) 3. ==[ beta ]==> (((a b) a)((a b)(a b))) REDUCED to normal form. ------ 185927/21692379. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(((a a) a)(a a))) REDUCED to normal form. ------ 185928/21692406. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a a)(^y.y))) REDUCED to normal form. ------ 185929/21692433. ------ 1. ==[ start ]==> ((a (b a))((a (a a))(b a))) REDUCED to normal form. ------ 185930/21692604. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 185931/21692667. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 185932/21692712. ------ 1. ==[ start ]==> (((^a.a)(b a))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b a))((a b)(^y.b))) 3. ==[ beta ]==> ((b a)((a b)(^y.b))) 4. ==[ alpha ]==> ((b a)((a b)(^x.b))) REDUCED to normal form. ------ 185933/21692739. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((a a) a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.(a a))) 6. ==[ alpha ]==> (((a a) a)(^x.(a a))) REDUCED to normal form. ------ 185934/21692775. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 185935/21692802. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a (a a))(^x.b))((b a)(b a))) REDUCED to normal form. ------ 185936/21692856. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 185937/21692874. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a a)(^y.(a a)))) 3. ==[ beta ]==> (b ((a a)(^y.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 185938/21692883. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)((a a)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 185939/21692910. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))(^z.z))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 185940/21692937. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 185941/21693216. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(b ((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(b b)) REDUCED to normal form. ------ 185942/21693270. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(b (a a))) REDUCED to normal form. ------ 185943/21693279. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.b) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1) b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 185944/21693558. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(b (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b (^z.z))) REDUCED to normal form. ------ 185945/21693603. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.z))) 5. ==[ beta ]==> (((^y.y) b)(^z.z)) 6. ==[ alpha ]==> (((^x.x) b)(^y.y)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 185946/21693657. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((b a)(^z.a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((b a)(^z.a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((b a)(^z.a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((b a)(^z.a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a)(^y.a))) 7. ==[ beta ]==> (((a a)(a a))((b a)(^y.a))) 8. ==[ alpha ]==> (((a a)(a a))((b a)(^x.a))) REDUCED to normal form. ------ 185947/21693693. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a (a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 185948/21693738. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a b)(^x1.a))) 3. ==[ beta ]==> (b ((a b)(^x1.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 185949/21693747. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 185950/21693801. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 185951/21693855. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 185952/21693873. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 185953/21694152. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185954/21694188. ------ 1. ==[ start ]==> ((a ((^a.a) b))(c (b a))) 2. ==[ alpha ]==> ((a ((^x.x) b))(c (b a))) 3. ==[ beta ]==> ((a b)(c (b a))) REDUCED to normal form. ------ 185955/21694503. ------ 1. ==[ start ]==> ((((^a.a) b) a)(c (^d.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(c (^y.a))) 3. ==[ beta ]==> ((b a)(c (^y.a))) 4. ==[ alpha ]==> ((b a)(c (^x.a))) REDUCED to normal form. ------ 185956/21694530. ------ 1. ==[ start ]==> (((a a)(^b.b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 185957/21694557. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a (^y1.y1))) REDUCED to normal form. ------ 185958/21694602. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 185959/21694638. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 185960/21694665. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a a)) REDUCED to normal form. ------ 185961/21694683. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 185962/21694692. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 185963/21694719. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)((a a) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 185964/21694746. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 185965/21694800. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 185966/21694827. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 185967/21695133. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(b (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(b (b a))) REDUCED to normal form. ------ 185968/21695160. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> ((b (a a))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((b (a a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 185969/21695187. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((b a)(a a))) REDUCED to normal form. ------ 185970/21695223. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 5. ==[ beta ]==> ((^y.(^z.z)) c) 6. ==[ alpha ]==> ((^x.(^y.y)) c) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185971/21695466. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((b a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185972/21695502. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 185973/21695529. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 185974/21695547. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a b)(^y.(y y)))) 3. ==[ beta ]==> (((a a)(a a))((a b)(^y.(y y)))) 4. ==[ alpha ]==> (((a a)(a a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 185975/21695574. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 185976/21695583. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 185977/21695610. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 185978/21695628. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (a a))(^y.b))) 3. ==[ beta ]==> (((b a)(b a))((a (a a))(^y.b))) 4. ==[ alpha ]==> (((b a)(b a))((a (a a))(^x.b))) REDUCED to normal form. ------ 185979/21695691. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 185980/21695718. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(b a))) 3. ==[ beta ]==> (((a b)(^x.b))(b a)) REDUCED to normal form. ------ 185981/21695772. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 185982/21695826. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 185983/21695853. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 185984/21695880. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 185985/21695943. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(c ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(c ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(c ((^y.y)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(c (a a))) REDUCED to normal form. ------ 185986/21695970. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b ((a a)(^z.z)))) REDUCED to normal form. ------ 185987/21695997. ------ 1. ==[ start ]==> (((a (a a))(b a))(a (b a))) REDUCED to normal form. ------ 185988/21696024. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 185989/21696051. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(a (^y.y)))) 6. ==[ alpha ]==> ((((a a) a)(a a))((a a)(a (^x.x)))) REDUCED to normal form. ------ 185990/21696078. ------ 1. ==[ start ]==> (((a b)(a b))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a b))((a b)((^x.x) a))) 3. ==[ beta ]==> (((a b)(a b))((a b) a)) REDUCED to normal form. ------ 185991/21696105. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 185992/21696132. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(^x1.x1))) 9. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 10. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 185993/21696186. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) a)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (a b))) REDUCED to normal form. ------ 185994/21696213. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 185995/21696240. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 185996/21696357. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((a a) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a) a)(^x2.(x2 x2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x2.(x2 x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185997/21696438. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.b))) 5. ==[ beta ]==> (b (a (^y.b))) 6. ==[ alpha ]==> (b (a (^x.b))) REDUCED to normal form. ------ 185998/21696546. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(a a)) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 185999/21696582. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b)(^z.a))) 3. ==[ beta ]==> ((b c)((^y.b)(^z.a))) 4. ==[ alpha ]==> ((b c)((^x.b)(^y.a))) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 186000/21696609. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 186001/21696717. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 186002/21696816. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b) c)) 3. ==[ beta ]==> (b ((^z.b) c)) 4. ==[ alpha ]==> (b ((^x.b) c)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 186003/21696960. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b (^z.(a a)))) 3. ==[ beta ]==> ((b (^y.a))(b (^z.(a a)))) 4. ==[ alpha ]==> ((b (^x.a))(b (^y.(a a)))) REDUCED to normal form. ------ 186004/21697428. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 186005/21697707. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(^y2.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(^y2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186006/21697824. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.z)(a b))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(a b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(a b))) 5. ==[ beta ]==> (a ((^y.y)(a b))) 6. ==[ alpha ]==> (a ((^x.x)(a b))) 7. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 186007/21697842. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a b) a)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a b) a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a b) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a b) a)) 5. ==[ beta ]==> ((^y.y)((a b) a)) 6. ==[ alpha ]==> ((^x.x)((a b) a)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 186008/21697869. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((a a) a) b)) 3. ==[ beta ]==> ((^y.y)(((a a) a) b)) 4. ==[ alpha ]==> ((^x.x)(((a a) a) b)) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 186009/21697932. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 186010/21697959. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186011/21698013. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.b)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 186012/21698148. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 186013/21698175. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (^y.a))) REDUCED to normal form. ------ 186014/21698247. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 186015/21698481. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (a (a a)))) REDUCED to normal form. ------ 186016/21698535. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a ((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a ((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((a a) a))) REDUCED to normal form. ------ 186017/21698562. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y)(^z.z))(a a))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x)(^y.y))(a a))) 5. ==[ beta ]==> ((b (a (a a)))((^y.y)(a a))) 6. ==[ alpha ]==> ((b (a (a a)))((^x.x)(a a))) 7. ==[ beta ]==> ((b (a (a a)))(a a)) REDUCED to normal form. ------ 186018/21698589. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (a a))(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (a a))(a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 186019/21698643. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(a (a a)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(a (a a)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 186020/21698661. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 186021/21698670. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)(^y.y))) REDUCED to normal form. ------ 186022/21699066. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b (^z.(z z)))) 3. ==[ beta ]==> (((^y.y) b)(b (^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) b)(b (^y.(y y)))) 5. ==[ beta ]==> (b (b (^y.(y y)))) 6. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 186023/21699093. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.(^z.z)))) REDUCED to normal form. ------ 186024/21699111. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (a a))(^z.z))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 186025/21699120. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(z z))(a a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((a a)(a a))) REDUCED to normal form. ------ 186026/21699138. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 186027/21699192. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a)(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(^y.(y y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)(^x.(x x)))) REDUCED to normal form. ------ 186028/21699228. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 7. ==[ beta ]==> ((^y.(y y))(^z.z)) 8. ==[ alpha ]==> ((^x.(x x))(^y.y)) 9. ==[ beta ]==> ((^y.y)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186029/21699255. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 186030/21699273. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y)) c)) 3. ==[ beta ]==> (b ((a (^y.y)) c)) 4. ==[ alpha ]==> (b ((a (^x.x)) c)) REDUCED to normal form. ------ 186031/21699417. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 186032/21699444. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.a)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 186033/21699498. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186034/21699516. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(((^z.z) a) a)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a) a)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a) a)) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 186035/21699525. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 186036/21699543. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1)) b)) REDUCED to normal form. ------ 186037/21699561. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b (a (^y.y)))) REDUCED to normal form. ------ 186038/21699588. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a ((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 186039/21699615. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z))(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z))(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 186040/21699642. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a a)(a (^x.x)))) REDUCED to normal form. ------ 186041/21699669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(c a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(c a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(c a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(c a)) 5. ==[ beta ]==> (((^y.y) b)(c a)) 6. ==[ alpha ]==> (((^x.x) b)(c a)) 7. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 186042/21699696. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b b)) REDUCED to normal form. ------ 186043/21699723. ------ 1. ==[ start ]==> (((a b)(b a))(a c)) REDUCED to normal form. ------ 186044/21699750. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b (a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b (a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (a a))) REDUCED to normal form. ------ 186045/21699777. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a (a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (a (^y.y)))) REDUCED to normal form. ------ 186046/21699831. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b a)) REDUCED to normal form. ------ 186047/21699858. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a b)) 5. ==[ beta ]==> ((b (^y.y))(a b)) 6. ==[ alpha ]==> ((b (^x.x))(a b)) REDUCED to normal form. ------ 186048/21699885. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a (a a))) REDUCED to normal form. ------ 186049/21708834. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.(^y1.(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186050/21711345. ------ 1. ==[ start ]==> ((^a.(^a.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186051/21711426. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186052/21711588. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (^x.(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (^x.((^z.z)((^x1.x1) b))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.z) b))) 7. ==[ beta ]==> (^x.((^z.z) b)) 8. ==[ alpha ]==> (^x.((^y.y) b)) 9. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 186053/21712281. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186054/21712581. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 186055/21713226. ------ 1. ==[ start ]==> ((^a.(a b))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.(a a))((^z.z)(a a))) b) 4. ==[ alpha ]==> (((^x.(a a))((^y.y)(a a))) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 186056/21713832. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.x)(^y.(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 186057/21714210. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 186058/21714495. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((((^z.(^x1.x1))(b a))((^z.(^x1.x1))(b a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y))(b a))((^z.(^x1.x1))(b a)))(^y1.y1)) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1))(b a)))(^y1.y1)) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(b a)))(^x1.x1)) 7. ==[ beta ]==> (((^y.(^z.z))(b a))(^x1.x1)) 8. ==[ alpha ]==> (((^x.(^y.y))(b a))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186059/21715344. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.((a a)(a a)))) 5. ==[ beta ]==> (b (^z.((a a)(a a)))) 6. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 186060/21715704. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 186061/21716739. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 186062/21717684. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 186063/21717981. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 186064/21718539. ------ 1. ==[ start ]==> (((a b)(^a.b))(^c.(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.a))) REDUCED to normal form. ------ 186065/21720033. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a a))(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(a a))(^x.(a a))) REDUCED to normal form. ------ 186066/21720246. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.x1)(^y1.(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186067/21720249. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 186068/21721194. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((a a) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((a a) a))) REDUCED to normal form. ------ 186069/21721356. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.a))) REDUCED to normal form. ------ 186070/21721488. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^z.(^x1.x1)))((b (^z.(^x1.x1)))(^y.y))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((b (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 186071/21722361. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(c (a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(c (a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 186072/21722409. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.a))) REDUCED to normal form. ------ 186073/21722490. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.z))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.z))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.y))) 7. ==[ beta ]==> (b (^y.(^z.y))) 8. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 186074/21722544. ------ 1. ==[ start ]==> (((a b)(b a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(a (^y.y)))) REDUCED to normal form. ------ 186075/21722598. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 186076/21722652. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 186077/21722679. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(a a))) 5. ==[ beta ]==> ((b (^y.y))(^z.(a a))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(a a))) REDUCED to normal form. ------ 186078/21722706. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 186079/21722763. ------ 1. ==[ start ]==> ((a (^a.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.x))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 186080/21722790. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 186081/21722817. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 186082/21722844. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))((a a) a))) REDUCED to normal form. ------ 186083/21722898. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186084/21722925. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 186085/21722952. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a b)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a b)(b a))) 3. ==[ beta ]==> ((a (^y.y))((a b)(b a))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(b a))) REDUCED to normal form. ------ 186086/21722979. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 186087/21723006. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.a))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.a))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 186088/21723087. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.a)((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.a)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 186089/21723114. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 186090/21723150. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a a)((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> ((a a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 186091/21723177. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 186092/21723204. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1))(^y1.a))) REDUCED to normal form. ------ 186093/21723231. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 186094/21723267. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 186095/21723294. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 186096/21723339. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 186097/21723420. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a b)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 186098/21723447. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a)) a)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 186099/21723555. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 186100/21723591. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a a)(a (a a)))((^z.z)(^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 186101/21723699. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 186102/21723996. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 186103/21724167. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 5. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 186104/21724221. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (a (((^z.z)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (a (((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (a ((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (a ((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 186105/21724302. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 186106/21724329. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a (a a))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 186107/21724383. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.y))(b (^z.z)))) 7. ==[ beta ]==> ((a a)((a (^y.y))(b (^z.z)))) 8. ==[ alpha ]==> ((a a)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 186108/21724446. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 186109/21724536. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)(a (a a)))) 5. ==[ beta ]==> ((a (a (a a)))(a (a a))) REDUCED to normal form. ------ 186110/21724563. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 186111/21724635. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> (b ((a a)(^y.(a a)))) 6. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 186112/21724644. ------ 1. ==[ start ]==> ((a (a b))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 186113/21724851. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a a)(^x.b))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y) a)) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 186114/21724905. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(a a)) c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(a a)) c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a)) c)) REDUCED to normal form. ------ 186115/21725049. ------ 1. ==[ start ]==> (((a a)(a b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 186116/21725076. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) b) REDUCED to normal form. ------ 186117/21725130. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 186118/21725157. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y) a)((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.z))) 7. ==[ beta ]==> (a ((^y.(y y))(^z.z))) 8. ==[ alpha ]==> (a ((^x.(x x))(^y.y))) 9. ==[ beta ]==> (a ((^y.y)(^y.y))) 10. ==[ alpha ]==> (a ((^x.x)(^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 186119/21725184. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x))) a) REDUCED to normal form. ------ 186120/21725247. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.(a a))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.(a a))(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 186121/21725274. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((b (^x1.x1))(a a))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(a a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(a a))) 5. ==[ beta ]==> ((b (^y.y))(a a)) 6. ==[ alpha ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 186122/21725328. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)((^z1.z1) a))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b)((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z) a))) 7. ==[ beta ]==> (((^y.y) b)((^z.z) a)) 8. ==[ alpha ]==> (((^x.x) b)((^y.y) a)) 9. ==[ beta ]==> (b ((^y.y) a)) 10. ==[ alpha ]==> (b ((^x.x) a)) 11. ==[ beta ]==> (b a) REDUCED to normal form. ------ 186123/21725409. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 186124/21725463. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)((a b)((^y.y)(a a)))) 6. ==[ alpha ]==> ((a a)((a b)((^x.x)(a a)))) 7. ==[ beta ]==> ((a a)((a b)(a a))) REDUCED to normal form. ------ 186125/21725490. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 186126/21725544. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (a a))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (a a))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (a a))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(a (^z.(^x1.x1))))) 9. ==[ beta ]==> ((^y.y)((a (a a))(a (^z.(^x1.x1))))) 10. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.(^z.z))))) 11. ==[ beta ]==> ((a (a a))(a (^y.(^z.z)))) 12. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 186127/21725625. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a a)(b (^z.z)))) 3. ==[ beta ]==> (b ((a a)(b (^z.z)))) 4. ==[ alpha ]==> (b ((a a)(b (^x.x)))) REDUCED to normal form. ------ 186128/21725661. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 186129/21725724. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(a b))((^z.z) a)) 4. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y) a)) 5. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 186130/21725751. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 186131/21725832. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(a a))(a b))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(a a))(a b))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))(a b))) 5. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 186132/21725850. ------ 1. ==[ start ]==> (((^a.b) c)((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((a b)(^y.(a a)))) 3. ==[ beta ]==> (b ((a b)(^y.(a a)))) 4. ==[ alpha ]==> (b ((a b)(^x.(a a)))) REDUCED to normal form. ------ 186133/21725859. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x))) b) REDUCED to normal form. ------ 186134/21725913. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 186135/21726093. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b) c)(((^x.x) b) c)) 3. ==[ beta ]==> (((a b) c)(b c)) REDUCED to normal form. ------ 186136/21726759. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a a)((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)((a a)(a a)))) REDUCED to normal form. ------ 186137/21726903. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 186138/21727011. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 186139/21727092. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 186140/21727119. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 186141/21727146. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((a a)(a a)) a)) 3. ==[ beta ]==> (((a a)(^y.a))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a)(a a)) a)) REDUCED to normal form. ------ 186142/21727173. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) b) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b b)) REDUCED to normal form. ------ 186143/21727290. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.a))) 6. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.a))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 186144/21727317. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.b)(^y.b))) 3. ==[ beta ]==> (((a (a a))(a b)) b) REDUCED to normal form. ------ 186145/21727371. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 186146/21727425. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a) a)((^y.a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a) a)((^x.a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 186147/21727452. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 186148/21727515. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) b)(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186149/21727596. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a a)(((a a)(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 186150/21727677. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(a b))) 3. ==[ beta ]==> (b (((a a) a)(a b))) REDUCED to normal form. ------ 186151/21727785. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186152/21727812. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 186153/21727902. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((b a)(^y.a))) REDUCED to normal form. ------ 186154/21727929. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.b)(((a a)(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(^z.(z z)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 186155/21727983. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.a))) REDUCED to normal form. ------ 186156/21728010. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((a a) a)(^z.b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)(^y.b))) REDUCED to normal form. ------ 186157/21728037. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(a a))) REDUCED to normal form. ------ 186158/21728127. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 186159/21728154. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(b a))((^z.z) b)) 4. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y) b)) 5. ==[ beta ]==> (((a (^x.x))(b a)) b) REDUCED to normal form. ------ 186160/21728181. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 186161/21728208. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 186162/21728289. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 186163/21728316. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.b)(^z.a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.b)(^y.a))) 5. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 186164/21728433. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(c (b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(c (b a))) 3. ==[ beta ]==> ((^y.y)(c (b a))) 4. ==[ alpha ]==> ((^x.x)(c (b a))) 5. ==[ beta ]==> (c (b a)) REDUCED to normal form. ------ 186165/21728460. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(b (a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(b (a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(b (a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 186166/21728595. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (b (((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 186167/21728703. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (a a))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186168/21728757. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z))(b a))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(b a))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(b a))) 5. ==[ beta ]==> (b ((a (^y.y))(b a))) 6. ==[ alpha ]==> (b ((a (^x.x))(b a))) REDUCED to normal form. ------ 186169/21728784. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 186170/21728874. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 186171/21728901. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a a)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((a a)(^y.(y y)))) REDUCED to normal form. ------ 186172/21728928. ------ 1. ==[ start ]==> (((a b)(^c.a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 186173/21728955. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(^z.a))) REDUCED to normal form. ------ 186174/21728982. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.b)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.b)) REDUCED to normal form. ------ 186175/21729099. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 186176/21729126. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 186177/21729207. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(^z.(z z)))) 7. ==[ beta ]==> ((a a)((^y.(a a))(^z.(z z)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(y y)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 186178/21729234. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a b)) b) REDUCED to normal form. ------ 186179/21729261. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.a)(^y.a))) 3. ==[ beta ]==> (((a b)((a a) a)) a) REDUCED to normal form. ------ 186180/21729288. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 186181/21729315. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 186182/21729396. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (a a))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (a a))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((b (a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 186183/21729459. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^y.y))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 186184/21729594. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a (a a))(a b))) 3. ==[ beta ]==> (b ((a (a a))(a b))) REDUCED to normal form. ------ 186185/21729738. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 186186/21729765. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a a)(^y.a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a a)(^x.a))) REDUCED to normal form. ------ 186187/21729819. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 186188/21729927. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 186189/21730008. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1)) b)) REDUCED to normal form. ------ 186190/21730152. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(x x))(^y.b))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((^y.b)(^y.b))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.b)(^y.b))) 5. ==[ beta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 186191/21730179. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 186192/21730449. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(c (^z.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(c (^z.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(c (^y.(a a)))) REDUCED to normal form. ------ 186193/21730476. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 186194/21730818. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b) c)) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b) c)) 3. ==[ beta ]==> ((b c)((a b) c)) REDUCED to normal form. ------ 186195/21730971. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(b ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b ((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b (a a))) REDUCED to normal form. ------ 186196/21731052. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a b)(a (^z.z)))) 3. ==[ beta ]==> (b ((a b)(a (^z.z)))) 4. ==[ alpha ]==> (b ((a b)(a (^x.x)))) REDUCED to normal form. ------ 186197/21731061. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b) c)) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 186198/21731088. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a) d)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a) d)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a) d)) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 186199/21731160. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1) a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186200/21731286. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 186201/21731340. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 186202/21731367. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(^x1.x1))) 9. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 10. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 186203/21731394. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)((a a) a))) 5. ==[ beta ]==> ((b a)((^y.a)((a a) a))) 6. ==[ alpha ]==> ((b a)((^x.a)((a a) a))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 186204/21731421. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 186205/21731448. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(a a))((^y.y)(a a))) 6. ==[ alpha ]==> (((a b)(a a))((^x.x)(a a))) 7. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 186206/21731475. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(a b))((^y.(a a))(^z.z))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(a a))(^y.y))) 5. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 186207/21731502. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 186208/21731556. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 186209/21731583. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> ((b a)((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> ((b a)(^y.y)) 10. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 186210/21731610. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 186211/21731664. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(a a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 186212/21731754. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) a)) 9. ==[ beta ]==> ((^y.y)((^z.z) a)) 10. ==[ alpha ]==> ((^x.x)((^y.y) a)) 11. ==[ beta ]==> ((^y.y) a) 12. ==[ alpha ]==> ((^x.x) a) 13. ==[ beta ]==> a REDUCED to normal form. ------ 186213/21731835. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))((a a) a))) 3. ==[ beta ]==> (b ((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a) a))) REDUCED to normal form. ------ 186214/21732060. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a a)(^z.b))) 3. ==[ beta ]==> (((^y.y) a)((a a)(^z.b))) 4. ==[ alpha ]==> (((^x.x) a)((a a)(^y.b))) 5. ==[ beta ]==> (a ((a a)(^y.b))) 6. ==[ alpha ]==> (a ((a a)(^x.b))) REDUCED to normal form. ------ 186215/21732240. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(b ((a a) a))) 3. ==[ beta ]==> (b (b ((a a) a))) REDUCED to normal form. ------ 186216/21732276. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.b) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.b) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b) a)) 5. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 186217/21732303. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^c.a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 186218/21732348. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186219/21732465. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((a a) a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.z))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.z))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 186220/21732501. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 186221/21732528. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(((^x1.x1) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a ((^x1.x1) a))) 6. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a ((^z.z) a))) 7. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a a)) REDUCED to normal form. ------ 186222/21732555. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a)(a (a a)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)(a (a a)))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 186223/21732582. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 186224/21732609. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.y1)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((a a) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((a a) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 186225/21732636. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(^y.y))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 186226/21732663. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 186227/21732690. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(^z.a))) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.a))) 7. ==[ beta ]==> (((a a)(a a))((^y.a)(^y.a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.a))) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 186228/21732717. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 186229/21732906. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (^y.(^z.z)))) REDUCED to normal form. ------ 186230/21732915. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)((^z.z)(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.z)) 7. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 186231/21733320. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a)(a (a a)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a a)(a (a a)))) 7. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 186232/21733356. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (a a))(^z.z))) REDUCED to normal form. ------ 186233/21733464. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a a)) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a)) a)) 5. ==[ beta ]==> ((^y.y)((a (a a)) a)) 6. ==[ alpha ]==> ((^x.x)((a (a a)) a)) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 186234/21733491. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1) a) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a b)) REDUCED to normal form. ------ 186235/21733509. ------ 1. ==[ start ]==> (((^a.b)(b a))(c (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(c (a (^y.y)))) 3. ==[ beta ]==> (b (c (a (^y.y)))) 4. ==[ alpha ]==> (b (c (a (^x.x)))) REDUCED to normal form. ------ 186236/21733572. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(z z)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 186237/21733617. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186238/21733680. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 186239/21733734. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186240/21733761. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(((^z.z) a) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a a)) REDUCED to normal form. ------ 186241/21733779. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(c (a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(c (a a))) REDUCED to normal form. ------ 186242/21733797. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 186243/21733824. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.a)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.a)) REDUCED to normal form. ------ 186244/21733851. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(c (^z.z))) 3. ==[ beta ]==> ((a (b (^y.y)))(c (^z.z))) 4. ==[ alpha ]==> ((a (b (^x.x)))(c (^y.y))) REDUCED to normal form. ------ 186245/21733878. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 186246/21733905. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a (^x1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a (^x1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (^z.a))) 5. ==[ beta ]==> (((^y.y) b)(a (^z.a))) 6. ==[ alpha ]==> (((^x.x) b)(a (^y.a))) 7. ==[ beta ]==> (b (a (^y.a))) 8. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 186247/21733932. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 186248/21733959. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a b)(b a))(a (^y.y))) 4. ==[ alpha ]==> (((a b)(b a))(a (^x.x))) REDUCED to normal form. ------ 186249/21733986. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 186250/21734013. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 186251/21734067. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 186252/21734094. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 186253/21734121. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x)(^y.y))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 186254/21734988. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186255/21745962. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 186256/21746184. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))(^z.(a a)))((((a a)(^y.y))(^z.(a a)))(((a a)(^y.y))(^z.(a a))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((((a a)(^z.z))(^x1.(a a)))(((a a)(^y1.y1))(^z1.(a a))))) REDUCED to normal form. ------ 186257/21746409. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186258/21746412. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 186259/21747480. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))(^z.(a a))) b) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a))) b) 5. ==[ beta ]==> (((a a)(^y.(a a))) b) 6. ==[ alpha ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 186260/21747681. ------ 1. ==[ start ]==> (((^a.a)(a b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a b)(^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a b)(^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a b)(^x.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 186261/21747867. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(^y1.b))((^z.(^x1.x1))(^y1.b)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(^x1.b))((^y1.(^z1.z1))(^x2.b)))) 5. ==[ beta ]==> (^x.((^z.z)((^y1.(^z1.z1))(^x2.b)))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(^y1.b)))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(^y1.b))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.b))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186262/21748473. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 186263/21750054. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(^y2.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 186264/21750336. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((x1 x1)(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186265/21750678. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(y y)))) 5. ==[ beta ]==> (^y.(^z.(y y))) 6. ==[ alpha ]==> (^x.(^y.(x x))) REDUCED to normal form. ------ 186266/21750945. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186267/21750993. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^c.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 186268/21751938. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 186269/21752259. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((((^y.(^z.(^x1.x1))) a)((^y.(^z.(^x1.x1))) a))(((^y.(^z.(^x1.x1))) a)((^y.(^z.(^x1.x1))) a))) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z))) a)((^x1.(^y1.(^z1.z1))) a))(((^x2.(^y2.(^z2.z2))) a)((^x3.(^y3.(^z3.z3))) a))) 5. ==[ beta ]==> (((^y.(^z.z))((^x1.(^y1.(^z1.z1))) a))(((^x2.(^y2.(^z2.z2))) a)((^x3.(^y3.(^z3.z3))) a))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1))) a))(((^z1.(^x2.(^y2.y2))) a)((^z2.(^x3.(^y3.y3))) a))) 7. ==[ beta ]==> ((^y.y)(((^z1.(^x2.(^y2.y2))) a)((^z2.(^x3.(^y3.y3))) a))) 8. ==[ alpha ]==> ((^x.x)(((^y.(^z.(^x1.x1))) a)((^y1.(^z1.(^x2.x2))) a))) 9. ==[ beta ]==> (((^y.(^z.(^x1.x1))) a)((^y1.(^z1.(^x2.x2))) a)) 10. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.(^z1.z1))) a)) 11. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1))) a)) 12. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186270/21752541. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186271/21754287. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 186272/21754917. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^b.(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.x)((^y.(^z.z)) a)) a) 4. ==[ beta ]==> (((^y.(^z.z)) a) a) 5. ==[ alpha ]==> (((^x.(^y.y)) a) a) 6. ==[ beta ]==> ((^y.y) a) 7. ==[ alpha ]==> ((^x.x) a) 8. ==[ beta ]==> a REDUCED to normal form. ------ 186273/21755088. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((a a) a))) REDUCED to normal form. ------ 186274/21755115. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(z b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(z b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(y b))) REDUCED to normal form. ------ 186275/21756186. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 186276/21756411. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(z (z z)))) REDUCED to normal form. ------ 186277/21756492. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 186278/21756591. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 186279/21756615. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 186280/21756744. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.c)) 5. ==[ beta ]==> (((^y.y) b)(^z.c)) 6. ==[ alpha ]==> (((^x.x) b)(^y.c)) 7. ==[ beta ]==> (b (^y.c)) 8. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 186281/21756798. ------ 1. ==[ start ]==> (((a b)(b a))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 186282/21756906. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 186283/21756933. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 186284/21757035. ------ 1. ==[ start ]==> (((^a.a) a)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x) a)((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (a ((b (^y.y))((^z.z) a))) 4. ==[ alpha ]==> (a ((b (^x.x))((^y.y) a))) 5. ==[ beta ]==> (a ((b (^x.x)) a)) REDUCED to normal form. ------ 186285/21757062. ------ 1. ==[ start ]==> (((a a) a)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 186286/21757089. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 186287/21757116. ------ 1. ==[ start ]==> (((^a.a) b)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 186288/21757143. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((b a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((b a)(a b))) 3. ==[ beta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 186289/21757170. ------ 1. ==[ start ]==> (((a a) b)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) b)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 186290/21757197. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) a)((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 186291/21757224. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(b a))) REDUCED to normal form. ------ 186292/21757251. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 186293/21757305. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 186294/21757377. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(b (^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 186295/21757386. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 186296/21757431. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> (a ((^y.(y (^z.z)))(a a))) 6. ==[ alpha ]==> (a ((^x.(x (^y.y)))(a a))) 7. ==[ beta ]==> (a ((a a)(^y.y))) 8. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 186297/21757530. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 186298/21757584. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((b a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((b a)(^y.b))) 3. ==[ beta ]==> ((a (a a))((b a)(^y.b))) 4. ==[ alpha ]==> ((a (a a))((b a)(^x.b))) REDUCED to normal form. ------ 186299/21757611. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 186300/21757647. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 186301/21757728. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 186302/21757755. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 186303/21757809. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 186304/21757836. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 186305/21757854. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(a (a a)))((a (a (^x.x))) a)) REDUCED to normal form. ------ 186306/21757881. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z) b)) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y) b)) 7. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 186307/21757908. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((b (^z.z)) c)) 3. ==[ beta ]==> ((a (a (^y.y)))((b (^z.z)) c)) 4. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y)) c)) REDUCED to normal form. ------ 186308/21757971. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186309/21758286. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (^y.y))) REDUCED to normal form. ------ 186310/21758520. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y) b)((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> (b ((a b)((a a)(^y.y)))) 6. ==[ alpha ]==> (b ((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 186311/21758547. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a) a)(b a))) REDUCED to normal form. ------ 186312/21758601. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a (a a)) b)) REDUCED to normal form. ------ 186313/21758628. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))(a ((a a)(a a)))) REDUCED to normal form. ------ 186314/21758655. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 186315/21758682. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a a)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186316/21758745. ------ 1. ==[ start ]==> (((a a)((a a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 186317/21758772. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(a a))(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 186318/21758799. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> ((a (a (a a)))(b (^y.(y y)))) 6. ==[ alpha ]==> ((a (a (a a)))(b (^x.(x x)))) REDUCED to normal form. ------ 186319/21758826. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a)) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a)) a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 186320/21758853. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b a)(^z.a))) 5. ==[ beta ]==> ((a (^y.y))((b a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 186321/21758880. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 186322/21758907. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> ((a (a b))((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((a (a b))((a a)(^x.(a a)))) REDUCED to normal form. ------ 186323/21758916. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 186324/21758997. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) IRREDUCIBLE: cycle. ------ 186325/21759078. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186326/21759105. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a b)((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a b)((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a b)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a b)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 186327/21759294. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 186328/21759465. ------ 1. ==[ start ]==> (((^a.b) b)(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(c ((a a)(a a)))) 3. ==[ beta ]==> (b (c ((a a)(a a)))) REDUCED to normal form. ------ 186329/21759681. ------ 1. ==[ start ]==> (((a b) b)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b) b)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 186330/21759708. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))(a b))) 5. ==[ beta ]==> (((a a) a)((a a)(a b))) REDUCED to normal form. ------ 186331/21759735. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a b)(a a))) REDUCED to normal form. ------ 186332/21759762. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a) a)((a a)(^z.z)))) REDUCED to normal form. ------ 186333/21759816. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (a a))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 186334/21759843. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) a)((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) a)((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)((^z.z) b))) 7. ==[ beta ]==> ((((^y.y) a)((^z.z) b))(((^y.y) a)((^z.z) b))) 8. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z) a)((^x1.x1) b))) 9. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)((^x1.x1) b))) 10. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((^z.z) b))) 11. ==[ beta ]==> ((a b)(((^y.y) a)((^z.z) b))) 12. ==[ alpha ]==> ((a b)(((^x.x) a)((^y.y) b))) 13. ==[ beta ]==> ((a b)(a ((^y.y) b))) 14. ==[ alpha ]==> ((a b)(a ((^x.x) b))) 15. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 186335/21759870. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 186336/21759897. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(b (^z.z)))) REDUCED to normal form. ------ 186337/21759960. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 186338/21759987. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(b (^z.a))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(b (^y.a))) REDUCED to normal form. ------ 186339/21760014. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((a a) a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 186340/21760041. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 186341/21760095. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> ((((a a) a) a)((a a)(^y.b))) 6. ==[ alpha ]==> ((((a a) a) a)((a a)(^x.b))) REDUCED to normal form. ------ 186342/21760122. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 186343/21760212. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.(y y))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 186344/21760347. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 186345/21760509. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.b)(^y.(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) b) REDUCED to normal form. ------ 186346/21760590. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 186347/21760653. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b ((a a)(a a)))) REDUCED to normal form. ------ 186348/21760743. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y) c)) 3. ==[ beta ]==> ((a (a b))((^y.y) c)) 4. ==[ alpha ]==> ((a (a b))((^x.x) c)) 5. ==[ beta ]==> ((a (a b)) c) REDUCED to normal form. ------ 186349/21761022. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(b (^z.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(b (^z.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(b (^z.(a a)))) 5. ==[ beta ]==> (b (b (^z.(a a)))) 6. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 186350/21761103. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 186351/21761211. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a))((a a) a))) 3. ==[ beta ]==> ((b a)((^y.(a a))((a a) a))) 4. ==[ alpha ]==> ((b a)((^x.(a a))((a a) a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 186352/21761238. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.b)(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a b))) 5. ==[ beta ]==> ((^y.b)(a b)) 6. ==[ alpha ]==> ((^x.b)(a b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 186353/21761292. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 186354/21761373. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186355/21761481. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 186356/21761760. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(a ((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186357/21762057. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 186358/21762075. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(b (^b.b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (^x1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 186359/21762084. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a) b)) REDUCED to normal form. ------ 186360/21762102. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(a (^z.(a a)))) 3. ==[ beta ]==> ((^y.y)(a (^z.(a a)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(a a)))) 5. ==[ beta ]==> (a (^y.(a a))) 6. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 186361/21762156. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(a (^x1.x1)))) 9. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 10. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 186362/21762237. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 186363/21762345. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186364/21762372. ------ 1. ==[ start ]==> ((a (^b.b))((^b.a)(b a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)(b a))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 186365/21762390. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a (^z.z))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 186366/21762417. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a a)(^y.y))) REDUCED to normal form. ------ 186367/21762444. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z) b) a)) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z) b) a)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) b) a)) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(b a)) REDUCED to normal form. ------ 186368/21762471. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a (^y.(^z.z))) b)) 3. ==[ beta ]==> (((a (a a))(a a))((a (^y.(^z.z))) b)) 4. ==[ alpha ]==> (((a (a a))(a a))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 186369/21762498. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((b a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((b a) c)) 3. ==[ beta ]==> (((^y.y)(a b))((b a) c)) 4. ==[ alpha ]==> (((^x.x)(a b))((b a) c)) 5. ==[ beta ]==> ((a b)((b a) c)) REDUCED to normal form. ------ 186370/21762723. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3))))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186371/21762975. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((a (a a))(a a))) REDUCED to normal form. ------ 186372/21763002. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((b a)(((^y.y) a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> ((b a)(a ((a a)(^y.y)))) 6. ==[ alpha ]==> ((b a)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 186373/21763020. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(c (^d.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(c (^z.a))) 3. ==[ beta ]==> (((^y.y) b)(c (^z.a))) 4. ==[ alpha ]==> (((^x.x) b)(c (^y.a))) 5. ==[ beta ]==> (b (c (^y.a))) 6. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 186374/21763029. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(b a))) REDUCED to normal form. ------ 186375/21763047. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(b (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(b (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 186376/21763056. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 186377/21763101. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 186378/21763182. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (b ((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 186379/21763290. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(y1 y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186380/21763362. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 186381/21763389. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (^x1.(^y1.y1))) a)) REDUCED to normal form. ------ 186382/21763416. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((b a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((b a) b)) 3. ==[ beta ]==> ((a (b a))((b a) b)) REDUCED to normal form. ------ 186383/21763686. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 186384/21763965. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(a (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186385/21764046. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 186386/21764073. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a (a a)))) 5. ==[ beta ]==> ((^y.b)(a (a a))) 6. ==[ alpha ]==> ((^x.b)(a (a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 186387/21764127. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 186388/21764208. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186389/21764316. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186390/21764577. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a b)(a b))((^x.(a a)) c)) 3. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 186391/21764856. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.b)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b)((^y2.y2) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b)((^y2.y2) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186392/21764937. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (b ((^z.(z z))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(x x))((a a) a))) 5. ==[ beta ]==> (b (((a a) a)((a a) a))) REDUCED to normal form. ------ 186393/21765153. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 186394/21765216. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c (a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c (a b))) 3. ==[ beta ]==> ((a (^y.y))(c (a b))) 4. ==[ alpha ]==> ((a (^x.x))(c (a b))) REDUCED to normal form. ------ 186395/21765234. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 186396/21765243. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(b (a a))) REDUCED to normal form. ------ 186397/21765324. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 186398/21765351. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.b))(((a a) a) a)) REDUCED to normal form. ------ 186399/21765432. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1) a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a ((a a) a))) REDUCED to normal form. ------ 186400/21765459. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))(a b))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))(a b))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))(a b))) REDUCED to normal form. ------ 186401/21765486. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 186402/21765549. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 186403/21765576. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((a a) a)(^y.a))) REDUCED to normal form. ------ 186404/21765603. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((a b)((^y.y)(^z.(z z)))) 8. ==[ alpha ]==> ((a b)((^x.x)(^y.(y y)))) 9. ==[ beta ]==> ((a b)(^y.(y y))) 10. ==[ alpha ]==> ((a b)(^x.(x x))) REDUCED to normal form. ------ 186405/21765630. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 186406/21765657. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((b a)(((^y.y) a)(^z.a))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.a))) 7. ==[ beta ]==> ((b a)(a (^y.a))) 8. ==[ alpha ]==> ((b a)(a (^x.a))) REDUCED to normal form. ------ 186407/21765684. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 186408/21765711. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a a)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a a))((a a)(^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))((a a)(^x.(a a)))) REDUCED to normal form. ------ 186409/21765738. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(a a)) a)) 3. ==[ beta ]==> (((a a)(a b))(((^y.y)(a a)) a)) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a)) a)) 5. ==[ beta ]==> (((a a)(a b))((a a) a)) REDUCED to normal form. ------ 186410/21765765. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a b) b)) REDUCED to normal form. ------ 186411/21766098. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c (^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (^x1.a))) 3. ==[ beta ]==> (b (c (^x1.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 186412/21766206. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186413/21766341. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)(a b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)(a b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(a b))) 5. ==[ beta ]==> ((^y.y)((^z.z)(a b))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a b))) 7. ==[ beta ]==> ((^y.y)(a b)) 8. ==[ alpha ]==> ((^x.x)(a b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 186414/21766368. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.z))) 5. ==[ beta ]==> ((^y.b)(^z.z)) 6. ==[ alpha ]==> ((^x.b)(^y.y)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 186415/21766422. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.a))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.a))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 186416/21766503. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186417/21766512. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 186418/21766539. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(a (a b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(a (a b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a (a b))) REDUCED to normal form. ------ 186419/21766566. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((a a) a)(a a))) REDUCED to normal form. ------ 186420/21766620. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a)) a)) REDUCED to normal form. ------ 186421/21766647. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> ((b (^x.(x x)))(a (a (a a)))) REDUCED to normal form. ------ 186422/21766674. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 186423/21766764. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 186424/21766791. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (a a))(^z.a))) REDUCED to normal form. ------ 186425/21766818. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a (^y.(y y)))) 6. ==[ alpha ]==> ((a ((a a)(a a)))(a (^x.(x x)))) REDUCED to normal form. ------ 186426/21766845. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 186427/21766899. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((a a) a) a)) REDUCED to normal form. ------ 186428/21766926. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z) b)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y) b)) 5. ==[ beta ]==> (((a b)((a a)(^x.x))) b) REDUCED to normal form. ------ 186429/21767061. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^c.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a) a)) 3. ==[ beta ]==> ((b (a (a a)))((^y.a) a)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a) a)) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 186430/21767088. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z)) b)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y)) b)) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 186431/21767160. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 186432/21767178. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^z.(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 186433/21767565. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> (b ((a (^y.y))((^z.z) a))) 6. ==[ alpha ]==> (b ((a (^x.x))((^y.y) a))) 7. ==[ beta ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 186434/21767583. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(y y)))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 186435/21767592. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a)(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a)(a (a a)))) REDUCED to normal form. ------ 186436/21767610. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 186437/21767637. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(y1 y1))(a a))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a a))) 5. ==[ beta ]==> ((^y.(y y))(a a)) 6. ==[ alpha ]==> ((^x.(x x))(a a)) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 186438/21767691. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 186439/21767772. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 186440/21767835. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (a (a a)))) REDUCED to normal form. ------ 186441/21767916. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 186442/21767997. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b c)) 5. ==[ beta ]==> ((^y.(^z.z))(b c)) 6. ==[ alpha ]==> ((^x.(^y.y))(b c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186443/21768015. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 186444/21768042. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 186445/21768060. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (^y.y)) b)) REDUCED to normal form. ------ 186446/21768114. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.a) a)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.a) a)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.a) a)) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 186447/21768141. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(^y.y)) b)) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 186448/21768168. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1) c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z) c)) 5. ==[ beta ]==> (((^y.y) b)((^z.z) c)) 6. ==[ alpha ]==> (((^x.x) b)((^y.y) c)) 7. ==[ beta ]==> (b ((^y.y) c)) 8. ==[ alpha ]==> (b ((^x.x) c)) 9. ==[ beta ]==> (b c) REDUCED to normal form. ------ 186449/21768195. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 186450/21768222. ------ 1. ==[ start ]==> (((a b)(b a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 186451/21768249. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a (^z.z)) a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a (^z.z)) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.y)) a)) REDUCED to normal form. ------ 186452/21768276. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a a) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a) b)) REDUCED to normal form. ------ 186453/21768330. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a)) b) REDUCED to normal form. ------ 186454/21768357. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a)(^x1.x1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a)(^z.z))) 5. ==[ beta ]==> ((b (^y.y))((a a)(^z.z))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 186455/21768384. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a a) a)) REDUCED to normal form. ------ 186456/21768437. ------ 1. ==[ start ]==> (^a.(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (^x.(((^y.(^z.z)) x)(x (^x1.x1)))) 3. ==[ beta ]==> (^x.((^z.z)(x (^x1.x1)))) 4. ==[ alpha ]==> (^x.((^y.y)(x (^z.z)))) 5. ==[ beta ]==> (^x.(x (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 186457/21768438. ------ 1. ==[ start ]==> (a (((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (a (((^x.(^y.y)) a)(a (^z.z)))) 3. ==[ beta ]==> (a ((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (a ((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (a (a (^y.y))) 6. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 186458/21769260. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186459/21773193. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> ((^x1.((x1 x1)(x1 x1)))(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(^z.z))) 5. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 7. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186460/21775110. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.(y (^z.(^x1.x1))))(^y.(y (^z.(^x1.x1)))))((^y.(y (^z.(^x1.x1))))(^y.(y (^z.(^x1.x1)))))) 4. ==[ alpha ]==> (((^x.(x (^y.(^z.z))))(^x1.(x1 (^y1.(^z1.z1)))))((^x2.(x2 (^y2.(^z2.z2))))(^x3.(x3 (^y3.(^z3.z3)))))) 5. ==[ beta ]==> (((^x1.(x1 (^y1.(^z1.z1))))(^y.(^z.z)))((^x2.(x2 (^y2.(^z2.z2))))(^x3.(x3 (^y3.(^z3.z3)))))) 6. ==[ alpha ]==> (((^x.(x (^y.(^z.z))))(^x1.(^y1.y1)))((^z1.(z1 (^x2.(^y2.y2))))(^z2.(z2 (^x3.(^y3.y3)))))) 7. ==[ beta ]==> (((^x1.(^y1.y1))(^y.(^z.z)))((^z1.(z1 (^x2.(^y2.y2))))(^z2.(z2 (^x3.(^y3.y3)))))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 (^z1.(^x2.x2))))(^y2.(y2 (^z2.(^x3.x3)))))) 9. ==[ beta ]==> ((^y.y)((^y1.(y1 (^z1.(^x2.x2))))(^y2.(y2 (^z2.(^x3.x3)))))) 10. ==[ alpha ]==> ((^x.x)((^y.(y (^z.(^x1.x1))))(^y1.(y1 (^z1.(^x2.x2)))))) 11. ==[ beta ]==> ((^y.(y (^z.(^x1.x1))))(^y1.(y1 (^z1.(^x2.x2))))) 12. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(x1 (^y1.(^z1.z1))))) 13. ==[ beta ]==> ((^x1.(x1 (^y1.(^z1.z1))))(^y.(^z.z))) 14. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(^y1.y1))) 15. ==[ beta ]==> ((^x1.(^y1.y1))(^y.(^z.z))) 16. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186461/21776190. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186462/21779865. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a))) a) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z))) a) 3. ==[ beta ]==> (((^y.y)(a (^z.z))) a) 4. ==[ alpha ]==> (((^x.x)(a (^y.y))) a) 5. ==[ beta ]==> ((a (^y.y)) a) 6. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 186463/21779871. ------ 1. ==[ start ]==> ((^a.a)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 5. ==[ beta ]==> ((^y.y)(a (^z.z))) 6. ==[ alpha ]==> ((^x.x)(a (^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 186464/21779898. ------ 1. ==[ start ]==> ((^a.(a a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x x))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((b (^y.y))((^z.z) a))((b (^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((b (^x.x))((^y.y) a))((b (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((b (^x.x)) a)((b (^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> (((b (^x.x)) a)((b (^y.y))((^z.z) a))) 7. ==[ beta ]==> (((b (^x.x)) a)((b (^y.y)) a)) REDUCED to normal form. ------ 186465/21779925. ------ 1. ==[ start ]==> ((^a.b)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.b)(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 186466/21780006. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((b a)(a b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((b a)(a b))) 3. ==[ beta ]==> (((b a)(a b))(^y.y)) 4. ==[ alpha ]==> (((b a)(a b))(^x.x)) REDUCED to normal form. ------ 186467/21780195. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) a)(b (^x1.x1)))) 3. ==[ eta ]==> ((^y.y)(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 186468/21780270. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 186469/21780366. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 186470/21780690. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186471/21780693. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 186472/21781143. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 186473/21781248. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((((^y.y) b)(a (a a)))(((^y.y) b)(a (a a))))(((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> (((((^x.x) b)(a (a a)))(((^y.y) b)(a (a a))))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> (((b (a (a a)))(((^y.y) b)(a (a a))))(((^z.z) b)(a (a a)))) 6. ==[ alpha ]==> (((b (a (a a)))(((^x.x) b)(a (a a))))(((^y.y) b)(a (a a)))) 7. ==[ beta ]==> (((b (a (a a)))(b (a (a a))))(((^y.y) b)(a (a a)))) 8. ==[ alpha ]==> (((b (a (a a)))(b (a (a a))))(((^x.x) b)(a (a a)))) 9. ==[ beta ]==> (((b (a (a a)))(b (a (a a))))(b (a (a a)))) REDUCED to normal form. ------ 186474/21781566. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 186475/21781581. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 186476/21781971. ------ 1. ==[ start ]==> (((a a)(^a.b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.b))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 186477/21782355. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(b (b (^z.z)))) 3. ==[ beta ]==> ((^y.y)((b (b (^z.z)))(b (b (^z.z))))) 4. ==[ alpha ]==> ((^x.x)((b (b (^y.y)))(b (b (^z.z))))) 5. ==[ beta ]==> ((b (b (^y.y)))(b (b (^z.z)))) 6. ==[ alpha ]==> ((b (b (^x.x)))(b (b (^y.y)))) REDUCED to normal form. ------ 186478/21783546. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 186479/21783786. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ eta ]==> (b (((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b ((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (b ((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 186480/21784266. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 186481/21784617. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186482/21784623. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(a ((a a)(a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 186483/21784626. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.((z z)(z z)))) REDUCED to normal form. ------ 186484/21786540. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a (a (^y.(^z.z))))(a (a (^y.(^z.z)))))((a (a (^y.(^z.z))))(a (a (^y.(^z.z)))))) 4. ==[ alpha ]==> (((a (a (^x.(^y.y))))(a (a (^z.(^x1.x1)))))((a (a (^y1.(^z1.z1))))(a (a (^x2.(^y2.y2)))))) REDUCED to normal form. ------ 186485/21786543. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 186486/21787380. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(^x1.(b x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))((a a)(^z.z))) b) 4. ==[ beta ]==> (((^y.y)((a a)(^z.z))) b) 5. ==[ alpha ]==> (((^x.x)((a a)(^y.y))) b) 6. ==[ beta ]==> (((a a)(^y.y)) b) 7. ==[ alpha ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 186487/21787620. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186488/21787623. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 186489/21788781. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(b (a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(b (a b))) 3. ==[ eta ]==> ((^y.(^z.z))(b (a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186490/21789396. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.z))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.y))) REDUCED to normal form. ------ 186491/21789585. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(^x1.(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.b))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.b))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 7. ==[ beta ]==> (^y.(^z.b)) 8. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 186492/21789600. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((a a) a)(^x1.x1))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 186493/21789918. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.((y y) y))) 3. ==[ beta ]==> ((b (a (a a)))(^y.((y y) y))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.((x x) x))) REDUCED to normal form. ------ 186494/21790023. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (^z.z))(a (a a)))(((a (^z.z))(a (a a)))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((a (^y.y))(a (a a)))(^z.z))) REDUCED to normal form. ------ 186495/21790476. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 186496/21790584. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (a a)))) 7. ==[ beta ]==> (^y.(a (a a))) 8. ==[ alpha ]==> (^x.(a (a a))) REDUCED to normal form. ------ 186497/21790692. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 186498/21790800. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 186499/21790881. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^z.a)) REDUCED to normal form. ------ 186500/21790896. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 186501/21790971. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x) a)(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.z)) 5. ==[ beta ]==> ((a (b (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 186502/21791025. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(a (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(a (^z.z)))) 7. ==[ beta ]==> (b (^y.(a (^z.z)))) 8. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 186503/21791241. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.b)) REDUCED to normal form. ------ 186504/21791295. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.x1)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.x1)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.z)) 5. ==[ beta ]==> ((a (^y.y))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 186505/21791307. ------ 1. ==[ start ]==> ((a a)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a (^z.z)))) 3. ==[ beta ]==> ((a a)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> ((a a)(a (^y.y))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 186506/21791334. ------ 1. ==[ start ]==> ((a (a a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a a))((b (^x.x))((^y.y) a))) 3. ==[ beta ]==> ((a (a a))((b (^x.x)) a)) REDUCED to normal form. ------ 186507/21791361. ------ 1. ==[ start ]==> ((a b)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 186508/21791415. ------ 1. ==[ start ]==> (((a a)(a a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 186509/21791442. ------ 1. ==[ start ]==> ((a (a (^a.a)))((b a)(a b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((b a)(a b))) REDUCED to normal form. ------ 186510/21791577. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y) b)) 7. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 186511/21791604. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 186512/21791631. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(a (b (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (b (^x.x)))) REDUCED to normal form. ------ 186513/21791676. ------ 1. ==[ start ]==> (((a (^a.a)) b)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 186514/21791703. ------ 1. ==[ start ]==> ((((^a.a) a) a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 186515/21791721. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((^y.y) a)((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> (a ((a (a (^y.y)))(^z.z))) 6. ==[ alpha ]==> (a ((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 186516/21791730. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a a)(^x.a))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 186517/21791748. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186518/21791802. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 186519/21791910. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(y y))(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((((a a)(^y.y))(^z.(a a)))(((a a)(^y.y))(^z.(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 186520/21791937. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 186521/21791973. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.b)(b a))) 3. ==[ beta ]==> ((a b)((^y.b)(b a))) 4. ==[ alpha ]==> ((a b)((^x.b)(b a))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 186522/21791991. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 186523/21792018. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 186524/21792027. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 186525/21792054. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 186526/21792081. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 186527/21792108. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 186528/21792126. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 186529/21792351. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 186530/21792378. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 186531/21792459. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 186532/21792549. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^y.y))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 186533/21792576. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (a (a (^y.y))))) REDUCED to normal form. ------ 186534/21792603. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(a a))) 6. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a a))) 7. ==[ beta ]==> ((a a)((^y.y)(a a))) 8. ==[ alpha ]==> ((a a)((^x.x)(a a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 186535/21792630. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 186536/21792657. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a a)(((a a)(a a))((^y.y) a))) 6. ==[ alpha ]==> ((a a)(((a a)(a a))((^x.x) a))) 7. ==[ beta ]==> ((a a)(((a a)(a a)) a)) REDUCED to normal form. ------ 186537/21792684. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> ((a ((a a) a))(b (a (a a)))) REDUCED to normal form. ------ 186538/21792945. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 186539/21792999. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 186540/21793017. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 186541/21793188. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.z))(a b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186542/21793206. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 186543/21793287. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) IRREDUCIBLE: cycle. ------ 186544/21793350. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 186545/21793377. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 186546/21793404. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 186547/21793422. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) a)) 5. ==[ beta ]==> (((^y.(^z.z)) a) a) 6. ==[ alpha ]==> (((^x.(^y.y)) a) a) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 186548/21793512. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.(z z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 186549/21793539. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 186550/21793755. ------ 1. ==[ start ]==> (((^a.b) b)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 186551/21793764. ------ 1. ==[ start ]==> (((a b)(a a))(c ((a a)(a a)))) REDUCED to normal form. ------ 186552/21793791. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(b (b (^y.y)))) 3. ==[ beta ]==> ((a (a a))(b (b (^y.y)))) 4. ==[ alpha ]==> ((a (a a))(b (b (^x.x)))) REDUCED to normal form. ------ 186553/21793881. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a)) c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a)) c)) 5. ==[ beta ]==> ((^y.y)((^y1.(a a)) c)) 6. ==[ alpha ]==> ((^x.x)((^y.(a a)) c)) 7. ==[ beta ]==> ((^y.(a a)) c) 8. ==[ alpha ]==> ((^x.(a a)) c) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 186554/21794160. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(c (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(c (^y.(a a)))) REDUCED to normal form. ------ 186555/21794403. ------ 1. ==[ start ]==> (((^a.b) c)((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(a a))(a b))) 3. ==[ beta ]==> (b ((^y.(a a))(a b))) 4. ==[ alpha ]==> (b ((^x.(a a))(a b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 186556/21794502. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 186557/21794637. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(a a)) b)) 3. ==[ beta ]==> (b (((a a)(a a)) b)) REDUCED to normal form. ------ 186558/21794646. ------ 1. ==[ start ]==> (((a b) c)((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 186559/21794673. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a) b)((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(^y.a))) 5. ==[ beta ]==> (((a a) b)(^y.a)) 6. ==[ alpha ]==> (((a a) b)(^x.a)) REDUCED to normal form. ------ 186560/21794700. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 186561/21794754. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 186562/21794781. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.b))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 186563/21794835. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186564/21794889. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 186565/21794916. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 186566/21794979. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 186567/21795006. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 186568/21795033. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> ((a (a b))(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> ((a (a b))(b (a (^y.y)))) 6. ==[ alpha ]==> ((a (a b))(b (a (^x.x)))) REDUCED to normal form. ------ 186569/21795060. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((a (^x.(^y.y)))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))((a a) a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 186570/21795087. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(a (a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((b a)(a (a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(a (a a)))) 7. ==[ beta ]==> ((^y.y)((b a)(a (a a)))) 8. ==[ alpha ]==> ((^x.x)((b a)(a (a a)))) 9. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 186571/21795114. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((a a)(^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(((a a)(^x.x))(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 186572/21795141. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a b) a)(((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> (((a b) a)(((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> (((a b) a)((a a)((a a) a))) REDUCED to normal form. ------ 186573/21795168. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((a b)(a b))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a b)(a b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a b)(a b))) REDUCED to normal form. ------ 186574/21795195. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(((a a) a)(a a))) REDUCED to normal form. ------ 186575/21795222. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (b a))((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (b a))((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> ((a (b a))((a a)(^y.y))) 6. ==[ alpha ]==> ((a (b a))((a a)(^x.x))) REDUCED to normal form. ------ 186576/21795393. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (b (b (^y.(^z.z)))) 6. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 186577/21795501. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((b a)(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> ((b a)(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> ((b a)((a a)(^y.a))) 6. ==[ alpha ]==> ((b a)((a a)(^x.a))) REDUCED to normal form. ------ 186578/21795528. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a b)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.b))) 5. ==[ beta ]==> ((a b)(^y.b)) 6. ==[ alpha ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 186579/21795564. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 186580/21795582. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 8. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 186581/21795591. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 186582/21795645. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 186583/21795663. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (^y.y))(^z.z))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.z))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 186584/21795672. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 186585/21795699. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))((a a)(a a))) REDUCED to normal form. ------ 186586/21796059. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a ((a a)(a a)))) REDUCED to normal form. ------ 186587/21796374. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(b (^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(b (^x1.x1))) REDUCED to normal form. ------ 186588/21796446. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 186589/21796455. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 186590/21796527. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 186591/21796536. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 186592/21796563. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)((a a) a))) 5. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 186593/21796590. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.a)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) a) REDUCED to normal form. ------ 186594/21796644. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(((a a)(^y1.y1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a)(^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 186595/21796941. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186596/21797148. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) d)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186597/21797319. ------ 1. ==[ start ]==> (((a a)(^b.b))(c (^d.a))) 2. ==[ alpha ]==> (((a a)(^x.x))(c (^y.a))) REDUCED to normal form. ------ 186598/21797346. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(b (^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 186599/21797391. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 186600/21797454. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 186601/21797472. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.(z z)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> (b ((a a)(^y.(y y)))) 6. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 186602/21797481. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 186603/21797508. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 186604/21797580. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a (a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186605/21797589. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^z1.z1)(a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)((^z1.z1)(a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)((^y1.y1)(a a)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(a a))) REDUCED to normal form. ------ 186606/21797616. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 186607/21797949. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(b (b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(b (b a))) 3. ==[ beta ]==> ((b (a a))(b (b a))) REDUCED to normal form. ------ 186608/21797976. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 186609/21798336. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (((a a)(a a))((a a)(^y.a))) 6. ==[ alpha ]==> (((a a)(a a))((a a)(^x.a))) REDUCED to normal form. ------ 186610/21798363. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(y y)))) 5. ==[ beta ]==> ((a b)(^y.(y y))) 6. ==[ alpha ]==> ((a b)(^x.(x x))) REDUCED to normal form. ------ 186611/21798372. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 186612/21798417. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (((b a)(b a))((^y.y)(^z.a))) 6. ==[ alpha ]==> (((b a)(b a))((^x.x)(^y.a))) 7. ==[ beta ]==> (((b a)(b a))(^y.a)) 8. ==[ alpha ]==> (((b a)(b a))(^x.a)) REDUCED to normal form. ------ 186613/21798480. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 186614/21798498. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 186615/21798507. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 186616/21798615. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 186617/21798642. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 186618/21798786. ------ 1. ==[ start ]==> (((a (a a))(b a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 186619/21798813. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(a (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(a (b a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(a (b a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(a (b a))) 5. ==[ beta ]==> (((a a)(^y.y))(a (b a))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (b a))) REDUCED to normal form. ------ 186620/21798840. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a)(^y.y))(a a))) 3. ==[ beta ]==> ((((a a) a)(a a))(((a a)(^y.y))(a a))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 186621/21798867. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a b))((a a)(a (^y.y)))) 4. ==[ alpha ]==> (((a b)(a b))((a a)(a (^x.x)))) REDUCED to normal form. ------ 186622/21798894. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a b)((^y.y) a))) 3. ==[ beta ]==> (((a a)((a a) a))((a b)((^y.y) a))) 4. ==[ alpha ]==> (((a a)((a a) a))((a b)((^x.x) a))) 5. ==[ beta ]==> (((a a)((a a) a))((a b) a)) REDUCED to normal form. ------ 186623/21798921. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 186624/21798975. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (a a))((a a) a))) REDUCED to normal form. ------ 186625/21799002. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z) a)(a b))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) a)(a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) a)(a b))) 5. ==[ beta ]==> ((b (a (^x.x)))(a (a b))) REDUCED to normal form. ------ 186626/21799029. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((a (^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a (^x.x))(a a))) REDUCED to normal form. ------ 186627/21799056. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 186628/21799146. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a b)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b)(^x2.a))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(^x2.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186629/21799227. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a (a a))(^z.a))) 3. ==[ beta ]==> (b ((a (a a))(^z.a))) 4. ==[ alpha ]==> (b ((a (a a))(^x.a))) REDUCED to normal form. ------ 186630/21799335. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((a a)(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186631/21799371. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 186632/21799398. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 186633/21799506. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.b))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 186634/21799533. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 186635/21799605. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(a a)) b)) 3. ==[ beta ]==> (b ((^z.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 186636/21799749. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c (^z.b))) 3. ==[ beta ]==> ((b (^y.a))(c (^z.b))) 4. ==[ alpha ]==> ((b (^x.a))(c (^y.b))) REDUCED to normal form. ------ 186637/21799776. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b (^z.(a a)))) REDUCED to normal form. ------ 186638/21800217. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(b (a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(b (a b))) 3. ==[ beta ]==> ((a (^y.y))(b (a b))) 4. ==[ alpha ]==> ((a (^x.x))(b (a b))) REDUCED to normal form. ------ 186639/21800307. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.a) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) c)) 5. ==[ beta ]==> ((^y.y)((^z.a) c)) 6. ==[ alpha ]==> ((^x.x)((^y.a) c)) 7. ==[ beta ]==> ((^y.a) c) 8. ==[ alpha ]==> ((^x.a) c) 9. ==[ beta ]==> a REDUCED to normal form. ------ 186640/21800496. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186641/21800613. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> (a ((^y.(^z.z))((a a) a))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((a a) a))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 186642/21800631. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a a)(^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a a)(^x1.b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)(^z.b))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.b))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.b))) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 186643/21800658. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a b) a)) 3. ==[ beta ]==> ((^y.y)((a b) a)) 4. ==[ alpha ]==> ((^x.x)((a b) a)) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 186644/21800712. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z)(^x1.x1)) c)) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1)) c)) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z)) c)) 7. ==[ beta ]==> ((b b)(((^y.y)(^z.z)) c)) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y)) c)) 9. ==[ beta ]==> ((b b)((^y.y) c)) 10. ==[ alpha ]==> ((b b)((^x.x) c)) 11. ==[ beta ]==> ((b b) c) REDUCED to normal form. ------ 186645/21800721. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 186646/21800748. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186647/21800802. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 186648/21800829. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.b)) REDUCED to normal form. ------ 186649/21800901. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186650/21800964. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (^y.(^z.z)))) REDUCED to normal form. ------ 186651/21801018. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(a (^x1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.b))) 5. ==[ beta ]==> ((^y.y)(a (^z.b))) 6. ==[ alpha ]==> ((^x.x)(a (^y.b))) 7. ==[ beta ]==> (a (^y.b)) 8. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 186652/21801036. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((a a) a)(^z.z))) REDUCED to normal form. ------ 186653/21801324. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(b (^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (^x1.x1))) REDUCED to normal form. ------ 186654/21801351. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a ((a a) a))) 3. ==[ beta ]==> ((b (a (a a)))(a ((a a) a))) REDUCED to normal form. ------ 186655/21801378. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y)(^z.z))(a a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(^y.y))(a a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(a a))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(a a))) 7. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 186656/21801432. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((a a)(((^y.y) a)((^z.z) a))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> ((a a)(a ((^y.y) a))) 8. ==[ alpha ]==> ((a a)(a ((^x.x) a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 186657/21801459. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 186658/21801855. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c (^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c (^z.a))) 3. ==[ beta ]==> (((^y.y) b)(c (^z.a))) 4. ==[ alpha ]==> (((^x.x) b)(c (^y.a))) 5. ==[ beta ]==> (b (c (^y.a))) 6. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 186659/21801882. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b (^y.(y y)))) REDUCED to normal form. ------ 186660/21801909. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 186661/21801927. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (a a))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 186662/21801981. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 186663/21802017. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a (a a)))) 7. ==[ beta ]==> ((^y.y)(a (a a))) 8. ==[ alpha ]==> ((^x.x)(a (a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 186664/21802044. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((^y1.y1)(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 186665/21802062. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y) a) b)) 3. ==[ beta ]==> (b (((^y.y) a) b)) 4. ==[ alpha ]==> (b (((^x.x) a) b)) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 186666/21802125. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(z z))) REDUCED to normal form. ------ 186667/21802170. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186668/21802206. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (^x1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (^x1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 186669/21802233. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.(y y)))) REDUCED to normal form. ------ 186670/21802287. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186671/21802305. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 186672/21802314. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z) a)) 5. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 186673/21802332. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 186674/21802377. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b (a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (a (^z.z)))) REDUCED to normal form. ------ 186675/21802404. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a ((^z.z) a))) 3. ==[ beta ]==> ((a (b (^y.y)))(a ((^z.z) a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a ((^y.y) a))) 5. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 186676/21802431. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a (^x.x))(a a))) REDUCED to normal form. ------ 186677/21802458. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(a (^z.z)))) 5. ==[ beta ]==> (((^y.y) b)((a a)(a (^z.z)))) 6. ==[ alpha ]==> (((^x.x) b)((a a)(a (^y.y)))) 7. ==[ beta ]==> (b ((a a)(a (^y.y)))) 8. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 186678/21802512. ------ 1. ==[ start ]==> (((a b)(b a))(b b)) REDUCED to normal form. ------ 186679/21802566. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b (a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b (a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b (a a))) REDUCED to normal form. ------ 186680/21802620. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a a)(a a))) REDUCED to normal form. ------ 186681/21802647. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b a)) 5. ==[ beta ]==> ((b (^y.y))(b a)) 6. ==[ alpha ]==> ((b (^x.x))(b a)) REDUCED to normal form. ------ 186682/21802674. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a b)) REDUCED to normal form. ------ 186683/21802728. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a a)) 5. ==[ beta ]==> ((a (^y.y))(a a)) 6. ==[ alpha ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 186684/21807492. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((^x1.(^y1.(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.(^y.(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.(a a)) 6. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 186685/21809409. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1)))))((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1)))))) 4. ==[ alpha ]==> (((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2)))))((^z2.(^x3.(^y3.(^z3.z3))))(^x4.(^y4.(^z4.(^x5.x5)))))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^z2.(^x3.(^y3.(^z3.z3))))(^x4.(^y4.(^z4.(^x5.x5)))))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.(^x2.x2))))(^y2.(^z2.(^x3.(^y3.y3)))))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186686/21814164. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a))) b) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z))) b) 3. ==[ beta ]==> (((^y.y)(a (^z.z))) b) 4. ==[ alpha ]==> (((^x.x)(a (^y.y))) b) 5. ==[ beta ]==> ((a (^y.y)) b) 6. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 186687/21814188. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186688/21814269. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186689/21814431. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (^y.(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (^x.(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 186690/21815019. ------ 1. ==[ start ]==> (((a a)(a (a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 186691/21815451. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 186692/21816069. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((^y.(^z.z))(a b)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(a b)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 186693/21816702. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> (((^x.(^y.y))(^z.b))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186694/21818574. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(a a)))) REDUCED to normal form. ------ 186695/21818934. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 186696/21818943. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((y1 y1)(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((y1 y1)(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((x1 x1)(x1 x1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186697/21819267. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) b))) 5. ==[ beta ]==> (^y.((^z.z) b)) 6. ==[ alpha ]==> (^x.((^y.y) b)) 7. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 186698/21819609. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x) a)((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(^z.z)) 5. ==[ beta ]==> ((a ((a a)(^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 186699/21819849. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 186700/21820554. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 186701/21820848. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(^z.(^x1.(^y1.y1))))((^y.y)(^z.(^x1.(^y1.y1)))))(((^y.y)(^z.(^x1.(^y1.y1))))((^y.y)(^z.(^x1.(^y1.y1)))))) 4. ==[ alpha ]==> ((((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.(^y2.y2)))))(((^z2.z2)(^x3.(^y3.(^z3.z3))))((^x4.x4)(^y4.(^z4.(^x5.x5)))))) 5. ==[ beta ]==> (((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.(^y2.y2)))))(((^z2.z2)(^x3.(^y3.(^z3.z3))))((^x4.x4)(^y4.(^z4.(^x5.x5)))))) 6. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2)))))(((^y2.y2)(^z2.(^x3.(^y3.y3))))((^z3.z3)(^x4.(^y4.(^z4.z4)))))) 7. ==[ beta ]==> ((^y.(^z.z))(((^y2.y2)(^z2.(^x3.(^y3.y3))))((^z3.z3)(^x4.(^y4.(^z4.z4)))))) 8. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.(^y1.(^z1.z1))))((^x2.x2)(^y2.(^z2.(^x3.x3)))))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186702/21820851. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 186703/21821130. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^c.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.(b a))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186704/21821928. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186705/21822903. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a b))(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a b))(^x.(a a))) REDUCED to normal form. ------ 186706/21823089. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(^z1.b))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186707/21824064. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((a a) a))) REDUCED to normal form. ------ 186708/21824226. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.a))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.a))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.a))) REDUCED to normal form. ------ 186709/21824892. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(z z)))) 7. ==[ beta ]==> (^y.(^z.(z z))) 8. ==[ alpha ]==> (^x.(^y.(y y))) REDUCED to normal form. ------ 186710/21825000. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.d)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.d)) REDUCED to normal form. ------ 186711/21825279. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.a))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 186712/21825360. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.z))) REDUCED to normal form. ------ 186713/21825414. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(a (^z.z)))) REDUCED to normal form. ------ 186714/21825522. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 186715/21825549. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(a a))) REDUCED to normal form. ------ 186716/21825603. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 186717/21825633. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 186718/21825660. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 186719/21825687. ------ 1. ==[ start ]==> (((^a.a)(a a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 186720/21825714. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 186721/21825768. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((b a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186722/21825795. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 186723/21825822. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 186724/21825849. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 186725/21825876. ------ 1. ==[ start ]==> ((a (^b.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 186726/21825957. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.a)(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 186727/21825984. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 186728/21826047. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 186729/21826074. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 186730/21826101. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 186731/21826164. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 186732/21826191. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 186733/21826209. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x)) a)((b a)(^y.b))) 3. ==[ beta ]==> ((a a)((b a)(^y.b))) 4. ==[ alpha ]==> ((a a)((b a)(^x.b))) REDUCED to normal form. ------ 186734/21826317. ------ 1. ==[ start ]==> (((a (a a)) a)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 186735/21826344. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 186736/21826371. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 186737/21826461. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> (((a a)(a (a a)))(a (a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 186738/21826488. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x)) a)((^x1.x1)(^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.z))) 7. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 8. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 186739/21826533. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x)) b)((b (^y.y)) c)) 3. ==[ beta ]==> ((b b)((b (^y.y)) c)) 4. ==[ alpha ]==> ((b b)((b (^x.x)) c)) REDUCED to normal form. ------ 186740/21826893. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 186741/21827037. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 186742/21827091. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(^z.z))(a b))) 5. ==[ beta ]==> (a (((a a)(^z.z))(a b))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(a b))) REDUCED to normal form. ------ 186743/21827172. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((a a) a)(b a))) 3. ==[ beta ]==> (((a a) a)(((a a) a)(b a))) REDUCED to normal form. ------ 186744/21827199. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 186745/21827253. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) a)((a a)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) a)((a a)(a a)))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((a a)(a a)))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((a a)(a a)))) 9. ==[ beta ]==> ((a a)(a ((a a)(a a)))) REDUCED to normal form. ------ 186746/21827433. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)(a (a a)))) 5. ==[ beta ]==> (((a (a a)) a)(a (a a))) REDUCED to normal form. ------ 186747/21827460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 186748/21827505. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) a)(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 186749/21827514. ------ 1. ==[ start ]==> ((a (a b))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(a b))) 3. ==[ beta ]==> ((a (a b))(^y.y)) 4. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 186750/21827667. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) b)(a (^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a) b)(a (^x.(a a)))) REDUCED to normal form. ------ 186751/21827775. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b (^x1.x1)) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b (^x1.x1)) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z)) b)) REDUCED to normal form. ------ 186752/21827919. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 186753/21827946. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 186754/21827973. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 186755/21828027. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (a ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 186756/21828054. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((^z.z)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 186757/21828081. ------ 1. ==[ start ]==> (((a b)(a a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 186758/21828117. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b (b (^z.z)))) 3. ==[ beta ]==> ((^y.(a a))(b (b (^z.z)))) 4. ==[ alpha ]==> ((^x.(a a))(b (b (^y.y)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 186759/21828144. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> (a ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (a ((^x.(^y.y)) a)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 186760/21828198. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (^y.y)))) 7. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 8. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 186761/21828279. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((b a)(^y.y))) 6. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 186762/21828333. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))(a b))) 5. ==[ beta ]==> ((a a)(((^y.y)(a a))(a b))) 6. ==[ alpha ]==> ((a a)(((^x.x)(a a))(a b))) 7. ==[ beta ]==> ((a a)((a a)(a b))) REDUCED to normal form. ------ 186763/21828360. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)((^y.y)(a a))) 6. ==[ alpha ]==> ((a b)((^x.x)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 186764/21828414. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(b a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(b a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(b a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(b a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(b a))) 9. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(b a))) 10. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(b a))) 11. ==[ beta ]==> (((^y.y)(^z.z))(b a)) 12. ==[ alpha ]==> (((^x.x)(^y.y))(b a)) 13. ==[ beta ]==> ((^y.y)(b a)) 14. ==[ alpha ]==> ((^x.x)(b a)) 15. ==[ beta ]==> (b a) REDUCED to normal form. ------ 186765/21828495. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 186766/21828594. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 186767/21828621. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)((^y.y) a))) 5. ==[ beta ]==> ((a ((a a) a))((^y.y) a)) 6. ==[ alpha ]==> ((a ((a a) a))((^x.x) a)) 7. ==[ beta ]==> ((a ((a a) a)) a) REDUCED to normal form. ------ 186768/21828648. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 186769/21828720. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (b ((a a)(^y.b))) 6. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 186770/21828729. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 186771/21828756. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 186772/21828963. ------ 1. ==[ start ]==> (((a b) c)(((a a)(a a)) b)) REDUCED to normal form. ------ 186773/21828990. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) b) c)) 3. ==[ beta ]==> (((a a) b)(((^y.y) b) c)) 4. ==[ alpha ]==> (((a a) b)(((^x.x) b) c)) 5. ==[ beta ]==> (((a a) b)(b c)) REDUCED to normal form. ------ 186774/21829629. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (b ((a (^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> (b ((a (^x.x))((^y.y) b))) 7. ==[ beta ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 186775/21829773. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((b a)(^y.(y y)))) REDUCED to normal form. ------ 186776/21829881. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 186777/21829908. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 186778/21829962. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 186779/21829989. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 186780/21830016. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 186781/21830043. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(a a)) a)) REDUCED to normal form. ------ 186782/21830106. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 186783/21830187. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 186784/21830214. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.b)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a a) a)((^y.b)(^z.b))) 6. ==[ alpha ]==> (((a a) a)((^x.b)(^y.b))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 186785/21830268. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 186786/21830322. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 186787/21830385. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a ((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a ((a a)(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186788/21830466. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((b a)((^z.z) a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((b a)((^z.z) a))) 5. ==[ beta ]==> ((a a)((b a)((^z.z) a))) 6. ==[ alpha ]==> ((a a)((b a)((^x.x) a))) 7. ==[ beta ]==> ((a a)((b a) a)) REDUCED to normal form. ------ 186789/21830547. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)((a a) a))) 3. ==[ beta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 186790/21830655. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1) a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186791/21830682. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 186792/21830709. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a a)((^z.z) b))) 3. ==[ beta ]==> ((^y.y)((a a)((^z.z) b))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.y) b))) 5. ==[ beta ]==> ((a a)((^y.y) b)) 6. ==[ alpha ]==> ((a a)((^x.x) b)) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 186793/21830772. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 186794/21830799. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((b a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((b a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((b a)(^z.a))) 5. ==[ beta ]==> ((^y.b)((b a)(^z.a))) 6. ==[ alpha ]==> ((^x.b)((b a)(^y.a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 186795/21830853. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 186796/21830880. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a b)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a b)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)(^y.a))) REDUCED to normal form. ------ 186797/21830907. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((a a) a)(^z.b))) REDUCED to normal form. ------ 186798/21830997. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.a)(b a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 186799/21831024. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 186800/21831051. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z) b)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y) b)) 7. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 186801/21831078. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 186802/21831105. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 186803/21831159. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 186804/21831186. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 186805/21831213. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b)(^z.a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 186806/21831267. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 186807/21831294. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 186808/21831465. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (b (((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 186809/21831573. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186810/21831627. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> (b (((^y.y) a)((a a)(^z.z)))) 6. ==[ alpha ]==> (b (((^x.x) a)((a a)(^y.y)))) 7. ==[ beta ]==> (b (a ((a a)(^y.y)))) 8. ==[ alpha ]==> (b (a ((a a)(^x.x)))) REDUCED to normal form. ------ 186811/21831654. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a (^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(b a))) 5. ==[ beta ]==> ((a (^y.y))(b a)) 6. ==[ alpha ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 186812/21831744. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))((b a)(^y.(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 186813/21831771. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 186814/21831798. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.a))((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((a b)(^x.a))((a a)(^y.(y y)))) REDUCED to normal form. ------ 186815/21831825. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 186816/21831906. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))(^y1.(a a)))) REDUCED to normal form. ------ 186817/21831933. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 186818/21831969. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(b a))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 186819/21831996. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 186820/21832023. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 186821/21832104. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(a b))(a a)) REDUCED to normal form. ------ 186822/21832131. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 186823/21832185. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 186824/21832239. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) a) REDUCED to normal form. ------ 186825/21832293. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 186826/21832329. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b a)(a a))) 3. ==[ beta ]==> ((^y.y)((b a)(a a))) 4. ==[ alpha ]==> ((^x.x)((b a)(a a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 186827/21832464. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> (b ((^y.y)((a a) a))) 6. ==[ alpha ]==> (b ((^x.x)((a a) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 186828/21832572. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186829/21832608. ------ 1. ==[ start ]==> ((((^a.a) b) b)((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((b a)(^y.y))) 3. ==[ beta ]==> ((b b)((b a)(^y.y))) 4. ==[ alpha ]==> ((b b)((b a)(^x.x))) REDUCED to normal form. ------ 186830/21832635. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 186831/21832689. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(^z.(z z)))) REDUCED to normal form. ------ 186832/21832716. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 186833/21832797. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a (^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 186834/21832824. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 186835/21832878. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((b a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a) a)) REDUCED to normal form. ------ 186836/21832932. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(a a)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a) c)) REDUCED to normal form. ------ 186837/21833022. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 186838/21833049. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(z z))(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))(^z.b))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.b)(^z.b))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)(^z.b))) 7. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 186839/21833076. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 186840/21833103. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 186841/21833373. ------ 1. ==[ start ]==> ((a (b (^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 186842/21833688. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(a a)) b)) 3. ==[ beta ]==> ((b c)(((^y.y)(a a)) b)) 4. ==[ alpha ]==> ((b c)(((^x.x)(a a)) b)) 5. ==[ beta ]==> ((b c)((a a) b)) REDUCED to normal form. ------ 186843/21833715. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b) c)) REDUCED to normal form. ------ 186844/21833922. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (b (((^z.z)(a a))(a a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 186845/21833931. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(a a)) b)) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 186846/21833958. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b) c)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b) c)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b) c)) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 186847/21834030. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a (a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186848/21834156. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 186849/21834183. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 186850/21834210. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((a b)((^y.a)((^z.z) a))) 6. ==[ alpha ]==> ((a b)((^x.a)((^y.y) a))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 186851/21834237. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 186852/21834264. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.(y y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((b a)((^y.y)((^z.z)(^x1.x1)))) 10. ==[ alpha ]==> ((b a)((^x.x)((^y.y)(^z.z)))) 11. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 12. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 13. ==[ beta ]==> ((b a)(^y.y)) 14. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 186853/21834291. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.a)((a a) a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) a) REDUCED to normal form. ------ 186854/21834318. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(a b))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 186855/21834345. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a b))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a b))((^y.y)(a a))) 6. ==[ alpha ]==> (((a a)(a b))((^x.x)(a a))) 7. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 186856/21834372. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 186857/21834453. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 186858/21834480. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 186859/21834534. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 186860/21834624. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.y)))) 7. ==[ beta ]==> (((a a) a)(a (^y.y))) 8. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 186861/21834705. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (a ((^x.x)(^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 186862/21835038. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z) c)) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y) c)) 5. ==[ beta ]==> (((a (a a))(^x.x)) c) REDUCED to normal form. ------ 186863/21835110. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (c ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (c (^y.y))) 6. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 186864/21835173. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.b) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) b) REDUCED to normal form. ------ 186865/21835218. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1)(^x2.x2))(a (^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(a (^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186866/21835227. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 186867/21835398. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 186868/21835425. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> ((a ((a a)(a a)))(a ((^y.y) a))) 8. ==[ alpha ]==> ((a ((a a)(a a)))(a ((^x.x) a))) 9. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 186869/21835452. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)(a (a a)))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 186870/21835479. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 186871/21835506. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)((a a) a))) 3. ==[ beta ]==> ((((a a) a)(b a))((a a) a)) REDUCED to normal form. ------ 186872/21835533. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 186873/21835560. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 186874/21835587. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(^z.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 186875/21835641. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 186876/21835668. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x)(^y.a))) 5. ==[ beta ]==> ((b (a (a a)))(^y.a)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.a)) REDUCED to normal form. ------ 186877/21835785. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(a (a a)))) 5. ==[ beta ]==> (((a (^z.z))(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 186878/21836172. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a) c)) 3. ==[ beta ]==> (((^y.y) b)((^z.a) c)) 4. ==[ alpha ]==> (((^x.x) b)((^y.a) c)) 5. ==[ beta ]==> (b ((^y.a) c)) 6. ==[ alpha ]==> (b ((^x.a) c)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 186879/21836190. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z) a))) 7. ==[ beta ]==> ((a (^y.y))((^z.z) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 186880/21836217. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a a)(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(a (a a)))) REDUCED to normal form. ------ 186881/21836334. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(^y.(y y))) 8. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 186882/21836361. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (a a)) a)) REDUCED to normal form. ------ 186883/21836487. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186884/21836523. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 186885/21836604. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186886/21836622. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b c)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b c)) 3. ==[ beta ]==> (((a a)(^y.y))(b c)) 4. ==[ alpha ]==> (((a a)(^x.x))(b c)) REDUCED to normal form. ------ 186887/21836631. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a)(^z.a))) REDUCED to normal form. ------ 186888/21836667. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 186889/21836694. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 186890/21836721. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.a)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.a)) REDUCED to normal form. ------ 186891/21836775. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (b (^y.(^z.z)))) 8. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 186892/21836802. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (^z.a))) REDUCED to normal form. ------ 186893/21836829. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 186894/21836856. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 186895/21836883. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 186896/21836937. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b (^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b (^z.z))) REDUCED to normal form. ------ 186897/21836964. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 186898/21836991. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(a a)) REDUCED to normal form. ------ 186899/21837045. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a (^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a (^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.z))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 186900/21837062. ------ 1. ==[ start ]==> (^a.((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (^x.((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (^x.(b (^z.z))) 4. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 186901/21837063. ------ 1. ==[ start ]==> (a ((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (a ((^x.(x (^y.y))) b)) 3. ==[ beta ]==> (a (b (^y.y))) 4. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 186902/21838776. ------ 1. ==[ start ]==> ((^a.(^a.b))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 186903/21846795. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.b))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 186904/21848091. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 186905/21848508. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b) a) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b) a) 3. ==[ beta ]==> ((b (^y.y)) a) 4. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 186906/21848514. ------ 1. ==[ start ]==> ((^a.a)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 3. ==[ beta ]==> ((^y.(y (^z.z))) b) 4. ==[ alpha ]==> ((^x.(x (^y.y))) b) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 186907/21848931. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 186908/21849108. ------ 1. ==[ start ]==> ((^a.(a (a a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.(x (x x)))((b a)(^y.b))) 3. ==[ beta ]==> (((b a)(^y.b))(((b a)(^y.b))((b a)(^y.b)))) 4. ==[ alpha ]==> (((b a)(^x.b))(((b a)(^y.b))((b a)(^z.b)))) REDUCED to normal form. ------ 186909/21849333. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186910/21850224. ------ 1. ==[ start ]==> ((^a.(^a.b))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 186911/21850227. ------ 1. ==[ start ]==> ((a (^a.b))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 186912/21850404. ------ 1. ==[ start ]==> ((^a.(a b))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(x b))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a)(^y.y))(^z.b)) b) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b)) b) REDUCED to normal form. ------ 186913/21850632. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (^y.((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> (^x.((^y.(^z.z)) a)) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186914/21852978. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 186915/21853278. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186916/21853869. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186917/21854601. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 186918/21856545. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186919/21857238. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 186920/21857868. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(a x1))) 3. ==[ eta ]==> (((^x.(^y.y))(b (^z.z))) a) 4. ==[ beta ]==> ((^y.y) a) 5. ==[ alpha ]==> ((^x.x) a) 6. ==[ beta ]==> a REDUCED to normal form. ------ 186921/21858066. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(z b))) REDUCED to normal form. ------ 186922/21858243. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a (^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a (^x1.b))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 186923/21858246. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.b))) REDUCED to normal form. ------ 186924/21858399. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 186925/21859137. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 186926/21859539. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)((^z1.z1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 186927/21859542. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 186928/21859614. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.z)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 186929/21859695. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.c)) REDUCED to normal form. ------ 186930/21859857. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.x1)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.z)) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 186931/21859938. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.a)) 5. ==[ beta ]==> ((a (^y.y))(^z.a)) 6. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 186932/21859956. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.z)) 3. ==[ beta ]==> ((b (^y.y))(^z.z)) 4. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 186933/21859968. ------ 1. ==[ start ]==> ((a a)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a a)((^x.(x (^y.y))) b)) 3. ==[ beta ]==> ((a a)(b (^y.y))) 4. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 186934/21859986. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (a (((^y.(^z.z)) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (a (((^x.(^y.y)) a)(a (^z.z)))) 5. ==[ beta ]==> (a ((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (a ((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 186935/21860013. ------ 1. ==[ start ]==> (((a a) a)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a) a)((b (^x.x))((^y.y) a))) 3. ==[ beta ]==> (((a a) a)((b (^x.x)) a)) REDUCED to normal form. ------ 186936/21860040. ------ 1. ==[ start ]==> (((a a)(^a.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 186937/21860067. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (b ((^x.x)(^y.y)))) 7. ==[ beta ]==> (b (b (^y.y))) 8. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 186938/21860094. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 186939/21860121. ------ 1. ==[ start ]==> (((a a) b)((b a)(a b))) REDUCED to normal form. ------ 186940/21860148. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 186941/21860175. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 186942/21860202. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(b a))) REDUCED to normal form. ------ 186943/21860256. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 186944/21860337. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))(^z.z))) REDUCED to normal form. ------ 186945/21860364. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((a a)((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> ((a a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 186946/21860382. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) a)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) a)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (a (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 186947/21860409. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 186948/21860481. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> (((a a) a)(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> (((a a) a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 186949/21860508. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 186950/21860562. ------ 1. ==[ start ]==> ((a (a (a a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (a (a a)))((b a)(^x.b))) REDUCED to normal form. ------ 186951/21860598. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186952/21860652. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)(b a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(b a))) 5. ==[ beta ]==> ((^y.y)((^z.b)(b a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 7. ==[ beta ]==> ((^y.b)(b a)) 8. ==[ alpha ]==> ((^x.b)(b a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 186953/21860706. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186954/21860760. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(b (^y.y)))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 186955/21860787. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 186956/21860805. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 186957/21860832. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a (a (^z.z))) a)) 3. ==[ beta ]==> (((a (^x.x)) a)((a (a (^z.z))) a)) 4. ==[ alpha ]==> (((a (^x.x)) a)((a (a (^y.y))) a)) REDUCED to normal form. ------ 186958/21860859. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z) b)) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) b)) 7. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 186959/21860886. ------ 1. ==[ start ]==> (((a (a a))(a a))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(a a))((b (^x.x)) c)) REDUCED to normal form. ------ 186960/21860922. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186961/21860949. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 186962/21861057. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 186963/21861138. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 186964/21861264. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((a a)((^y.(y (^z.z))) a)) 6. ==[ alpha ]==> ((a a)((^x.(x (^y.y))) a)) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 186965/21861471. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (b (((^y.y)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (b ((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 186966/21861498. ------ 1. ==[ start ]==> ((((a a) a) a)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 186967/21861552. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 186968/21861579. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a (^x.(x x)))((a (a a)) b)) REDUCED to normal form. ------ 186969/21861606. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 186970/21861633. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(b (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186971/21861660. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 186972/21861678. ------ 1. ==[ start ]==> ((a (^a.b))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 186973/21861696. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.(^y.y)) a)(^z.z))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 186974/21861723. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 186975/21861750. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> ((a (a (a a)))(((a a)(a a))(^y.a))) 4. ==[ alpha ]==> ((a (a (a a)))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 186976/21861777. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> (((a (a a)) a)(b (^y.(y y)))) 6. ==[ alpha ]==> (((a (a a)) a)(b (^x.(x x)))) REDUCED to normal form. ------ 186977/21861804. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 186978/21861831. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((b a)(^x.a))) REDUCED to normal form. ------ 186979/21861858. ------ 1. ==[ start ]==> ((a (a b))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 186980/21861867. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(a b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 186981/21862029. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (b ((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 186982/21862056. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 186983/21862083. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 7. ==[ beta ]==> ((^y.(^z.z)) a) 8. ==[ alpha ]==> ((^x.(^y.y)) a) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 186984/21862218. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 186985/21862632. ------ 1. ==[ start ]==> (((a b) b)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((b a)((^x.x)(^y.y)))) 3. ==[ beta ]==> (((a b) b)((b a)(^y.y))) 4. ==[ alpha ]==> (((a b) b)((b a)(^x.x))) REDUCED to normal form. ------ 186986/21862659. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> (((a a) a)(((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 186987/21862686. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((a a)(a b))) REDUCED to normal form. ------ 186988/21862713. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a b)(a a))) REDUCED to normal form. ------ 186989/21862767. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)(b a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(b a))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 186990/21862794. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.(y y))((a (a a))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((^x.(x x))((a (a a))(a (^y.(^z.z))))) 7. ==[ beta ]==> (((a (a a))(a (^y.(^z.z))))((a (a a))(a (^y.(^z.z))))) 8. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (a a))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 186991/21862821. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a ((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(a ((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)(^x.a))(a b)) REDUCED to normal form. ------ 186992/21862839. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(c (^z.(a a)))) 3. ==[ beta ]==> (b (c (^z.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 186993/21862848. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))((a a)(a a)))) REDUCED to normal form. ------ 186994/21862875. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(b (^y.y)))) REDUCED to normal form. ------ 186995/21862911. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b (^y.y))(^z.z))) 3. ==[ beta ]==> (((a a)(a a))((b (^y.y))(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 186996/21862938. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 186997/21862965. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y) b)(^z.a))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b)(^y.a))) 5. ==[ beta ]==> ((a ((a a) a))(b (^y.a))) 6. ==[ alpha ]==> ((a ((a a) a))(b (^x.a))) REDUCED to normal form. ------ 186998/21862992. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 186999/21863019. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))((b a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 187000/21863073. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a a)(^z.b))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((a a)(^y.b))) REDUCED to normal form. ------ 187001/21863100. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a b)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a b)(^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((a b)(^x.(a a)))) REDUCED to normal form. ------ 187002/21863163. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187003/21863379. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187004/21863460. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(a a))(^z.b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(a a))(^y.b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 187005/21863694. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a)) b)) 3. ==[ beta ]==> ((a (a b))((^y.(a a)) b)) 4. ==[ alpha ]==> ((a (a b))((^x.(a a)) b)) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 187006/21863721. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.b) c)) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.x) c)) 3. ==[ beta ]==> (((a (a a))((a a) a)) c) REDUCED to normal form. ------ 187007/21863973. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(c (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(c (^z.z))) 3. ==[ beta ]==> (((^y.b)(^y.b))(c (^z.z))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(c (^z.z))) 5. ==[ beta ]==> (b (c (^z.z))) 6. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 187008/21864054. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(a a))(a a))) 3. ==[ beta ]==> (b ((^z.(a a))(a a))) 4. ==[ alpha ]==> (b ((^x.(a a))(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 187009/21864162. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 187010/21864189. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(a a))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a) a))) 5. ==[ beta ]==> ((^y.(a a))((a a) a)) 6. ==[ alpha ]==> ((^x.(a a))((a a) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187011/21864243. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a b))((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 187012/21864324. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((^y.a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 187013/21864432. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 187014/21864450. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 187015/21864711. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(b ((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187016/21865008. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (b a))) REDUCED to normal form. ------ 187017/21865035. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.x1))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 187018/21865053. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(b (^z.z))) 3. ==[ beta ]==> ((^y.y)(b (^z.z))) 4. ==[ alpha ]==> ((^x.x)(b (^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187019/21865107. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.z)(a a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.z)(a a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)(a a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(a a))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(a a))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 187020/21865188. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187021/21865296. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187022/21865323. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.x))(((a a)(^z.z))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 187023/21865368. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 187024/21865395. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a a)(^z.z))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a a)(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 187025/21865422. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((^y.y) b) a)) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y) b) a)) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x) b) a)) 5. ==[ beta ]==> (((a (a a))(a a))(b a)) REDUCED to normal form. ------ 187026/21865449. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z))) b)) 5. ==[ beta ]==> ((a b)((a (^y.(^z.z))) b)) 6. ==[ alpha ]==> ((a b)((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 187027/21865476. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((b a) c)) REDUCED to normal form. ------ 187028/21865647. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 7. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187029/21865926. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)(a b)) REDUCED to normal form. ------ 187030/21865953. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((b a)((a (a a))((^y.y)(a a)))) 4. ==[ alpha ]==> ((b a)((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> ((b a)((a (a a))(a a))) REDUCED to normal form. ------ 187031/21865980. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.x))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 187032/21866007. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (^y1.y1))(b a))) REDUCED to normal form. ------ 187033/21866052. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(a (^z.z))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 187034/21866133. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187035/21866241. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187036/21866340. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 187037/21866367. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (^y.(^z.z))) a)) 3. ==[ beta ]==> ((a (b a))((a (^y.(^z.z))) a)) 4. ==[ alpha ]==> ((a (b a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 187038/21866394. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((b a) b)) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((b a) b)) REDUCED to normal form. ------ 187039/21867024. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.(a a))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(a a))((^y.y) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187040/21867078. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 187041/21867159. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (b ((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 187042/21867528. ------ 1. ==[ start ]==> (((a b)(a b))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y)) b)) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 187043/21867555. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(a a)) c)) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(a a)) c)) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(a a)) c)) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 187044/21867807. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(a a))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(a a))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(a a))(a (^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(a a))(a (^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187045/21867888. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187046/21867996. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.y1)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187047/21868104. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 187048/21868131. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187049/21868185. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a)(^z1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 187050/21868275. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a a)(a a))) REDUCED to normal form. ------ 187051/21868302. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.b))((a b)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a b)(a (^y.y)))) REDUCED to normal form. ------ 187052/21868383. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (a a))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (a a))(^x1.x1))) REDUCED to normal form. ------ 187053/21868410. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((b (^x.a))(a ((a a) a))) REDUCED to normal form. ------ 187054/21868437. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (^z.z))(a b))) REDUCED to normal form. ------ 187055/21868500. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 187056/21868527. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 187057/21868554. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)(^y.a))) 5. ==[ beta ]==> ((a b)(((a a) a)(^y.a))) 6. ==[ alpha ]==> ((a b)(((a a) a)(^x.a))) REDUCED to normal form. ------ 187058/21868581. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(z z))) REDUCED to normal form. ------ 187059/21868608. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)((a (a a))(^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 187060/21868662. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a (^y.y))(^z.b))) 3. ==[ beta ]==> (((a b)(a a))((a (^y.y))(^z.b))) 4. ==[ alpha ]==> (((a b)(a a))((a (^x.x))(^y.b))) REDUCED to normal form. ------ 187061/21868689. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a a)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b))((a a)(^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))((a a)(^x.(a a)))) REDUCED to normal form. ------ 187062/21868716. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((a a) a)) REDUCED to normal form. ------ 187063/21869049. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d (^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (d (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (d (^x.(^y.y)))) REDUCED to normal form. ------ 187064/21869157. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187065/21869292. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 7. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187066/21869319. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.x1)(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a b))) 5. ==[ beta ]==> ((^y.y)(a b)) 6. ==[ alpha ]==> ((^x.x)(a b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 187067/21869373. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)((^y.a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.a)(^y.(^z.z)))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 187068/21869454. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 187069/21869463. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(c (^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.z))) REDUCED to normal form. ------ 187070/21869490. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b ((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(b ((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b ((a a) a))) REDUCED to normal form. ------ 187071/21869517. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(a (a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (a b))) REDUCED to normal form. ------ 187072/21869571. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(a (^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(a (^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.y1))) REDUCED to normal form. ------ 187073/21869598. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (a a))((^y.y) a))) 5. ==[ beta ]==> ((b (^x.(x x)))((a (a a)) a)) REDUCED to normal form. ------ 187074/21869625. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (a (a a)))) REDUCED to normal form. ------ 187075/21869679. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((a a) a))) 5. ==[ beta ]==> ((^y.y)((a a)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((a a)((a a) a))) 7. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 187076/21869697. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a (^a.b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.b))) REDUCED to normal form. ------ 187077/21869715. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((a a) a)(^z.z))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 187078/21869742. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 187079/21869769. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a (a a))(^y.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a (a a))(^y.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a (a a))(^x.a))) REDUCED to normal form. ------ 187080/21869796. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> (((a (a a)) b)(a (^y.(y y)))) 6. ==[ alpha ]==> (((a (a a)) b)(a (^x.(x x)))) REDUCED to normal form. ------ 187081/21869823. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 187082/21869850. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a a)(^x.a))) REDUCED to normal form. ------ 187083/21869877. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 187084/21869904. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z)) b)) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y)) b)) 7. ==[ beta ]==> (((a a)(a a))((^y.y) b)) 8. ==[ alpha ]==> (((a a)(a a))((^x.x) b)) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 187085/21869931. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (a a)) c)) REDUCED to normal form. ------ 187086/21870111. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x))(a ((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 187087/21870516. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> (b (((^y.y) a)(a (^z.z)))) 6. ==[ alpha ]==> (b (((^x.x) a)(a (^y.y)))) 7. ==[ beta ]==> (b (a (a (^y.y)))) 8. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 187088/21870543. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((a (^y.y)) a)) REDUCED to normal form. ------ 187089/21870561. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b (^z.(z z)))) 3. ==[ beta ]==> ((a (a (^y.y)))(b (^z.(z z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(y y)))) REDUCED to normal form. ------ 187090/21870570. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)(a (a a)))) REDUCED to normal form. ------ 187091/21870588. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 187092/21870642. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a)(a (^y.y)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 187093/21870723. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.z))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 5. ==[ beta ]==> (b ((^y.y)(^y.y))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187094/21870786. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(b a)) REDUCED to normal form. ------ 187095/21870867. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 187096/21870894. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))((a a) a)) REDUCED to normal form. ------ 187097/21870966. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 187098/21870975. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b c)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b c)) REDUCED to normal form. ------ 187099/21870993. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1) a)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1) a)) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 187100/21871011. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(((^y.y) a) a)) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a a)) REDUCED to normal form. ------ 187101/21871038. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1)) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z)) b)) REDUCED to normal form. ------ 187102/21871065. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a) c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a) c)) 3. ==[ beta ]==> ((a (b (^y.y)))((a a) c)) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a) c)) REDUCED to normal form. ------ 187103/21871092. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^b.a) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.a) a)) 3. ==[ beta ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 187104/21871119. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1)) b)) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) b)) 7. ==[ beta ]==> (b ((^y.(^z.z)) b)) 8. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187105/21871173. ------ 1. ==[ start ]==> (((a b)(b a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 187106/21871200. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 187107/21871227. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a (^z.z)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^z.z)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y)) a)) REDUCED to normal form. ------ 187108/21871281. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 187109/21871308. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1) b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((b (^y.y))((^z.z) b)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) b)) 7. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 187110/21871335. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 187111/21871389. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.x1) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z) a)) 5. ==[ beta ]==> ((a (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 187112/21871407. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a a)) 3. ==[ beta ]==> ((b (^y.y))(a a)) 4. ==[ alpha ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 187113/21871415. ------ 1. ==[ start ]==> (^a.((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (^x.((x (x (^y.y)))(x x))) REDUCED to normal form. ------ 187114/21871416. ------ 1. ==[ start ]==> (a ((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (a ((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 187115/21882444. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187116/21882861. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b) b) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b) b) 3. ==[ beta ]==> ((b (^y.y)) b) 4. ==[ alpha ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 187117/21882870. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a)) a) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a)) a) REDUCED to normal form. ------ 187118/21882876. ------ 1. ==[ start ]==> ((^a.a)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))(a a)) 4. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 187119/21882885. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187120/21882903. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((^y.(^z.z)) a)(a (^x1.x1)))(((^y.(^z.z)) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 5. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 7. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(a (^x1.x1)))) 9. ==[ beta ]==> ((a (^x.x))((^z.z)(a (^x1.x1)))) 10. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z)))) 11. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 12. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 187121/21882930. ------ 1. ==[ start ]==> ((^a.b)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.b)((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 187122/21883011. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a (^z.(^x1.x1)))((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 187123/21883200. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (a a))((a a)(a a)))) 3. ==[ eta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 187124/21883302. ------ 1. ==[ start ]==> (((a a)(^b.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 187125/21883371. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 187126/21884175. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(^y.(y (y (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(y (y (^z.z))))) 6. ==[ alpha ]==> ((a a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 187127/21884253. ------ 1. ==[ start ]==> ((^a.((a a) a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> (((((a a)(a a))((^y.y) a))(((a a)(a a))((^y.y) a)))(((a a)(a a))((^y.y) a))) 4. ==[ alpha ]==> (((((a a)(a a))((^x.x) a))(((a a)(a a))((^y.y) a)))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> (((((a a)(a a)) a)(((a a)(a a))((^y.y) a)))(((a a)(a a))((^z.z) a))) 6. ==[ alpha ]==> (((((a a)(a a)) a)(((a a)(a a))((^x.x) a)))(((a a)(a a))((^y.y) a))) 7. ==[ beta ]==> (((((a a)(a a)) a)(((a a)(a a)) a))(((a a)(a a))((^y.y) a))) 8. ==[ alpha ]==> (((((a a)(a a)) a)(((a a)(a a)) a))(((a a)(a a))((^x.x) a))) 9. ==[ beta ]==> (((((a a)(a a)) a)(((a a)(a a)) a))(((a a)(a a)) a)) REDUCED to normal form. ------ 187128/21886578. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(b (^z.z)))) REDUCED to normal form. ------ 187129/21886791. ------ 1. ==[ start ]==> ((^a.(b a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(((a a) a)((^y.y)(a a)))) 3. ==[ eta ]==> (b (((a a) a)((^y.y)(a a)))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 187130/21887298. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.((a a)(a a)))) REDUCED to normal form. ------ 187131/21887340. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) b) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) b) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187132/21887628. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(b ((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(b ((^x1.x1) b))) 3. ==[ beta ]==> ((b ((^x1.x1) b))(^y.(^z.z))) 4. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.z))) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 187133/21888231. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187134/21889545. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(b (b a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(b (b a))) 3. ==[ beta ]==> (((b (b a))(b (b a)))((b (b a))(b (b a)))) REDUCED to normal form. ------ 187135/21889863. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b b)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 187136/21890133. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^b.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(x1 a))) REDUCED to normal form. ------ 187137/21890412. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(^a.(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(^y.(b y))) 3. ==[ eta ]==> ((((a a) a)((^x.x)(a a))) b) 4. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 187138/21890625. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187139/21892230. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.b))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.b))) 5. ==[ beta ]==> (^y.(^z.b)) 6. ==[ alpha ]==> (^x.(^y.b)) REDUCED to normal form. ------ 187140/21892428. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.z))) REDUCED to normal form. ------ 187141/21892950. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.((y y) y))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.((y y) y))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.((x x) x))) REDUCED to normal form. ------ 187142/21893028. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> ((((^z.z) a)((^x1.x1) a))((((^z.z) a)((^x1.x1) a))(^y.y))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((((^z.z) a)((^x1.x1) a))(^y1.y1))) 5. ==[ beta ]==> ((a ((^y.y) a))((((^z.z) a)((^x1.x1) a))(^y1.y1))) 6. ==[ alpha ]==> ((a ((^x.x) a))((((^y.y) a)((^z.z) a))(^x1.x1))) 7. ==[ beta ]==> ((a a)((((^y.y) a)((^z.z) a))(^x1.x1))) 8. ==[ alpha ]==> ((a a)((((^x.x) a)((^y.y) a))(^z.z))) 9. ==[ beta ]==> ((a a)((a ((^y.y) a))(^z.z))) 10. ==[ alpha ]==> ((a a)((a ((^x.x) a))(^y.y))) 11. ==[ beta ]==> ((a a)((a a)(^y.y))) 12. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 187143/21893616. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(a (a a)))) REDUCED to normal form. ------ 187144/21893901. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(^y1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187145/21893904. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.a))) REDUCED to normal form. ------ 187146/21894003. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.((^y.y) x))) 3. ==[ eta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 187147/21894192. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 187148/21894219. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(a a))) 5. ==[ beta ]==> ((b (^y.y))(^z.(a a))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(a a))) REDUCED to normal form. ------ 187149/21894300. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(x1 x1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(z z))) 5. ==[ beta ]==> ((a (^y.y))(^z.(z z))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 187150/21894318. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187151/21894327. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 187152/21894339. ------ 1. ==[ start ]==> ((a a)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a a)((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 187153/21894348. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 187154/21894366. ------ 1. ==[ start ]==> ((a (a a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a)(a (^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(a (^y.y)))) 5. ==[ beta ]==> ((a (a a))(a (^y.y))) 6. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 187155/21894393. ------ 1. ==[ start ]==> ((a b)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a b)((b (^x.x))((^y.y) a))) 3. ==[ beta ]==> ((a b)((b (^x.x)) a)) REDUCED to normal form. ------ 187156/21894447. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 187157/21894474. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 187158/21894609. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 187159/21894636. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x))(a a))((^z.z) b)) 6. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y) b)) 7. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 187160/21894663. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 187161/21894735. ------ 1. ==[ start ]==> ((((^a.a) a) a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a a)(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 187162/21894762. ------ 1. ==[ start ]==> (((a a)(^b.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 187163/21894780. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 187164/21894789. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 187165/21894834. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 187166/21894924. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 187167/21894942. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a)(^z.b))) 3. ==[ beta ]==> ((^y.(y y))((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.(x x))((b a)(^y.b))) 5. ==[ beta ]==> (((b a)(^y.b))((b a)(^y.b))) 6. ==[ alpha ]==> (((b a)(^x.b))((b a)(^y.b))) REDUCED to normal form. ------ 187168/21894969. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 187169/21895005. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a b)((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 187170/21895032. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.b)(b a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.b)(b a))) 3. ==[ beta ]==> (((a (a a)) a) b) REDUCED to normal form. ------ 187171/21895050. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a a))(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 187172/21895077. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187173/21895086. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 187174/21895113. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 187175/21895140. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 187176/21895437. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 187177/21895491. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.a))((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 187178/21895518. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187179/21895608. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(b (^y.y))) REDUCED to normal form. ------ 187180/21895635. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((a ((^y.y) a))(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(a (a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (a (^y.y))))) 6. ==[ alpha ]==> ((a a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 187181/21895662. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> (((a (a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 187182/21895689. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a a)((b (^y.y))(a (^z.z)))) 6. ==[ alpha ]==> ((a a)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 187183/21895716. ------ 1. ==[ start ]==> ((a ((a a) a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a) a))(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> ((a ((a a) a))(((a a)(a a)) a)) REDUCED to normal form. ------ 187184/21896238. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.b)(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 187185/21896382. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(x x))((^y.y) b))) 3. ==[ beta ]==> ((((a a) a) b)(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> ((((a a) a) b)(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> ((((a a) a) b)(b ((^y.y) b))) 6. ==[ alpha ]==> ((((a a) a) b)(b ((^x.x) b))) 7. ==[ beta ]==> ((((a a) a) b)(b b)) REDUCED to normal form. ------ 187186/21896400. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (b (a (^y.(a a)))) 6. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 187187/21896409. ------ 1. ==[ start ]==> (((a b) a)((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.a)((a a)(a a)))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 187188/21896436. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 187189/21896508. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((b (^y.y)) b)) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b (^y.y)) b)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b (^x.x)) b)) REDUCED to normal form. ------ 187190/21896544. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((^y.a)((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> ((^x.a)((^y.(a a))(^z.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 187191/21896571. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 187192/21896598. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187193/21896787. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(y y))(^z.z))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.z))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 5. ==[ beta ]==> (b ((^y.y)(^y.y))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187194/21897219. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.(a a)))) REDUCED to normal form. ------ 187195/21897435. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (b ((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187196/21897669. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b (^z.z)) a)) 3. ==[ beta ]==> (b ((b (^z.z)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 187197/21897678. ------ 1. ==[ start ]==> (((a b) c)((^d.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 187198/21897705. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 187199/21897732. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.a)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.a)) REDUCED to normal form. ------ 187200/21897813. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 187201/21897867. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.b)(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.b)(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187202/21897948. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.(^y1.(^z1.z1)))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 187203/21897975. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 187204/21898011. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b ((a a)(a a)))) REDUCED to normal form. ------ 187205/21898038. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(a (b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(a (b (^y.y)))) REDUCED to normal form. ------ 187206/21898065. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((a (a b))(((a a)(a a))(a a))) REDUCED to normal form. ------ 187207/21898092. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x) b)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(b (a (^y.y)))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(b (a (^x.x)))) REDUCED to normal form. ------ 187208/21898119. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))((^z1.z1) a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))((^y1.y1) a))) 7. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((^y1.y1) a))) 8. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1) a))) 9. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 10. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 11. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 187209/21898146. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((b a)(a (a a)))) REDUCED to normal form. ------ 187210/21898173. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)(((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)(((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b) a)(((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (((a b) a)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 187211/21898200. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((a a)((a a) a))) REDUCED to normal form. ------ 187212/21898227. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a b)(a b))) REDUCED to normal form. ------ 187213/21898254. ------ 1. ==[ start ]==> ((a (b a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b a))(((a a) a)((^x.x)(a a)))) 3. ==[ beta ]==> ((a (b a))(((a a) a)(a a))) REDUCED to normal form. ------ 187214/21898425. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> (b (((a a)(a a))(^z.z))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.x))) REDUCED to normal form. ------ 187215/21898488. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 187216/21898533. ------ 1. ==[ start ]==> (((^a.a)(b a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b a)(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 187217/21898596. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.b)(a b))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.b)(a b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.b)(a b))) 5. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 187218/21898614. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a) a)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a b))(((a a) a)(^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 187219/21898623. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b)) a) REDUCED to normal form. ------ 187220/21898677. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((b a)(b a))) REDUCED to normal form. ------ 187221/21898695. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 187222/21898704. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 187223/21898731. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 187224/21898758. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((a a)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(a a))) REDUCED to normal form. ------ 187225/21898803. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) b) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) b) b)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 187226/21899082. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187227/21899091. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(b ((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(b ((^z.z) b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(b b)) REDUCED to normal form. ------ 187228/21899181. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1))) c)) 5. ==[ beta ]==> ((a a)((^z.(^x1.(^y1.y1))) c)) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) c)) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 187229/21899478. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) b)(^x1.x1))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) b)(^z.z))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y) b)(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)(^y.y))) 9. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 10. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 187230/21899487. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 187231/21899514. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 187232/21899559. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 187233/21899568. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187234/21899595. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 187235/21899622. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.b)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) b) REDUCED to normal form. ------ 187236/21899667. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187237/21899676. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 187238/21899694. ------ 1. ==[ start ]==> ((a (^b.b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 187239/21899973. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.a)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187240/21900180. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^d.a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a) c)) 3. ==[ beta ]==> (b ((^z.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 187241/21900459. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.(^y1.y1)))(a a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.(^x1.x1)))(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187242/21900504. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 187243/21900513. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 187244/21900540. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 187245/21900567. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 187246/21900612. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187247/21900621. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 187248/21900648. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(z z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.x))(((^z.z)(a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((b (^x.x))((a a)((^z.z)(a a)))) 8. ==[ alpha ]==> ((b (^x.x))((a a)((^y.y)(a a)))) 9. ==[ beta ]==> ((b (^x.x))((a a)(a a))) REDUCED to normal form. ------ 187249/21900981. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(c ((a a)(^y.y)))) 3. ==[ beta ]==> ((b (a a))(c ((a a)(^y.y)))) 4. ==[ alpha ]==> ((b (a a))(c ((a a)(^x.x)))) REDUCED to normal form. ------ 187250/21901008. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(b (b a))) REDUCED to normal form. ------ 187251/21901044. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187252/21901323. ------ 1. ==[ start ]==> ((((^a.a) b) b)(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) b)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b b)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b b)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 187253/21901368. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 187254/21901395. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.a)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.a)) 7. ==[ beta ]==> ((a a)(^y.a)) 8. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 187255/21901404. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 187256/21901431. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.b)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.b)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)(a (a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 187257/21901449. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 187258/21901512. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(y y))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a b)(a b))) REDUCED to normal form. ------ 187259/21901530. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (b (a (^y.(a a)))) 6. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 187260/21901539. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 187261/21901593. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b a)) REDUCED to normal form. ------ 187262/21901638. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((a a)(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187263/21901647. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 187264/21901674. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 187265/21901701. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 187266/21901818. ------ 1. ==[ start ]==> (((a (a a))(b a))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(c ((^x.x)(a a)))) 3. ==[ beta ]==> (((a (a a))(b a))(c (a a))) REDUCED to normal form. ------ 187267/21901845. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(b ((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^y.y))(b ((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(b ((a a)(^y.y)))) REDUCED to normal form. ------ 187268/21901872. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(a (b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(a (b a))) 3. ==[ beta ]==> ((((a a) a)(a a))(a (b a))) REDUCED to normal form. ------ 187269/21901899. ------ 1. ==[ start ]==> (((a b)(a b))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 187270/21901926. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a)((a a) a))((a a)(a (^y.y)))) 6. ==[ alpha ]==> (((a a)((a a) a))((a a)(a (^x.x)))) REDUCED to normal form. ------ 187271/21901953. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a b)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a b)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a b) a)) REDUCED to normal form. ------ 187272/21902007. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(^x1.x1))) 9. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 10. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 187273/21902034. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (a a))((a a) a))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (a a))((a a) a))) REDUCED to normal form. ------ 187274/21902061. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x) a)(a b))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a (a b))) REDUCED to normal form. ------ 187275/21902088. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 187276/21902178. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(a a))(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(a a))(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187277/21902259. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 187278/21902403. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 187279/21902430. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a a)) REDUCED to normal form. ------ 187280/21902538. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((a (^x.x))((^z.a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.a))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 187281/21902565. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 187282/21902637. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187283/21903339. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b) b)) 5. ==[ beta ]==> ((^y.y)((^z.b) b)) 6. ==[ alpha ]==> ((^x.x)((^y.b) b)) 7. ==[ beta ]==> ((^y.b) b) 8. ==[ alpha ]==> ((^x.b) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 187284/21903528. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a b)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187285/21903645. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187286/21903690. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.b))) 5. ==[ beta ]==> ((a a)(^y.b)) 6. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 187287/21903744. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((a a) a) b)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((a a) a) b)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((a a) a) b)) 5. ==[ beta ]==> ((b ((^y.y) b))(((a a) a) b)) 6. ==[ alpha ]==> ((b ((^x.x) b))(((a a) a) b)) 7. ==[ beta ]==> ((b b)(((a a) a) b)) REDUCED to normal form. ------ 187288/21903753. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 187289/21903780. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187290/21903834. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 187291/21903861. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 187292/21903888. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.b)) REDUCED to normal form. ------ 187293/21904050. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(b (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.a))) 5. ==[ beta ]==> ((^y.y)(b (^z.a))) 6. ==[ alpha ]==> ((^x.x)(b (^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 187294/21904383. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b (a (a a)))(b (^y.y))) 6. ==[ alpha ]==> ((b (a (a a)))(b (^x.x))) REDUCED to normal form. ------ 187295/21904410. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a ((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(a ((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a ((a a) a))) REDUCED to normal form. ------ 187296/21904464. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(a (^y.y)))) 5. ==[ beta ]==> ((a a)((a (a a))(a (^y.y)))) 6. ==[ alpha ]==> ((a a)((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 187297/21904491. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a ((^z.z) a))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(a ((^y.y) a))) 5. ==[ beta ]==> ((a (a (a (^x.x))))(a a)) REDUCED to normal form. ------ 187298/21904905. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a) c)) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) c)) 5. ==[ beta ]==> ((^y.y)((^z.a) c)) 6. ==[ alpha ]==> ((^x.x)((^y.a) c)) 7. ==[ beta ]==> ((^y.a) c) 8. ==[ alpha ]==> ((^x.a) c) 9. ==[ beta ]==> a REDUCED to normal form. ------ 187299/21904941. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b (^z.(z z)))) REDUCED to normal form. ------ 187300/21905013. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 187301/21905049. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187302/21905076. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 187303/21905094. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.b)(b a))((a (a a)) a)) 3. ==[ beta ]==> (b ((a (a a)) a)) REDUCED to normal form. ------ 187304/21905157. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 187305/21905202. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187306/21905238. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 187307/21905265. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b (^y.a))) REDUCED to normal form. ------ 187308/21905319. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187309/21905337. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 187310/21905346. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 187311/21905364. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.a))) REDUCED to normal form. ------ 187312/21905436. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b (a (^z.z)))) 3. ==[ beta ]==> ((a (b (^y.y)))(b (a (^z.z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(b (a (^y.y)))) REDUCED to normal form. ------ 187313/21905463. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a ((^x.x) a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 187314/21905490. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z))(a a))) 5. ==[ beta ]==> (((^y.y) b)((a (^z.z))(a a))) 6. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(a a))) 7. ==[ beta ]==> (b ((a (^y.y))(a a))) 8. ==[ alpha ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 187315/21905517. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a)(a (^z.z)))) REDUCED to normal form. ------ 187316/21905544. ------ 1. ==[ start ]==> (((a b)(b a))(c a)) REDUCED to normal form. ------ 187317/21905571. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b b)) REDUCED to normal form. ------ 187318/21905652. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (a (^z.z)))) REDUCED to normal form. ------ 187319/21905679. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a)(a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a)(a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a)(a a))) 5. ==[ beta ]==> ((b (^y.y))((a a)(a a))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(a a))) REDUCED to normal form. ------ 187320/21905706. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(b a)) REDUCED to normal form. ------ 187321/21905760. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a (a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a (a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (a a))) 5. ==[ beta ]==> ((a (^y.y))(a (a a))) 6. ==[ alpha ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 187322/21905778. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a (^z.z))) 3. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 4. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 187323/21905787. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a a)) REDUCED to normal form. ------ 187324/21907509. ------ 1. ==[ start ]==> ((^a.(^a.b))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 187325/21917241. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b) c) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b) c) 3. ==[ beta ]==> ((b (^y.y)) c) 4. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 187326/21917250. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a)) b) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a)) b) REDUCED to normal form. ------ 187327/21917274. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187328/21917355. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187329/21917517. ------ 1. ==[ start ]==> ((^a.(^b.a))((a b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.x))((a b)(b a))) 3. ==[ beta ]==> (^y.((a b)(b a))) 4. ==[ alpha ]==> (^x.((a b)(b a))) REDUCED to normal form. ------ 187330/21917859. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))((a a) a))(((^y.(^z.(^x1.x1)))((a a) a))((^y.(^z.(^x1.x1)))((a a) a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(((^x1.(^y1.(^z1.z1)))((a a) a))((^x2.(^y2.(^z2.z2)))((a a) a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.(^z1.z1)))((a a) a))((^x2.(^y2.(^z2.z2)))((a a) a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.(^y1.y1)))((a a) a))((^z1.(^x2.(^y2.y2)))((a a) a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187331/21918132. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 187332/21918564. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 187333/21918975. ------ 1. ==[ start ]==> ((^a.(^a.b))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 187334/21918978. ------ 1. ==[ start ]==> ((a (^a.b))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.b))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 187335/21918996. ------ 1. ==[ start ]==> (((a a)((a a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 187336/21919749. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.a)(^x1.(a a)))((^z.a)(^x1.(a a))))) 4. ==[ alpha ]==> ((^x.x)(((^y.a)(^z.(a a)))((^x1.a)(^y1.(a a))))) 5. ==[ beta ]==> (((^y.a)(^z.(a a)))((^x1.a)(^y1.(a a)))) 6. ==[ alpha ]==> (((^x.a)(^y.(a a)))((^z.a)(^x1.(a a)))) 7. ==[ beta ]==> (a ((^z.a)(^x1.(a a)))) 8. ==[ alpha ]==> (a ((^x.a)(^y.(a a)))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187337/21920424. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((^z.b)((^x1.x1)(a a)))((^z.b)((^x1.x1)(a a))))(^y.y)) 4. ==[ alpha ]==> ((((^x.b)((^y.y)(a a)))((^z.b)((^x1.x1)(a a))))(^y1.y1)) 5. ==[ beta ]==> ((b ((^z.b)((^x1.x1)(a a))))(^y1.y1)) 6. ==[ alpha ]==> ((b ((^x.b)((^y.y)(a a))))(^z.z)) 7. ==[ beta ]==> ((b b)(^z.z)) 8. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 187338/21922017. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^x1.(^y1.y1))(^z1.z1))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187339/21922722. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a (a a))((^x.x)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(^y.y)) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 187340/21922935. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 187341/21923667. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 187342/21923973. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.(y (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(x (^y.(^z.z)))) REDUCED to normal form. ------ 187343/21924522. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^c.(^d.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.a))) REDUCED to normal form. ------ 187344/21925014. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(c (^z.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187345/21925566. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (b (^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.((x x)(^y.y)))) REDUCED to normal form. ------ 187346/21925800. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 187347/21926016. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^y.(a a))) REDUCED to normal form. ------ 187348/21926175. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.a)(^y1.a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187349/21926994. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a a)((a a) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 187350/21927015. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 187351/21927177. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((a a) a))) REDUCED to normal form. ------ 187352/21927339. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.(^z.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.a))) REDUCED to normal form. ------ 187353/21928131. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187354/21928290. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187355/21928311. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^y.a)) REDUCED to normal form. ------ 187356/21928392. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.a))) REDUCED to normal form. ------ 187357/21928473. ------ 1. ==[ start ]==> (((a b)(b a))(^a.(^b.a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.x))) REDUCED to normal form. ------ 187358/21928527. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(a (^z.z)))) REDUCED to normal form. ------ 187359/21928581. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 187360/21928635. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187361/21928689. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187362/21928707. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.a)) 3. ==[ beta ]==> ((b (^y.y))(^z.a)) 4. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 187363/21928716. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 187364/21928746. ------ 1. ==[ start ]==> ((a (^a.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 187365/21928755. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (a ((^y.(y (^z.z))) b)) 4. ==[ alpha ]==> (a ((^x.(x (^y.y))) b)) 5. ==[ beta ]==> (a (b (^y.y))) 6. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 187366/21928773. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 187367/21928800. ------ 1. ==[ start ]==> (((^a.a)(a a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a a)((b (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((a a)((b (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((a a)((b (^x.x)) a)) REDUCED to normal form. ------ 187368/21928827. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 187369/21928881. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187370/21928908. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((b a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b a)(a b))) 3. ==[ beta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 187371/21928935. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 187372/21928962. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 187373/21928989. ------ 1. ==[ start ]==> ((a (^b.a))((a b)(b a))) 2. ==[ alpha ]==> ((a (^x.a))((a b)(b a))) REDUCED to normal form. ------ 187374/21929070. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.a)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.a)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 187375/21929097. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(b (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(b (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 187376/21929151. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> (((^y.y) a)((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> (((^x.x) a)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> (a ((a a)(a (a (^y.y))))) 6. ==[ alpha ]==> (a ((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 187377/21929187. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a (^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 187378/21929214. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187379/21929304. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 187380/21929331. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a (a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 187381/21929403. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 187382/21929457. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 187383/21929484. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 187384/21929574. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 187385/21929601. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> (((a (^x.x)) a)(a (a (^z.z)))) 6. ==[ alpha ]==> (((a (^x.x)) a)(a (a (^y.y)))) REDUCED to normal form. ------ 187386/21929628. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (a (^x.x)))((^x1.x1)(^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 187387/21929646. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> ((b b)(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> ((b b)(((^x.(^y.y)) a) b)) 5. ==[ beta ]==> ((b b)((^y.y) b)) 6. ==[ alpha ]==> ((b b)((^x.x) b)) 7. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 187388/21930033. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(y (^z.z))))) 7. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 8. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 187389/21930150. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (((^y.y) b)(a (a a))) 6. ==[ alpha ]==> (((^x.x) b)(a (a a))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 187390/21930204. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b a)((a a) a))) 5. ==[ beta ]==> (a ((b a)((a a) a))) REDUCED to normal form. ------ 187391/21930285. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a b)((a a)(^y.y)))) 3. ==[ beta ]==> (((a a) a)((a b)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a) a)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 187392/21930312. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(b a))) 5. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 187393/21930366. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a a))((^z.z) b))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (a a))((^z.z) b))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (a a))((^y.y) b))) 7. ==[ beta ]==> ((a a)((a (a a))((^y.y) b))) 8. ==[ alpha ]==> ((a a)((a (a a))((^x.x) b))) 9. ==[ beta ]==> ((a a)((a (a a)) b)) REDUCED to normal form. ------ 187394/21930447. ------ 1. ==[ start ]==> ((a (^a.b))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (^x.b))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 187395/21930465. ------ 1. ==[ start ]==> (((a a)((a a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 187396/21930573. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 187397/21930600. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 187398/21930618. ------ 1. ==[ start ]==> (((^a.b) a)((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.b) a)((b a)(^y.a))) 3. ==[ beta ]==> (b ((b a)(^y.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 187399/21930780. ------ 1. ==[ start ]==> ((((a a) a) b)((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a) b)((a (a a))(^x.x))) REDUCED to normal form. ------ 187400/21930807. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b) a)(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> (((a b) a)(a (^y.(a a)))) 4. ==[ alpha ]==> (((a b) a)(a (^x.(a a)))) REDUCED to normal form. ------ 187401/21930888. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 187402/21930915. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b (^y.y)) b)) REDUCED to normal form. ------ 187403/21930942. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(a a)) c)) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(a a)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a)) c)) 5. ==[ beta ]==> ((^y.a)(((a a)(a a)) c)) 6. ==[ alpha ]==> ((^x.a)(((a a)(a a)) c)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 187404/21931086. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 187405/21931113. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a))) b) REDUCED to normal form. ------ 187406/21931167. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 187407/21931194. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)(^y.y))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 187408/21931221. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 187409/21931230. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c ((a a)(a a)))) 3. ==[ beta ]==> ((^y.(a a))(c ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(c ((a a)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187410/21931257. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(b (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(b (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(b (b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 187411/21931311. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(a a))) 5. ==[ beta ]==> ((^y.y)((b (^y1.y1))(a a))) 6. ==[ alpha ]==> ((^x.x)((b (^y.y))(a a))) 7. ==[ beta ]==> ((b (^y.y))(a a)) 8. ==[ alpha ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 187412/21931392. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 187413/21931446. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y))((a a) a))) 5. ==[ beta ]==> ((a a)(((a a)(^y.y))((a a) a))) 6. ==[ alpha ]==> ((a a)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 187414/21931473. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a b))) 5. ==[ beta ]==> (((^y.y)(a a))(a b)) 6. ==[ alpha ]==> (((^x.x)(a a))(a b)) 7. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 187415/21931527. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a) a)((a a)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a) a)((a a)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)((a a)(^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)((a a)(^x1.x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)((a a)(^z.z)))) 9. ==[ beta ]==> ((^y.y)(((a a) a)((a a)(^z.z)))) 10. ==[ alpha ]==> ((^x.x)(((a a) a)((a a)(^y.y)))) 11. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 12. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 187416/21931608. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (b (((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (b (a ((^y.y) b))) 6. ==[ alpha ]==> (b (a ((^x.x) b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 187417/21931761. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^y.y))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(^x.x))((^z.z) a)) 6. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 187418/21931788. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 187419/21931833. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b) c)(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 187420/21931842. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 187421/21931869. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))(a b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(a b))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 187422/21931896. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 187423/21932076. ------ 1. ==[ start ]==> (((a b) c)((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b) c)((b (^x.x)) a)) REDUCED to normal form. ------ 187424/21932103. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a) b)(((a a)(a a)) b)) REDUCED to normal form. ------ 187425/21932130. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) b) c)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b c)) REDUCED to normal form. ------ 187426/21932742. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (((^z.z) a)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b (((^x.x) a)(a (^y.(^z.z))))) 7. ==[ beta ]==> (b (a (a (^y.(^z.z))))) 8. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 187427/21932886. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 187428/21932994. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a b)(^z.b))) 3. ==[ beta ]==> ((a (^y.(a a)))((a b)(^z.b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a b)(^y.b))) REDUCED to normal form. ------ 187429/21933021. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 187430/21933102. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 187431/21933129. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 187432/21933219. ------ 1. ==[ start ]==> (((a a)(b a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 187433/21933246. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 187434/21933300. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 187435/21933327. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((a a) a)((^y.(a a))(^z.a))) 6. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 187436/21933354. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.b)(^x1.b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.b)(^z.b))) 5. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 187437/21933381. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 187438/21933408. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 187439/21933489. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 187440/21933498. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b ((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b ((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b ((^x1.x1) b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187441/21933579. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((a a)((a (^z.(^x1.x1)))(a (^y1.y1)))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 187442/21933660. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b ((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 187443/21933768. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187444/21933795. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(b a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (b a))) REDUCED to normal form. ------ 187445/21933822. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 187446/21933885. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(b (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(b (^y.y))) REDUCED to normal form. ------ 187447/21933912. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 187448/21933966. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 187449/21933993. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 187450/21934020. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a b)(^z.a))) REDUCED to normal form. ------ 187451/21934074. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(^z1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(a a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(a a))) REDUCED to normal form. ------ 187452/21934110. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(((a a)(^x1.x1))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 187453/21934137. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 187454/21934164. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 187455/21934191. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)((^y.y) b))) 5. ==[ beta ]==> (((a (a a))(a a))((^y.y) b)) 6. ==[ alpha ]==> (((a (a a))(a a))((^x.x) b)) 7. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 187456/21934218. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.y)(^z.z))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 187457/21934245. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 187458/21934326. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 187459/21934407. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 187460/21934578. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a)(a (^z.z)))) 3. ==[ beta ]==> (b ((b a)(a (^z.z)))) 4. ==[ alpha ]==> (b ((b a)(a (^x.x)))) REDUCED to normal form. ------ 187461/21934686. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187462/21934740. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> (b ((a (a a))((^y.y)(a a)))) 6. ==[ alpha ]==> (b ((a (a a))((^x.x)(a a)))) 7. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 187463/21934767. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((^y1.y1) a)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y) a)((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x) a)((a a)(^y.y))) 7. ==[ beta ]==> (a ((a a)(^y.y))) 8. ==[ alpha ]==> (a ((a a)(^x.x))) REDUCED to normal form. ------ 187464/21934821. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 187465/21934857. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.(a a))((a (^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((^x.(a a))((a (^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187466/21934884. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 187467/21934911. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 187468/21934938. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 187469/21934965. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 187470/21935019. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(^x2.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.b)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.b)) REDUCED to normal form. ------ 187471/21935046. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 187472/21935082. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) b)((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 187473/21935109. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 187474/21935136. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (b a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (b a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 187475/21935163. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 187476/21935217. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.x)) REDUCED to normal form. ------ 187477/21935244. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> (((a b)((a a) a))(a a)) REDUCED to normal form. ------ 187478/21935271. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 187479/21935352. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((^y1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(a a))(^y1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a a)) REDUCED to normal form. ------ 187480/21935379. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 187481/21935442. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (a (^y.(^z.z))))) 5. ==[ beta ]==> (a (a (^y.(^z.z)))) 6. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 187482/21935577. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (((a a) a)(^y.y))) 6. ==[ alpha ]==> (b (((a a) a)(^x.x))) REDUCED to normal form. ------ 187483/21935685. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a (^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187484/21935748. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((b a)(^x.x))) REDUCED to normal form. ------ 187485/21935802. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.a))) REDUCED to normal form. ------ 187486/21935829. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)(^x1.(x1 x1)))) REDUCED to normal form. ------ 187487/21935910. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a (a a))(^y.b))) REDUCED to normal form. ------ 187488/21935937. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.b))(a (^y.(a a)))) REDUCED to normal form. ------ 187489/21936045. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a)(^x1.x1)) b)) REDUCED to normal form. ------ 187490/21936072. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(a a)) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(a a)) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(a a)) c)) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a) c)) REDUCED to normal form. ------ 187491/21936162. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 187492/21936189. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((^x1.b)(^x1.b))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(^x1.b))) 7. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 187493/21936216. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 187494/21936486. ------ 1. ==[ start ]==> ((a (b (^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(c (^y.(a a)))) REDUCED to normal form. ------ 187495/21936801. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a)(^y.y)) a)) 3. ==[ beta ]==> ((b c)(((a a)(^y.y)) a)) 4. ==[ alpha ]==> ((b c)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 187496/21936828. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a) b)) REDUCED to normal form. ------ 187497/21937035. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(a ((a a)(^z.z)))) 3. ==[ beta ]==> (b (a ((a a)(^z.z)))) 4. ==[ alpha ]==> (b (a ((a a)(^x.x)))) REDUCED to normal form. ------ 187498/21937044. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 187499/21937071. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(a a)) b)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(a a)) b)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a)) b)) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 187500/21937143. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187501/21937269. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 187502/21937296. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 187503/21937323. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((a b)((^y.b)(a (^z.z)))) 6. ==[ alpha ]==> ((a b)((^x.b)(a (^y.y)))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 187504/21937377. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 187505/21937404. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)(^z.z))) 9. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 10. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 187506/21937431. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)((a a) a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)((a a) a))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 187507/21937458. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 187508/21937485. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 187509/21937539. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 187510/21937566. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)(^z.a))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.a))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.a))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 187511/21937593. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 187512/21937647. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 187513/21937737. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a b)(a a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a b)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(a a))) 5. ==[ beta ]==> ((^y.y)((a b)(a a))) 6. ==[ alpha ]==> ((^x.x)((a b)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 187514/21937818. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(a (a a)))) 3. ==[ beta ]==> (b ((a (a a))(a (a a)))) REDUCED to normal form. ------ 187515/21938043. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a (((^y.y) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.x) a)(^y.(^z.z)))) 7. ==[ beta ]==> (a (a (^y.(^z.z)))) 8. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 187516/21938151. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((a a) a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a) b)) REDUCED to normal form. ------ 187517/21938331. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((a a) a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187518/21938340. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 187519/21938367. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 187520/21938466. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)((a a) a))) REDUCED to normal form. ------ 187521/21938484. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a (^a.b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(a (^z.b))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.b))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.b))) REDUCED to normal form. ------ 187522/21938511. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 187523/21938538. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 187524/21938565. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> (((a (a a)) b)(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> (((a (a a)) b)(a ((^y.y) a))) 8. ==[ alpha ]==> (((a (a a)) b)(a ((^x.x) a))) 9. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 187525/21938592. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(a (a a)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(a (a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 187526/21938619. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 187527/21938646. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)((a a) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 187528/21938700. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 187529/21938754. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 187530/21938781. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 187531/21938898. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((((^z.z) a)((^x1.x1) a))(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.z)) 7. ==[ beta ]==> ((a ((^y.y) a))(^z.z)) 8. ==[ alpha ]==> ((a ((^x.x) a))(^y.y)) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 187532/21939285. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(z z)) b)) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z)) b)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y)) b)) 5. ==[ beta ]==> (b ((^y.(y y)) b)) 6. ==[ alpha ]==> (b ((^x.(x x)) b)) 7. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 187533/21939303. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (^z.z)))) 7. ==[ beta ]==> (((^y.y) a)(a (^z.z))) 8. ==[ alpha ]==> (((^x.x) a)(a (^y.y))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 187534/21939312. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a) c)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a) c)) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 187535/21939330. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.x)))((a (^y.y)) a)) REDUCED to normal form. ------ 187536/21939357. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a a)))) 5. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 187537/21939447. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.a))) 7. ==[ beta ]==> ((a (^y.y))(^z.a)) 8. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 187538/21939474. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 187539/21939555. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z)) c)) REDUCED to normal form. ------ 187540/21939600. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(a (a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187541/21939636. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a) b)) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 187542/21939717. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187543/21939744. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 187544/21939762. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b c)) REDUCED to normal form. ------ 187545/21939780. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))((^z.z) a)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y) a)) 5. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 187546/21939807. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 187547/21939834. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 187548/21939861. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)(^y.a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.a)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.a)) REDUCED to normal form. ------ 187549/21939888. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(c (^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(c (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(c (^z.z))) 5. ==[ beta ]==> (((^y.y) b)(c (^z.z))) 6. ==[ alpha ]==> (((^x.x) b)(c (^y.y))) 7. ==[ beta ]==> (b (c (^y.y))) 8. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 187550/21939915. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 187551/21939942. ------ 1. ==[ start ]==> (((a b)(b a))(a (^b.a))) 2. ==[ alpha ]==> (((a b)(b a))(a (^x.a))) REDUCED to normal form. ------ 187552/21939969. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 187553/21939996. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 187554/21940050. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.x1))) REDUCED to normal form. ------ 187555/21940077. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b (^z.z))) 5. ==[ beta ]==> ((b (^y.y))(b (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 187556/21940104. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 187557/21940158. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 187558/21940176. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 187559/21940185. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a (^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a (^y.y))) REDUCED to normal form. ------ 187560/21940202. ------ 1. ==[ start ]==> (^a.((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1))) x)) 3. ==[ eta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187561/21940203. ------ 1. ==[ start ]==> (a ((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (a ((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> (a (^y.(^z.z))) 4. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 187562/21951681. ------ 1. ==[ start ]==> ((^a.a)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 4. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187563/21951708. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.(x x))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (((^y.(y (^z.z))) b)((^y.(y (^z.z))) b)) 4. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.(z (^x1.x1))) b)) 5. ==[ beta ]==> ((b (^y.y))((^z.(z (^x1.x1))) b)) 6. ==[ alpha ]==> ((b (^x.x))((^y.(y (^z.z))) b)) 7. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 187564/21952107. ------ 1. ==[ start ]==> (((a a)(^b.a))(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 187565/21952125. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 187566/21952500. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187567/21952626. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187568/21953571. ------ 1. ==[ start ]==> ((^a.(a b))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.(x b))((b a)(^y.a))) 3. ==[ beta ]==> (((b a)(^y.a)) b) 4. ==[ alpha ]==> (((b a)(^x.a)) b) REDUCED to normal form. ------ 187569/21953958. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))((^x2.(^y2.(^z2.z2)))(^x3.(^y3.y3))))) 5. ==[ beta ]==> (^x.((^z.(^x1.x1))((^x2.(^y2.(^z2.z2)))(^x3.(^y3.y3))))) 6. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2))))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187570/21954840. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((((a b)(^z.(a a)))((a b)(^z.(a a))))(^y.y)) 4. ==[ alpha ]==> ((((a b)(^x.(a a)))((a b)(^y.(a a))))(^z.z)) REDUCED to normal form. ------ 187571/21955014. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 187572/21957036. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187573/21958083. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 187574/21958389. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 187575/21958668. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.(b a))) 3. ==[ beta ]==> ((b b)(^y.(b a))) 4. ==[ alpha ]==> ((b b)(^x.(b a))) REDUCED to normal form. ------ 187576/21959982. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187577/21959991. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 187578/21960873. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187579/21961410. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b (^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b (^x1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 187580/21961593. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.(^c.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 187581/21962439. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(a (a a)))) 3. ==[ beta ]==> (b (^y.(a (a a)))) 4. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 187582/21962547. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187583/21962706. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187584/21962889. ------ 1. ==[ start ]==> (((a b)(b a))(^b.c)) 2. ==[ alpha ]==> (((a b)(b a))(^x.c)) REDUCED to normal form. ------ 187585/21963051. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 187586/21963123. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(z z))) 3. ==[ beta ]==> ((b (^y.y))(^z.(z z))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(y y))) REDUCED to normal form. ------ 187587/21963132. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.a)) REDUCED to normal form. ------ 187588/21963155. ------ 1. ==[ start ]==> (^a.(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^x.(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 187589/21963156. ------ 1. ==[ start ]==> (a (^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (a (^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (a (^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187590/21963162. ------ 1. ==[ start ]==> ((a a)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a a)(^y.(^z.z))) 4. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 187591/21963180. ------ 1. ==[ start ]==> (((^a.a) a)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y)))(a a))) 3. ==[ beta ]==> (a ((a (a (^y.y)))(a a))) 4. ==[ alpha ]==> (a ((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 187592/21963189. ------ 1. ==[ start ]==> ((a (a a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y))) b)) 3. ==[ beta ]==> ((a (a a))(b (^y.y))) 4. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 187593/21963207. ------ 1. ==[ start ]==> (((a a) a)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a)(a (^z.z)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (((a a) a)(a (^y.y))) 6. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 187594/21963234. ------ 1. ==[ start ]==> (((a a)(^a.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 187595/21963261. ------ 1. ==[ start ]==> (((^a.a) b)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x) b)(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (b (((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 187596/21963288. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187597/21963315. ------ 1. ==[ start ]==> (((a a) b)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 187598/21963342. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b a)(a b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b a)(a b))) REDUCED to normal form. ------ 187599/21963369. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 187600/21963396. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 187601/21963450. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 187602/21963531. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b)(a (b (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a (b (^y.y)))) REDUCED to normal form. ------ 187603/21963558. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a a)((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a a)((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 187604/21963576. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (a (b (^y.(y (^z.z))))) 6. ==[ alpha ]==> (a (b (^x.(x (^y.y))))) REDUCED to normal form. ------ 187605/21963585. ------ 1. ==[ start ]==> (((a a)(^b.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 187606/21963603. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187607/21963675. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((b (^y.y))(^z.a))) 3. ==[ beta ]==> (((a a) a)((b (^y.y))(^z.a))) 4. ==[ alpha ]==> (((a a) a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 187608/21963702. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a))(^z.(z z)))) REDUCED to normal form. ------ 187609/21963729. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 187610/21963765. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.(y y))((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> (((^y.(^z.(^x1.x1)))((a a) a))((^y.(^z.(^x1.x1)))((a a) a))) 6. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.(^z1.z1)))((a a) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))((a a) a))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187611/21963846. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187612/21963873. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.b)(b a))) 3. ==[ beta ]==> ((a (a a))((^y.b)(b a))) 4. ==[ alpha ]==> ((a (a a))((^x.b)(b a))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 187613/21963954. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> (((a a)(a a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 187614/21963981. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 187615/21964026. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) a)((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 187616/21964053. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a (a (^z.z))) a)) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a (^z.z))) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y))) a)) REDUCED to normal form. ------ 187617/21964080. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y) b)) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x) b)) 5. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 187618/21964107. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b (^z.z)) c)) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z)) c)) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) c)) REDUCED to normal form. ------ 187619/21964278. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187620/21964485. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 187621/21964665. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> (b (((a a)(^y.y))(a b))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(a b))) REDUCED to normal form. ------ 187622/21964692. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((((a a) a) a)((a a)(a a))) REDUCED to normal form. ------ 187623/21964746. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)(b a))) REDUCED to normal form. ------ 187624/21964773. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (^x.(x x)))(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 187625/21964800. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(^x.a))((a (a a)) b)) REDUCED to normal form. ------ 187626/21964827. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187627/21964854. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 187628/21964917. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.(^y1.y1)) a)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 187629/21964944. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (a a)))((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (a a)))((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 187630/21964971. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> (((a (a a)) a)(((a a)(a a))(^y.a))) 4. ==[ alpha ]==> (((a (a a)) a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 187631/21964998. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.(z z)))) 7. ==[ beta ]==> ((a (^x.x))(b (^z.(z z)))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 187632/21965025. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 187633/21965052. ------ 1. ==[ start ]==> ((a (a b))((b a)(^c.a))) 2. ==[ alpha ]==> ((a (a b))((b a)(^x.a))) REDUCED to normal form. ------ 187634/21965142. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.b)((a a)(^x1.x1)))) IRREDUCIBLE: cycle. ------ 187635/21965223. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (b ((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> (b (((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> (b (((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> (b (b ((^y.y) b))) 8. ==[ alpha ]==> (b (b ((^x.x) b))) 9. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 187636/21965250. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((a b)((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.a)((a a)(a a)))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 187637/21965277. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187638/21965412. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 187639/21965439. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 187640/21965655. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187641/21965826. ------ 1. ==[ start ]==> (((a b) b)((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b) b)((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 187642/21965853. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) a)((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a) a)((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a) a)((b a)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((b a)(^x.x))) REDUCED to normal form. ------ 187643/21965880. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 187644/21965907. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((a a)(a b))) REDUCED to normal form. ------ 187645/21965961. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)((a a)(^z.z)))) REDUCED to normal form. ------ 187646/21965988. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(^x1.x1))(b a))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z)(^x1.x1))(b a))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))(b a))) 7. ==[ beta ]==> ((((^y.y)(^z.z))(b a))(((^y.y)(^z.z))(b a))) 8. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))(b a))) 9. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(b a))) 10. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(b a))) 11. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(b a))) 12. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(b a))) 13. ==[ beta ]==> ((b a)((^y.y)(b a))) 14. ==[ alpha ]==> ((b a)((^x.x)(b a))) 15. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 187647/21966015. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 187648/21966042. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a ((^x1.x1) b))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((^z.z) b))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 187649/21966069. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 187650/21966132. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 187651/21966159. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 187652/21966186. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(b (^z.a))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.a))) REDUCED to normal form. ------ 187653/21966213. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 187654/21966240. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a) a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 187655/21966267. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 187656/21966294. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (((a a)(a a))((a a)(^y.b))) 6. ==[ alpha ]==> (((a a)(a a))((a a)(^x.b))) REDUCED to normal form. ------ 187657/21966321. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 187658/21966357. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.a)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.a)((a a)(^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 187659/21966492. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 187660/21966573. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 187661/21966600. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187662/21966735. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 187663/21966942. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1) c)) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1) c)) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) c)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) c)) 7. ==[ beta ]==> ((^y.y)((^z.z) c)) 8. ==[ alpha ]==> ((^x.x)((^y.y) c)) 9. ==[ beta ]==> ((^y.y) c) 10. ==[ alpha ]==> ((^x.x) c) 11. ==[ beta ]==> c REDUCED to normal form. ------ 187664/21967437. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.b)(a b))) 3. ==[ beta ]==> (((a b)(a b))((^y.b)(a b))) 4. ==[ alpha ]==> (((a b)(a b))((^x.b)(a b))) 5. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 187665/21967518. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(y y))(b a))) 3. ==[ beta ]==> (b ((^y.(y y))(b a))) 4. ==[ alpha ]==> (b ((^x.(x x))(b a))) 5. ==[ beta ]==> (b ((b a)(b a))) REDUCED to normal form. ------ 187666/21967644. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) b) b)) 3. ==[ beta ]==> (((a a)(b a))(b b)) REDUCED to normal form. ------ 187667/21967923. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187668/21968202. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (a a))((a a)(^z.z)))) REDUCED to normal form. ------ 187669/21968229. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a (b a))) REDUCED to normal form. ------ 187670/21968247. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (c (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (c (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187671/21968517. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 187672/21968589. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 187673/21968616. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a a)(^y.y))) 3. ==[ beta ]==> (((a (a a))(a a))((a a)(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))((a a)(^x.x))) REDUCED to normal form. ------ 187674/21968643. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z) b) a)) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z) b) a)) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) b) a)) 5. ==[ beta ]==> ((a b)(((^y.y) b) a)) 6. ==[ alpha ]==> ((a b)(((^x.x) b) a)) 7. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 187675/21968670. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 187676/21968697. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((b a) c)) 3. ==[ beta ]==> (((a b)(^y.y))((b a) c)) 4. ==[ alpha ]==> (((a b)(^x.x))((b a) c)) REDUCED to normal form. ------ 187677/21968841. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187678/21969120. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 187679/21969147. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(a b))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(a b))) 5. ==[ beta ]==> ((b a)((^y.y)(a b))) 6. ==[ alpha ]==> ((b a)((^x.x)(a b))) 7. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 187680/21969174. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))((a (a a))(a a))) REDUCED to normal form. ------ 187681/21969201. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1) a)((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a ((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a ((a a)(^y1.y1)))) REDUCED to normal form. ------ 187682/21969246. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 187683/21969507. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 187684/21969561. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 187685/21969588. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 187686/21969615. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((b a) b)) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((b a) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b a) b)) 5. ==[ beta ]==> (((^y.y)(a a))((b a) b)) 6. ==[ alpha ]==> (((^x.x)(a a))((b a) b)) 7. ==[ beta ]==> ((a a)((b a) b)) REDUCED to normal form. ------ 187687/21969642. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(a b))(((a a)(^x.x)) c)) REDUCED to normal form. ------ 187688/21969867. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187689/21970110. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(c (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187690/21970146. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a a)(b a))) 3. ==[ beta ]==> ((b b)((a a)(b a))) REDUCED to normal form. ------ 187691/21970218. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187692/21970272. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((b a)(b a))((^y.b)(a (a a)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.b)(a (a a)))) 5. ==[ beta ]==> (((b a)(b a)) b) REDUCED to normal form. ------ 187693/21970353. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(y y))(a b))) 3. ==[ beta ]==> (b ((^y.(y y))(a b))) 4. ==[ alpha ]==> (b ((^x.(x x))(a b))) 5. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 187694/21970776. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(a a)) c)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a)) c)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 187695/21971082. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (b ((^z.a)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.a)(a (a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 187696/21971190. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.z1))((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187697/21971298. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)(^z.a))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 187698/21971460. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 187699/21971469. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 187700/21971496. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> (((a a)(^x.b))((a a)(a a))) REDUCED to normal form. ------ 187701/21971577. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (a a))) REDUCED to normal form. ------ 187702/21971604. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.a))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((b (^x.a))((a (a a))(^y.y))) REDUCED to normal form. ------ 187703/21971631. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a ((a a) a))) REDUCED to normal form. ------ 187704/21971721. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 187705/21971748. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)((a b)(^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 187706/21971775. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((a a) a)(^z.a))) REDUCED to normal form. ------ 187707/21971802. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((b a)((^y.y)(^z.(z z)))) 8. ==[ alpha ]==> ((b a)((^x.x)(^y.(y y)))) 9. ==[ beta ]==> ((b a)(^y.(y y))) 10. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 187708/21971829. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 187709/21971856. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> (((a b)(a a))(a (^y.a))) 6. ==[ alpha ]==> (((a b)(a a))(a (^x.a))) REDUCED to normal form. ------ 187710/21971883. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a (^y.y))(^z.b))) 3. ==[ beta ]==> (((a a)(a b))((a (^y.y))(^z.b))) 4. ==[ alpha ]==> (((a a)(a b))((a (^x.x))(^y.b))) REDUCED to normal form. ------ 187711/21971910. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 187712/21971964. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a b) b)) REDUCED to normal form. ------ 187713/21971991. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((a a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((a a) a) c)) 3. ==[ beta ]==> ((b ((^y.y) a))(((a a) a) c)) 4. ==[ alpha ]==> ((b ((^x.x) a))(((a a) a) c)) 5. ==[ beta ]==> ((b a)(((a a) a) c)) REDUCED to normal form. ------ 187714/21972351. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(a (^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187715/21972486. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 187716/21972513. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187717/21972567. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.b)(^x1.x1))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.b)(^x1.x1))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.b)(^z.z))) 7. ==[ beta ]==> ((b b)((^y.b)(^z.z))) 8. ==[ alpha ]==> ((b b)((^x.b)(^y.y))) 9. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 187718/21972648. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> (b ((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 187719/21972657. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d (a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d (a (a a)))) REDUCED to normal form. ------ 187720/21972684. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(c (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.y))) REDUCED to normal form. ------ 187721/21972711. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b ((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b ((a a) a))) REDUCED to normal form. ------ 187722/21972765. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a) a)(a a))) REDUCED to normal form. ------ 187723/21972792. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> ((b (^x.(x x)))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 187724/21972819. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a (a a)) a)) REDUCED to normal form. ------ 187725/21972873. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 187726/21972891. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b (^c.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b (^z.a))) REDUCED to normal form. ------ 187727/21972936. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 187728/21972963. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.z))) 8. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 187729/21972990. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (a a))(^y.a))) 3. ==[ beta ]==> (((a (a a)) b)((a (a a))(^y.a))) 4. ==[ alpha ]==> (((a (a a)) b)((a (a a))(^x.a))) REDUCED to normal form. ------ 187730/21973017. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(x1 x1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 187731/21973044. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 187732/21973071. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)(^c.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 187733/21973098. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a) a) a)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a) a) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a) a)) 5. ==[ beta ]==> (((a a)(a a))(((a a) a) a)) REDUCED to normal form. ------ 187734/21973125. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(a b)) b) REDUCED to normal form. ------ 187735/21973287. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((a a)((^y.(^z.z)) b)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) b)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 187736/21973305. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (a a))(a (^z.z)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 187737/21973710. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (a a))(a a))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))(a a))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))(a a))) 5. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 187738/21973737. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a (a (^z.z)))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(a (a (^y.y)))) REDUCED to normal form. ------ 187739/21973764. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((a (^z.z)) a)) REDUCED to normal form. ------ 187740/21973782. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b (^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(b (^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 187741/21973836. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(y y))(a a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(y y))(a a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(x x))(a a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 187742/21973872. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c c)) 3. ==[ beta ]==> (((^y.y)(^z.z))(c c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c c)) 5. ==[ beta ]==> ((^y.y)(c c)) 6. ==[ alpha ]==> ((^x.x)(c c)) 7. ==[ beta ]==> (c c) REDUCED to normal form. ------ 187743/21973917. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (b ((^y.y)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 187744/21973980. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c (a (^z.z)))) REDUCED to normal form. ------ 187745/21974025. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187746/21974061. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 187747/21974088. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 187748/21974160. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.a)(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(a a))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 187749/21974187. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 187750/21974205. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(^y.a))) REDUCED to normal form. ------ 187751/21974232. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(((^x1.x1) a) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 187752/21974259. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z)) b)) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z)) b)) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 187753/21974313. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.a) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.a) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a) a)) 5. ==[ beta ]==> (((^y.y) b)((^z.a) a)) 6. ==[ alpha ]==> (((^x.x) b)((^y.a) a)) 7. ==[ beta ]==> (b ((^y.a) a)) 8. ==[ alpha ]==> (b ((^x.a) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 187754/21974340. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 187755/21974367. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a) c)) 2. ==[ alpha ]==> (((a b)(b a))((^x.x) c)) 3. ==[ beta ]==> (((a b)(b a)) c) REDUCED to normal form. ------ 187756/21974394. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 187757/21974421. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 187758/21974475. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a a) b)) REDUCED to normal form. ------ 187759/21974502. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 187760/21974529. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x) b)) 3. ==[ beta ]==> ((((a a)(a a))(a (a a))) b) REDUCED to normal form. ------ 187761/21974583. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a a) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a) a)) 5. ==[ beta ]==> ((a (^y.y))((a a) a)) 6. ==[ alpha ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 187762/21974601. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a (a a))) 3. ==[ beta ]==> ((b (^y.y))(a (a a))) 4. ==[ alpha ]==> ((b (^x.x))(a (a a))) REDUCED to normal form. ------ 187763/21974610. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(a a)) a) REDUCED to normal form. ------ 187764/21974634. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a)))) a) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1)))) a) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187765/21974636. ------ 1. ==[ start ]==> (^a.(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(x ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (^x.(x (^z.(^x1.x1)))) 4. ==[ alpha ]==> (^x.(x (^y.(^z.z)))) REDUCED to normal form. ------ 187766/21974637. ------ 1. ==[ start ]==> (a (a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (a (a ((^x.x)(^y.(^z.z))))) 3. ==[ beta ]==> (a (a (^y.(^z.z)))) 4. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 187767/21974640. ------ 1. ==[ start ]==> ((^a.a)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187768/21986115. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187769/21986118. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a)))) a) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z)))) a) 3. ==[ beta ]==> ((a (^y.(^z.z))) a) 4. ==[ alpha ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 187770/21986124. ------ 1. ==[ start ]==> ((^a.a)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 187771/21986127. ------ 1. ==[ start ]==> ((a a)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187772/21986133. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187773/21986151. ------ 1. ==[ start ]==> ((^a.(a a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(x x))((a (a (^y.y)))(a a))) 3. ==[ beta ]==> (((a (a (^y.y)))(a a))((a (a (^y.y)))(a a))) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 187774/21986178. ------ 1. ==[ start ]==> ((^a.b)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.b)(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 187775/21986259. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^z.z) b)((^x1.x1)(^y1.y1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.z)) 7. ==[ beta ]==> ((b (^y.y))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 187776/21986448. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ eta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 187777/21986577. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 187778/21986619. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 187779/21987450. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 187780/21987501. ------ 1. ==[ start ]==> ((^a.((a a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((((b (^y.y))(a (^z.z)))((b (^y.y))(a (^z.z))))((b (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((((b (^x.x))(a (^y.y)))((b (^z.z))(a (^x1.x1))))((b (^y1.y1))(a (^z1.z1)))) REDUCED to normal form. ------ 187781/21988278. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^z.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 187782/21989457. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187783/21989466. ------ 1. ==[ start ]==> (((a b) c)(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(x (^y.y)))) REDUCED to normal form. ------ 187784/21989853. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((a (a b))(^y.(b (^z.z)))) 4. ==[ alpha ]==> ((a (a b))(^x.(b (^y.y)))) REDUCED to normal form. ------ 187785/21990039. ------ 1. ==[ start ]==> ((^a.(b a))((a b)(a b))) 2. ==[ alpha ]==> ((^x.(b x))((a b)(a b))) 3. ==[ eta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 187786/21990588. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a)(a a)) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187787/21991275. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 187788/21991479. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187789/21992247. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187790/21993138. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 187791/21993687. ------ 1. ==[ start ]==> (((a b)(a b))(^a.(b a))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(b x))) 3. ==[ eta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 187792/21993873. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z) a)(a b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187793/21994191. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((a a)(^z.z)))) 3. ==[ beta ]==> ((b c)(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> ((b c)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 187794/21994434. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 187795/21994659. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 187796/21996276. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (^z.z)))(((a (a a))(a (^z.z)))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((a (a a))(a (^y.y)))(^z.z))) REDUCED to normal form. ------ 187797/21996882. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.(z z)))) 3. ==[ beta ]==> (b (^y.(^z.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 187798/21997107. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187799/21997149. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187800/21997278. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))((^z.z) b))(^y1.y1)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.x1)) 5. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.z)) 7. ==[ beta ]==> (((^y.y) b)(^z.z)) 8. ==[ alpha ]==> (((^x.x) b)(^y.y)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187801/21997332. ------ 1. ==[ start ]==> (((a b)(b a))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(a (^y.y)))) REDUCED to normal form. ------ 187802/21997467. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(z (^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 187803/21997548. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.b)) 5. ==[ beta ]==> ((a (^y.y))(^z.b)) 6. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 187804/21997566. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187805/21997575. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(y y))) REDUCED to normal form. ------ 187806/21997599. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187807/21997602. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.x1)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187808/21997607. ------ 1. ==[ start ]==> (^a.(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 187809/21997608. ------ 1. ==[ start ]==> (a (^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 187810/21997614. ------ 1. ==[ start ]==> ((a a)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(a ((^x.x)(^y.(^z.z))))) 3. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 187811/21997623. ------ 1. ==[ start ]==> ((a (^a.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187812/21997641. ------ 1. ==[ start ]==> ((a (a a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (a a))((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 187813/21997650. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((^y.(y (^z.z))) b) 6. ==[ alpha ]==> ((^x.(x (^y.y))) b) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187814/21997668. ------ 1. ==[ start ]==> ((a b)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a)(a (^z.z)))) 3. ==[ beta ]==> ((a b)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> ((a b)(a (^y.y))) 6. ==[ alpha ]==> ((a b)(a (^x.x))) REDUCED to normal form. ------ 187815/21997722. ------ 1. ==[ start ]==> (((a a)(a a))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 187816/21997749. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x)))(b (^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 187817/21997884. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a b)(b a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a b)(b a))) REDUCED to normal form. ------ 187818/21997911. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 187819/21997938. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a a)((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a a)((^y.y) b)) 8. ==[ alpha ]==> ((a a)((^x.x) b)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 187820/21998037. ------ 1. ==[ start ]==> (((a a)(^b.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 187821/21998064. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 187822/21998091. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 187823/21998109. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 187824/21998199. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 187825/21998244. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 187826/21998280. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 187827/21998307. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 187828/21998334. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.b)(b a))) 3. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 187829/21998352. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187830/21998361. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) a) REDUCED to normal form. ------ 187831/21998388. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187832/21998415. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 187833/21998523. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((b b)((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((b b)((^x.(x (^y.y)))(^z.z))) 5. ==[ beta ]==> ((b b)((^z.z)(^y.y))) 6. ==[ alpha ]==> ((b b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b b)(^y.y)) 8. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 187834/21998568. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187835/21998658. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.y))) REDUCED to normal form. ------ 187836/21998712. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187837/21998739. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 187838/21998820. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187839/21998910. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a ((^y.y) a))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)(b ((^y.(^z.z)) a))) 6. ==[ alpha ]==> ((a a)(b ((^x.(^y.y)) a))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 187840/21998937. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (a (a (^y.y))))) REDUCED to normal form. ------ 187841/21998964. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(a a))) 6. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a a))) 7. ==[ beta ]==> ((a a)((^y.y)(a a))) 8. ==[ alpha ]==> ((a a)((^x.x)(a a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 187842/21998991. ------ 1. ==[ start ]==> ((a ((a a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 187843/21999027. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a)) d)) 3. ==[ beta ]==> ((^y.y)((^y1.(a a)) d)) 4. ==[ alpha ]==> ((^x.x)((^y.(a a)) d)) 5. ==[ beta ]==> ((^y.(a a)) d) 6. ==[ alpha ]==> ((^x.(a a)) d) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187844/21999342. ------ 1. ==[ start ]==> (((a a)((a a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((a a) a))((a a)((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a a)((a a) a))((a a)(^y.y))) 4. ==[ alpha ]==> (((a a)((a a) a))((a a)(^x.x))) REDUCED to normal form. ------ 187845/21999495. ------ 1. ==[ start ]==> (((^a.b) a)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 187846/21999513. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.b)((b a)(^z.a))) 4. ==[ alpha ]==> ((^x.b)((b a)(^y.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 187847/21999594. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b)(^z.(^x1.x1)))) IRREDUCIBLE: cycle. ------ 187848/21999657. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 187849/21999675. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a (a a))(^z.z))) 3. ==[ beta ]==> (b ((a (a a))(^z.z))) 4. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 187850/21999684. ------ 1. ==[ start ]==> (((a b) a)((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a b) a)((^x.(x x))((^y.y) b))) 3. ==[ beta ]==> (((a b) a)(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> (((a b) a)(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> (((a b) a)(b ((^y.y) b))) 6. ==[ alpha ]==> (((a b) a)(b ((^x.x) b))) 7. ==[ beta ]==> (((a b) a)(b b)) REDUCED to normal form. ------ 187851/21999702. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((a b)(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> ((a b)(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> ((a b)(a (^y.(a a)))) 6. ==[ alpha ]==> ((a b)(a (^x.(a a)))) REDUCED to normal form. ------ 187852/21999711. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 187853/21999765. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187854/21999783. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.(^y.y)) a) a)) 5. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y) a)) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x) a)) 7. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 187855/21999873. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.(z z))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 187856/22000062. ------ 1. ==[ start ]==> (((^a.b) b)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187857/22000557. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)(b (^y.y)))) 3. ==[ beta ]==> (((a a)(a a))((a a)(b (^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 187858/22000710. ------ 1. ==[ start ]==> (((^a.b) c)((^d.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 187859/22000809. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 187860/22000953. ------ 1. ==[ start ]==> (((a b) c)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.x)(b (^y.y)))) 3. ==[ beta ]==> (((a b) c)(b (^y.y))) 4. ==[ alpha ]==> (((a b) c)(b (^x.x))) REDUCED to normal form. ------ 187861/22001025. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) b) c)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b) c)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b) c)) 5. ==[ beta ]==> (((a a)(^x.x))(b c)) REDUCED to normal form. ------ 187862/22001061. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 187863/22001142. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(^y1.b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187864/22001169. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) b) REDUCED to normal form. ------ 187865/22001196. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 187866/22001250. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.(^y1.(^z1.z1)))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 187867/22001313. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(b ((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b ((a a)(a a)))) REDUCED to normal form. ------ 187868/22001340. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(a (b (^y.y)))) 3. ==[ beta ]==> ((a (a b))(a (b (^y.y)))) 4. ==[ alpha ]==> ((a (a b))(a (b (^x.x)))) REDUCED to normal form. ------ 187869/22001367. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 187870/22001394. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)(a (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(a (^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(((^z.z) b)(a (^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (^z.z)))) 9. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 10. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 11. ==[ beta ]==> (b (a (^y.y))) 12. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 187871/22001421. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((a (^x.(^y.y)))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 187872/22001448. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((b a)(a (a a)))) 3. ==[ beta ]==> (((a b) a)((b a)(a (a a)))) REDUCED to normal form. ------ 187873/22001475. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(((a a)(^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 187874/22001502. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)((a a) a))) REDUCED to normal form. ------ 187875/22001529. ------ 1. ==[ start ]==> ((a (b a))((a b)(a b))) REDUCED to normal form. ------ 187876/22001763. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(a (^y.y))) REDUCED to normal form. ------ 187877/22001808. ------ 1. ==[ start ]==> (((^a.a)(b a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((b a)(^y.(y y)))) 3. ==[ beta ]==> ((b a)((b a)(^y.(y y)))) 4. ==[ alpha ]==> ((b a)((b a)(^x.(x x)))) REDUCED to normal form. ------ 187878/22001835. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187879/22001871. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))((a a) a))) 5. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 187880/22001889. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a b)(^y.b))) 3. ==[ beta ]==> (((a b)(a b))((a b)(^y.b))) 4. ==[ alpha ]==> (((a b)(a b))((a b)(^x.b))) REDUCED to normal form. ------ 187881/22001898. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.b)(a b))) 3. ==[ beta ]==> (((a (a a))(^x.b)) b) REDUCED to normal form. ------ 187882/22001952. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187883/22001979. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(y y))(b a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((b a)(b a))) REDUCED to normal form. ------ 187884/22002006. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 187885/22002033. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 187886/22002078. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(a a)) a)) REDUCED to normal form. ------ 187887/22002357. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187888/22002456. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z) b)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z) b)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z) b)) 5. ==[ beta ]==> ((a a)((^z.z) b)) 6. ==[ alpha ]==> ((a a)((^x.x) b)) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 187889/22002762. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 187890/22002789. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.x1)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(a a))) 5. ==[ beta ]==> ((^y.b)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 187891/22002834. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> (b ((b a)(^x1.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 187892/22002897. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 187893/22002942. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((a a) a)(^x1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187894/22002969. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(a a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 187895/22003248. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187896/22003455. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 187897/22003734. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(a (^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(a (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a (^z.z))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187898/22003761. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 187899/22003779. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 187900/22003788. ------ 1. ==[ start ]==> (((a b)(^c.a))((^d.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 187901/22003815. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187902/22003842. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 187903/22003923. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 187904/22004625. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 187905/22004643. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((b a)(^y.y))) 3. ==[ beta ]==> (((a a)(a a))((b a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a a))((b a)(^x.x))) REDUCED to normal form. ------ 187906/22004670. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 187907/22004679. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 187908/22004706. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 187909/22004724. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a b)(^y.(y y)))) 3. ==[ beta ]==> (((b a)(b a))((a b)(^y.(y y)))) 4. ==[ alpha ]==> (((b a)(b a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 187910/22004787. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 187911/22004805. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (a a))(^y.b))) 3. ==[ beta ]==> (b ((a (a a))(^y.b))) 4. ==[ alpha ]==> (b ((a (a a))(^x.b))) REDUCED to normal form. ------ 187912/22004814. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a b)(^x.b))((a b)(a b))) REDUCED to normal form. ------ 187913/22004868. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 187914/22004913. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((b a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((b a) a)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187915/22004949. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 187916/22004976. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 187917/22005147. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(b ((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a a))(b ((a a)(^y.y)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 187918/22005174. ------ 1. ==[ start ]==> (((a b)(a b))(a (b a))) REDUCED to normal form. ------ 187919/22005201. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((a a)(^y.y))(a a))) 3. ==[ beta ]==> (((a a)((a a) a))(((a a)(^y.y))(a a))) 4. ==[ alpha ]==> (((a a)((a a) a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 187920/22005228. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1)(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(a (^z.z)))) REDUCED to normal form. ------ 187921/22005282. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a) a)(a (a a)))) REDUCED to normal form. ------ 187922/22005309. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b (a (^x.x)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(^z.z))) 9. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 10. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 187923/22005336. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a (a a))((a a) a))) REDUCED to normal form. ------ 187924/22005363. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(a b))) 3. ==[ beta ]==> ((a (b (^x.x)))(a (a b))) REDUCED to normal form. ------ 187925/22005453. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a)(^x2.x2))(^y2.y2))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x2.x2))(^y2.y2))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187926/22005534. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 187927/22005642. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187928/22005678. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> ((b c)((^y.y)((a a)(^z.z)))) 4. ==[ alpha ]==> ((b c)((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> ((b c)((a a)(^y.y))) 6. ==[ alpha ]==> ((b c)((a a)(^x.x))) REDUCED to normal form. ------ 187929/22005705. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 187930/22005750. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b) c)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b) c)) 3. ==[ beta ]==> ((b (^y.y))((a b) c)) 4. ==[ alpha ]==> ((b (^x.x))((a b) c)) REDUCED to normal form. ------ 187931/22005813. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 187932/22005921. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 187933/22006146. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 187934/22006614. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(a a)) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a)) a)) 5. ==[ beta ]==> ((^y.y)((^z.(a a)) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(a a)) a)) 7. ==[ beta ]==> ((^y.(a a)) a) 8. ==[ alpha ]==> ((^x.(a a)) a) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 187935/22006695. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1)) d)) 3. ==[ beta ]==> (b ((^x1.(^y1.y1)) d)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) d)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 187936/22006920. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(a (a a)))) 5. ==[ beta ]==> (a ((^y.(y y))(a (a a)))) 6. ==[ alpha ]==> (a ((^x.(x x))(a (a a)))) 7. ==[ beta ]==> (a ((a (a a))(a (a a)))) REDUCED to normal form. ------ 187937/22006938. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 187938/22006965. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.a))) 5. ==[ beta ]==> ((a (^y.y))(^z.a)) 6. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 187939/22007019. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a b) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a b) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a b) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a b) a)) 5. ==[ beta ]==> ((b ((^y.y) b))((a b) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))((a b) a)) 7. ==[ beta ]==> ((b b)((a b) a)) REDUCED to normal form. ------ 187940/22007028. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 187941/22007109. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 187942/22007136. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 187943/22007163. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 187944/22007208. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.b) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187945/22007361. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((a a) a))) REDUCED to normal form. ------ 187946/22007658. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c (a (a a)))) 3. ==[ beta ]==> ((b (a (a a)))(c (a (a a)))) REDUCED to normal form. ------ 187947/22007685. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(b (^y.y))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(b (^x.x))) REDUCED to normal form. ------ 187948/22007739. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(a a))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a a))) 7. ==[ beta ]==> ((a a)((^y.y)(a a))) 8. ==[ alpha ]==> ((a a)((^x.x)(a a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 187949/22007766. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 187950/22008180. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 x1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z)) b)) 5. ==[ beta ]==> ((^y.y)((^z.(z z)) b)) 6. ==[ alpha ]==> ((^x.x)((^y.(y y)) b)) 7. ==[ beta ]==> ((^y.(y y)) b) 8. ==[ alpha ]==> ((^x.(x x)) b) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 187951/22008207. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a) c)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a) c)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a) c)) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 187952/22008288. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (a a))(^y.y))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (a a))(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (a a))(^x.x))) REDUCED to normal form. ------ 187953/22008324. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z)))) 7. ==[ beta ]==> ((^y.a)(a (^z.z))) 8. ==[ alpha ]==> ((^x.a)(a (^y.y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 187954/22008351. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 187955/22008369. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a a)(^y.(y y)))) 3. ==[ beta ]==> (b ((a a)(^y.(y y)))) 4. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 187956/22008432. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 187957/22008594. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187958/22008612. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 187959/22008621. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^b.a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.a)(a a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 187960/22008639. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 187961/22008657. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b c)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b c)) REDUCED to normal form. ------ 187962/22008711. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(c (a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(c (a a))) 3. ==[ beta ]==> ((a (b (^y.y)))(c (a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(c (a a))) REDUCED to normal form. ------ 187963/22008738. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(b (a (^x.x)))) REDUCED to normal form. ------ 187964/22008765. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a ((^z.z) a))) 5. ==[ beta ]==> (((^y.y) b)(a ((^z.z) a))) 6. ==[ alpha ]==> (((^x.x) b)(a ((^y.y) a))) 7. ==[ beta ]==> (b (a ((^y.y) a))) 8. ==[ alpha ]==> (b (a ((^x.x) a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 187965/22008792. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a (^z.z))(a a))) REDUCED to normal form. ------ 187966/22008819. ------ 1. ==[ start ]==> (((a b)(b a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((a a)(a (^x.x)))) REDUCED to normal form. ------ 187967/22008873. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b b)) REDUCED to normal form. ------ 187968/22008927. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b (a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b (a a))) REDUCED to normal form. ------ 187969/22008954. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a (a (^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a (a (^z.z)))) 5. ==[ beta ]==> ((b (^y.y))(a (a (^z.z)))) 6. ==[ alpha ]==> ((b (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 187970/22008981. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 187971/22009035. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a b)) 5. ==[ beta ]==> ((a (^y.y))(a b)) 6. ==[ alpha ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 187972/22009053. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 187973/22009062. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a (a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a (a a))) REDUCED to normal form. ------ 187974/22009086. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a)))) b) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1)))) b) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187975/22009089. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 187976/22009097. ------ 1. ==[ start ]==> (^a.((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^x.(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 187977/22009098. ------ 1. ==[ start ]==> (a ((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187978/22009101. ------ 1. ==[ start ]==> ((^a.a)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 187979/22009110. ------ 1. ==[ start ]==> ((^a.(^a.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187980/22020576. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187981/22020579. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a)))) b) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z)))) b) 3. ==[ beta ]==> ((a (^y.(^z.z))) b) 4. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 187982/22020588. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a)))) a) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1)))) a) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 4. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187983/22020594. ------ 1. ==[ start ]==> ((^a.a)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 187984/22020597. ------ 1. ==[ start ]==> ((a a)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 187985/22020603. ------ 1. ==[ start ]==> ((^a.(^a.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187986/22020606. ------ 1. ==[ start ]==> ((a (^a.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.x))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 187987/22020684. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187988/22020846. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (^x.(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (^x.((a a)((a a)(^z.z)))) 6. ==[ alpha ]==> (^x.((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 187989/22021188. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y.y)((^z.z)(^x1.x1)))((^y.y)((^z.z)(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)((^y1.y1)(^z1.z1)))((^x2.x2)((^y2.y2)(^z2.z2))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)((^y1.y1)(^z1.z1)))((^x2.x2)((^y2.y2)(^z2.z2))))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)((^x1.x1)(^y1.y1)))((^z1.z1)((^x2.x2)(^y2.y2))))) 7. ==[ beta ]==> ((^y.y)(((^z.z)((^x1.x1)(^y1.y1)))((^z1.z1)((^x2.x2)(^y2.y2))))) 8. ==[ alpha ]==> ((^x.x)(((^y.y)((^z.z)(^x1.x1)))((^y1.y1)((^z1.z1)(^x2.x2))))) 9. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)((^z1.z1)(^x2.x2)))) 10. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 11. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 12. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 13. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 14. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 15. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 16. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 17. ==[ beta ]==> ((^y.y)(^z.z)) 18. ==[ alpha ]==> ((^x.x)(^y.y)) 19. ==[ beta ]==> (^y.y) 20. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187990/22021488. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 187991/22021920. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 187992/22022304. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 187993/22022352. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 187994/22022484. ------ 1. ==[ start ]==> ((^a.(a b))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) b) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) b) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187995/22023078. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((^z.(z z))(^x1.x1))((^z.(z z))(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(y y))(^z.z))((^x1.(x1 x1))(^y1.y1)))) 5. ==[ beta ]==> (((^y.(y y))(^z.z))((^x1.(x1 x1))(^y1.y1))) 6. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.x1))) 9. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 11. ==[ beta ]==> ((^y.(y y))(^z.z)) 12. ==[ alpha ]==> ((^x.(x x))(^y.y)) 13. ==[ beta ]==> ((^y.y)(^y.y)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 187996/22023171. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> (((^x.(x x))(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.z1))) 7. ==[ beta ]==> ((^y.y)(^y1.(^z1.z1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 187997/22023753. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(a a))(a b))) 3. ==[ beta ]==> ((((^z.(a a))(a b))((^z.(a a))(a b)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(a a))(a b))((^y.(a a))(a b)))(^z.z)) 5. ==[ beta ]==> (((a a)((^y.(a a))(a b)))(^z.z)) 6. ==[ alpha ]==> (((a a)((^x.(a a))(a b)))(^y.y)) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 187998/22023936. ------ 1. ==[ start ]==> (((a b) c)(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 187999/22024683. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.((a a)(a a)))) 3. ==[ beta ]==> (b (^z.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 188000/22025346. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^x1.a)(^y1.(^z1.(^x2.x2))))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.a)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 5. ==[ beta ]==> (a (^y1.(^z1.z1))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 188001/22026078. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(a b))(^x1.x1)) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.z)) 5. ==[ beta ]==> (((^y.y)(a b))(^z.z)) 6. ==[ alpha ]==> (((^x.x)(a b))(^y.y)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 188002/22026264. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 188003/22027023. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 188004/22027263. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.a)(^z.(^x1.x1)))((^y.a)(^z.(^x1.x1))))(((^y.a)(^z.(^x1.x1)))((^y.a)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.a)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1))))(((^x2.a)(^y2.(^z2.z2)))((^x3.a)(^y3.(^z3.z3))))) 5. ==[ beta ]==> ((a ((^x1.a)(^y1.(^z1.z1))))(((^x2.a)(^y2.(^z2.z2)))((^x3.a)(^y3.(^z3.z3))))) 6. ==[ alpha ]==> ((a ((^x.a)(^y.(^z.z))))(((^x1.a)(^y1.(^z1.z1)))((^x2.a)(^y2.(^z2.z2))))) 7. ==[ beta ]==> ((a a)(((^x1.a)(^y1.(^z1.z1)))((^x2.a)(^y2.(^z2.z2))))) 8. ==[ alpha ]==> ((a a)(((^x.a)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1))))) 9. ==[ beta ]==> ((a a)(a ((^x1.a)(^y1.(^z1.z1))))) 10. ==[ alpha ]==> ((a a)(a ((^x.a)(^y.(^z.z))))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 188005/22028661. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188006/22029504. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188007/22029597. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(z z)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(y y)))) 7. ==[ beta ]==> (^y.((^z.z)(y y))) 8. ==[ alpha ]==> (^x.((^y.y)(x x))) 9. ==[ beta ]==> (^x.(x x)) REDUCED to normal form. ------ 188008/22029786. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188009/22030191. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.(z1 b))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(z1 b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188010/22030323. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 188011/22030371. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 188012/22030533. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.((a a) a))) 5. ==[ beta ]==> (((a a)(a a))(^y.((a a) a))) 6. ==[ alpha ]==> (((a a)(a a))(^x.((a a) a))) REDUCED to normal form. ------ 188013/22031619. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(c b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(c b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188014/22031667. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^z.a)) REDUCED to normal form. ------ 188015/22031748. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.a))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.a))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.a))) 7. ==[ beta ]==> (b (^y.(^z.a))) 8. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 188016/22031829. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(^x1.z))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(^x1.z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 188017/22031937. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 188018/22032018. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(a a))) 5. ==[ beta ]==> ((a (^y.y))(^z.(a a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 188019/22032036. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.a)) 3. ==[ beta ]==> ((b (^y.y))(^z.a)) 4. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 188020/22032045. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 188021/22032069. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188022/22032072. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 188023/22032081. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188024/22032093. ------ 1. ==[ start ]==> ((a a)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188025/22032102. ------ 1. ==[ start ]==> ((a (^a.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.x))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 188026/22032111. ------ 1. ==[ start ]==> (((^a.a) a)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (a ((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (a ((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 188027/22032129. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a (^y.y)))(a a)) 6. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 188028/22032138. ------ 1. ==[ start ]==> (((a a) a)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y))) b)) 3. ==[ beta ]==> (((a a) a)(b (^y.y))) 4. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 188029/22032156. ------ 1. ==[ start ]==> (((^a.a)(a a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a (^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 188030/22032183. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 188031/22032237. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188032/22032264. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 188033/22032291. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b a)(a b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b a)(a b))) 3. ==[ beta ]==> ((a (^y.y))((b a)(a b))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(a b))) REDUCED to normal form. ------ 188034/22032318. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 188035/22032345. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.a))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.a))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 188036/22032426. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 188037/22032453. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 188038/22032507. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (a ((a (^y.y))((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> (a ((a (^x.x))((^y.(^z.z)) a))) 7. ==[ beta ]==> (a ((a (^x.x))(^z.z))) 8. ==[ alpha ]==> (a ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 188039/22032534. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a a)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 188040/22032570. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 188041/22032678. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 188042/22032687. ------ 1. ==[ start ]==> ((a (a (a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 188043/22032759. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 188044/22032840. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 188045/22032867. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 188046/22032930. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.a)(b (^y.y)))) 3. ==[ beta ]==> (((a a)(a (a a))) a) REDUCED to normal form. ------ 188047/22032957. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 188048/22032984. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 188049/22033002. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (a (^y.y))) a)) 3. ==[ beta ]==> ((b b)((a (a (^y.y))) a)) 4. ==[ alpha ]==> ((b b)((a (a (^x.x))) a)) REDUCED to normal form. ------ 188050/22033011. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a (a a))(a a))((^z.z)(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 188051/22033416. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 188052/22033506. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 188053/22033560. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (a ((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (a ((a (^x.(^y.y)))(^x1.x1))) 8. ==[ alpha ]==> (a ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 188054/22033641. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a)((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> (((a a) a)((a a)((^x.x)(a a)))) 7. ==[ beta ]==> (((a a) a)((a a)(a a))) REDUCED to normal form. ------ 188055/22033668. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)((a a)(^y.y))) 6. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 188056/22033722. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 9. ==[ beta ]==> ((a a)((^y.y)(a (^z.(^x1.x1))))) 10. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 11. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 12. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 188057/22033803. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 188058/22033848. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(a (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 188059/22033956. ------ 1. ==[ start ]==> ((((a a) a)(a a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(a (a a))) REDUCED to normal form. ------ 188060/22033974. ------ 1. ==[ start ]==> (((^a.b) a)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 188061/22033983. ------ 1. ==[ start ]==> ((a (a b))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 188062/22034136. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a) b)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a) b)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a) b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188063/22034163. ------ 1. ==[ start ]==> (((a b) a)((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a b) a)((a (a a))(^x.x))) REDUCED to normal form. ------ 188064/22034190. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(a (^y.(a a)))) REDUCED to normal form. ------ 188065/22034271. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((^z.z) a)) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y) a)) 5. ==[ beta ]==> (((a (a a))(^x.(x x))) a) REDUCED to normal form. ------ 188066/22034298. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b (^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.a))((b (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z)) b)) 5. ==[ beta ]==> ((^y.a)((b (^z.z)) b)) 6. ==[ alpha ]==> ((^x.a)((b (^y.y)) b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 188067/22034388. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 188068/22034469. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a a)) REDUCED to normal form. ------ 188069/22034496. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (a ((^y.b)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a ((^x.b)(^y.(^z.z)))) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 188070/22034550. ------ 1. ==[ start ]==> (((a b)(a a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 188071/22034577. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))(^z.z))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))(^y.y))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^y.y))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 188072/22034613. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(c ((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(c ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(c ((a a)(a a)))) 5. ==[ beta ]==> (c ((a a)(a a))) REDUCED to normal form. ------ 188073/22034667. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a ((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.y)(a ((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.x)(a ((^y.(^z.z)) a))) 7. ==[ beta ]==> (a ((^y.(^z.z)) a)) 8. ==[ alpha ]==> (a ((^x.(^y.y)) a)) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 188074/22034748. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> (b (((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> (b (((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (b (b ((^y.y) a))) 6. ==[ alpha ]==> (b (b ((^x.x) a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 188075/22034802. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)((b a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)((b a)((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)((b a)(^y.y))) 8. ==[ alpha ]==> ((a a)((b a)(^x.x))) REDUCED to normal form. ------ 188076/22034829. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((a a) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 188077/22034883. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a b)((^y1.y1)(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a b)((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a b)((^x1.x1)(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a b)((^x1.x1)(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a b)((^z.z)(a a)))) 9. ==[ beta ]==> ((^y.y)((a b)((^z.z)(a a)))) 10. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(a a)))) 11. ==[ beta ]==> ((a b)((^y.y)(a a))) 12. ==[ alpha ]==> ((a b)((^x.x)(a a))) 13. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 188078/22034964. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 188079/22035144. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a (a a))((^y.y)((^z.z) a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y) a))) 7. ==[ beta ]==> ((a (a a))((^y.y) a)) 8. ==[ alpha ]==> ((a (a a))((^x.x) a)) 9. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 188080/22035171. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((((a a) a) a)((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((((a a) a) a)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.y))) REDUCED to normal form. ------ 188081/22035189. ------ 1. ==[ start ]==> (((^a.b) c)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 188082/22035252. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(a a))(a b))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 188083/22035432. ------ 1. ==[ start ]==> (((a b) c)((a a)(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 188084/22035459. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((b (^y.y)) a)) 3. ==[ beta ]==> (((a a) b)((b (^y.y)) a)) 4. ==[ alpha ]==> (((a a) b)((b (^x.x)) a)) REDUCED to normal form. ------ 188085/22035486. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(a a)) b)) REDUCED to normal form. ------ 188086/22035765. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 188087/22036098. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (a a))(b a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (a a))(b a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (a a))(b a))) 5. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 188088/22036179. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (b ((a a)((a a)(a a)))) REDUCED to normal form. ------ 188089/22036242. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(b (^y.(^z.z)))) REDUCED to normal form. ------ 188090/22036350. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> ((a (^x.(a a)))((a a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.(a a)))((a a)(^y.a))) REDUCED to normal form. ------ 188091/22036377. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a b)(^y.b))) REDUCED to normal form. ------ 188092/22036431. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 188093/22036485. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.a))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.a))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 188094/22036512. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 188095/22036575. ------ 1. ==[ start ]==> (((a a)(b a))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(a a))(^y.y))) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 188096/22036602. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 188097/22036629. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(^y1.a))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 188098/22036710. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 188099/22036737. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.b)(^y.b))) 3. ==[ beta ]==> (((a b)(a (a a))) b) REDUCED to normal form. ------ 188100/22036791. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 188101/22036845. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 188102/22036935. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z) b)(a a))) 5. ==[ beta ]==> ((a a)(((^z.z) b)(a a))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)(a a))) 7. ==[ beta ]==> ((a a)(b (a a))) REDUCED to normal form. ------ 188103/22037016. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 188104/22037124. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1)(^z1.z1))((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188105/22037151. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))((a a)(^z.z)))) REDUCED to normal form. ------ 188106/22037178. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(b a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b a))) 5. ==[ beta ]==> (((^y.y) a)(b a)) 6. ==[ alpha ]==> (((^x.x) a)(b a)) 7. ==[ beta ]==> (a (b a)) REDUCED to normal form. ------ 188107/22037232. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a a)((^z.z) b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a a)((^z.z) b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)((^z.z) b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)((^z.z) b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)((^y.y) b))) 7. ==[ beta ]==> (((a a)(a a))((a a)((^y.y) b))) 8. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x) b))) 9. ==[ beta ]==> (((a a)(a a))((a a) b)) REDUCED to normal form. ------ 188108/22037268. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> ((^y.b)(((^z.z) b)(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(((^y.y) b)(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 188109/22037322. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 188110/22037349. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 188111/22037376. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 188112/22037430. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a) a)(^x1.b))) REDUCED to normal form. ------ 188113/22037466. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 188114/22037493. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(((a a)(^z.z))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 188115/22037520. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.a)(b a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.a)(b a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.a)(b a))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 188116/22037547. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 188117/22037574. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((a b)((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a b)((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a b)((^y.y) b)) 8. ==[ alpha ]==> ((a b)((^x.x) b)) 9. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 188118/22037601. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(^y.y))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 188119/22037628. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 188120/22037736. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) b) REDUCED to normal form. ------ 188121/22037763. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(^z.b))) 3. ==[ beta ]==> ((a b)((^y.a)(^z.b))) 4. ==[ alpha ]==> ((a b)((^x.a)(^y.b))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 188122/22037934. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 188123/22038042. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188124/22038096. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))(a b))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(a b))) 7. ==[ beta ]==> (b ((^y.y)(a b))) 8. ==[ alpha ]==> (b ((^x.x)(a b))) 9. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 188125/22038123. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a (a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(a a))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(a a))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 188126/22038177. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a (^z.z))(b a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (^z.z))(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (^z.z))(b a))) REDUCED to normal form. ------ 188127/22038240. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 188128/22038267. ------ 1. ==[ start ]==> (((a b)(^c.a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 188129/22038294. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 188130/22038321. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 188131/22038402. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((b (^x.x))((^z.z)(^x1.b))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.b))) 7. ==[ beta ]==> ((b (^x.x))(^z.b)) 8. ==[ alpha ]==> ((b (^x.x))(^y.b)) REDUCED to normal form. ------ 188132/22038438. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.(y y))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) b)(((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> (((a a) b)((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> (((a a) b)((a a)((^x.x)(a a)))) 9. ==[ beta ]==> (((a a) b)((a a)(a a))) REDUCED to normal form. ------ 188133/22038465. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) a) REDUCED to normal form. ------ 188134/22038492. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 188135/22038519. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 188136/22038546. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))(^y1.y1))) 7. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(^y1.y1))) 8. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.x1))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 188137/22038600. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 188138/22038627. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(z z)))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 188139/22038654. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) b) REDUCED to normal form. ------ 188140/22038708. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.x1)) REDUCED to normal form. ------ 188141/22038735. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((b (a a))((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> ((b (a a))((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> ((b (a a))((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> ((b (a a))(a a)) REDUCED to normal form. ------ 188142/22038762. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 188143/22038798. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (b a))) 3. ==[ beta ]==> ((^y.y)(b (b a))) 4. ==[ alpha ]==> ((^x.x)(b (b a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 188144/22038933. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a b)(a (a a)))) 3. ==[ beta ]==> (b ((a b)(a (a a)))) REDUCED to normal form. ------ 188145/22039041. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1) a)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188146/22039158. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 188147/22039185. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a))(^y1.a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(^y1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.a))) REDUCED to normal form. ------ 188148/22039266. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.a)) 6. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 188149/22039293. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (a a))(^y.b))) REDUCED to normal form. ------ 188150/22039347. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 188151/22039401. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((b a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((b a) a)) REDUCED to normal form. ------ 188152/22039428. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a)(^x1.x1)) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a)(^z.z)) b)) REDUCED to normal form. ------ 188153/22039491. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.b)(^y.(y y)))) 3. ==[ beta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 188154/22039518. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 188155/22039545. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 188156/22039572. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(x x))(^y.b))) 3. ==[ beta ]==> (((a (a a))(b a))((^y.b)(^y.b))) 4. ==[ alpha ]==> (((a (a a))(b a))((^x.b)(^y.b))) 5. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 188157/22039599. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 188158/22040157. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a)(^y.(^z.z)))) 3. ==[ beta ]==> ((b c)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 188159/22040184. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 188160/22040391. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (b (b ((^z.z)(a a)))) 4. ==[ alpha ]==> (b (b ((^x.x)(a a)))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 188161/22040427. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 188162/22040499. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((a a) a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188163/22040625. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 188164/22040679. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(a a))(a a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a))(a a))) 5. ==[ beta ]==> ((a b)((^y.(a a))(a a))) 6. ==[ alpha ]==> ((a b)((^x.(a a))(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 188165/22040706. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 188166/22040733. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((b a)((^y.a)((^z.z) a))) 6. ==[ alpha ]==> ((b a)((^x.a)((^y.y) a))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 188167/22040760. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 188168/22040787. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(y y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a b)(a a))((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((a b)(a a))((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.z))) 10. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.y))) 11. ==[ beta ]==> (((a b)(a a))(^y.y)) 12. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 188169/22040814. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a a)(a b))((^y.a)((a a) a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.a)((a a) a))) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 188170/22040841. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 188171/22040895. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a a)) REDUCED to normal form. ------ 188172/22040922. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 188173/22041003. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 188174/22041093. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.y)(a ((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.x)(a ((^y.y)(a a)))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 188175/22041174. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 188176/22041282. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188177/22041399. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (a a))(^z.(z z)))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) a)((a (a a))(^y.(y y)))) 5. ==[ beta ]==> (a ((a (a a))(^y.(y y)))) 6. ==[ alpha ]==> (a ((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 188178/22041507. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a b) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a b) a)) REDUCED to normal form. ------ 188179/22041534. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((a a) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a) b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a) b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188180/22041588. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (a a)) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a)) d)) REDUCED to normal form. ------ 188181/22041687. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(a (a b))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188182/22041696. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 188183/22041723. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a) b)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a) b)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a) b)) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 188184/22041750. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 188185/22041822. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 188186/22041840. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b (^c.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(b (^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.a))) REDUCED to normal form. ------ 188187/22041867. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.b))) REDUCED to normal form. ------ 188188/22041921. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 188189/22041948. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(((^x1.x1) a)((^x1.x1) a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((^x1.x1) a))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(a ((^x1.x1) a))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z) a))) 11. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 188190/22041975. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 188191/22042002. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 188192/22042029. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)((a a) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)((a a) a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)((a a) a))) 7. ==[ beta ]==> (((a a)(a a))((a a) a)) REDUCED to normal form. ------ 188193/22042056. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 188194/22042110. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1))(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.a)(^y1.a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(^y1.a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 188195/22042137. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)(^y.(y y)))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 188196/22042164. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 188197/22042236. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 188198/22042254. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))(a (^z.z)))) 5. ==[ beta ]==> (((a (a a))(a (^z.z)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 188199/22042641. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) a)) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188200/22042659. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (a a))(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(a a))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a a))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 188201/22042668. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(a a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(y y)) b)) 3. ==[ beta ]==> (((a (a (^x.x))) a)(b b)) REDUCED to normal form. ------ 188202/22042686. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 188203/22042695. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a) c)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 188204/22042713. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 188205/22042803. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 188206/22042830. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.a))) REDUCED to normal form. ------ 188207/22042911. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z) a) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a b)) REDUCED to normal form. ------ 188208/22042956. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b ((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188209/22042992. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z)) a)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 188210/22043019. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.a) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 188211/22043100. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 188212/22043118. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(c b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(c b)) REDUCED to normal form. ------ 188213/22043136. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 188214/22043163. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1) a)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z) a)) 7. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 188215/22043190. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.z))) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 188216/22043217. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 188217/22043244. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.a))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.a))) 7. ==[ beta ]==> (b ((^y.y)(^z.a))) 8. ==[ alpha ]==> (b ((^x.x)(^y.a))) 9. ==[ beta ]==> (b (^y.a)) 10. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 188218/22043298. ------ 1. ==[ start ]==> (((a b)(b a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 188219/22043325. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a (^z.a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a (^z.a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.a))) REDUCED to normal form. ------ 188220/22043352. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 188221/22043406. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 188222/22043433. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 188223/22043460. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(b (^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 188224/22043514. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 188225/22043532. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a) a)) 3. ==[ beta ]==> ((b (^y.y))((a a) a)) 4. ==[ alpha ]==> ((b (^x.x))((a a) a)) REDUCED to normal form. ------ 188226/22043541. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 188227/22043568. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a (^x1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 188228/22043577. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188229/22043598. ------ 1. ==[ start ]==> ((^a.(^a.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188230/22048053. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.((a a)(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188231/22055064. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188232/22055076. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a)))) b) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1)))) b) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1))) b) 4. ==[ alpha ]==> ((^x.(^y.(^z.z))) b) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188233/22055100. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188234/22055103. ------ 1. ==[ start ]==> ((a (^a.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 188235/22055112. ------ 1. ==[ start ]==> (((^a.a) a)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a (^y.((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a (^x.((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^x.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188236/22055118. ------ 1. ==[ start ]==> ((^a.(a a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1))) a)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.(^z1.z1))) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1))) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188237/22055145. ------ 1. ==[ start ]==> ((^a.b)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.b)((^y.(y (^z.z))) b)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 188238/22055586. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 188239/22055685. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)(^z.(^x1.x1)))((((^y.y) b)(^z.(^x1.x1)))(((^y.y) b)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((((^x1.x1) b)(^y1.(^z1.z1)))(((^x2.x2) b)(^y2.(^z2.z2))))) 5. ==[ beta ]==> ((b (^y.(^z.z)))((((^x1.x1) b)(^y1.(^z1.z1)))(((^x2.x2) b)(^y2.(^z2.z2))))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((((^z.z) b)(^x1.(^y1.y1)))(((^z1.z1) b)(^x2.(^y2.y2))))) 7. ==[ beta ]==> ((b (^x.(^y.y)))((b (^x1.(^y1.y1)))(((^z1.z1) b)(^x2.(^y2.y2))))) 8. ==[ alpha ]==> ((b (^x.(^y.y)))((b (^z.(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2))))) 9. ==[ beta ]==> ((b (^x.(^y.y)))((b (^z.(^x1.x1)))(b (^z1.(^x2.x2))))) 10. ==[ alpha ]==> ((b (^x.(^y.y)))((b (^z.(^x1.x1)))(b (^y1.(^z1.z1))))) REDUCED to normal form. ------ 188240/22055910. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188241/22056036. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188242/22056801. ------ 1. ==[ start ]==> ((^a.(^a.b))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 188243/22056981. ------ 1. ==[ start ]==> ((^a.(a b))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(^x1.(^y1.y1))) b) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 188244/22057263. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^x.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 188245/22057368. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(((^z.z)(^x1.(x1 x1)))((^z.z)(^x1.(x1 x1))))) 4. ==[ alpha ]==> (^x.(((^y.y)(^z.(z z)))((^x1.x1)(^y1.(y1 y1))))) 5. ==[ beta ]==> (^x.((^z.(z z))((^x1.x1)(^y1.(y1 y1))))) 6. ==[ alpha ]==> (^x.((^y.(y y))((^z.z)(^x1.(x1 x1))))) 7. ==[ beta ]==> (^x.(((^z.z)(^x1.(x1 x1)))((^z.z)(^x1.(x1 x1))))) 8. ==[ alpha ]==> (^x.(((^y.y)(^z.(z z)))((^x1.x1)(^y1.(y1 y1))))) IRREDUCIBLE: cycle. ------ 188246/22058250. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((((^z.z)(a a))(^x1.b))(((^z.z)(a a))(^x1.b)))(^y.y)) 4. ==[ alpha ]==> (((((^x.x)(a a))(^y.b))(((^z.z)(a a))(^x1.b)))(^y1.y1)) 5. ==[ beta ]==> ((((a a)(^y.b))(((^z.z)(a a))(^x1.b)))(^y1.y1)) 6. ==[ alpha ]==> ((((a a)(^x.b))(((^y.y)(a a))(^z.b)))(^x1.x1)) 7. ==[ beta ]==> ((((a a)(^x.b))((a a)(^z.b)))(^x1.x1)) 8. ==[ alpha ]==> ((((a a)(^x.b))((a a)(^y.b)))(^z.z)) REDUCED to normal form. ------ 188247/22059555. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)((a a)(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188248/22059558. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((a a)(a a)))) REDUCED to normal form. ------ 188249/22060242. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^y.b)) REDUCED to normal form. ------ 188250/22060446. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188251/22060575. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^c.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.z))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 188252/22061214. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(a a))(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 188253/22062123. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 188254/22062393. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^b.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^y1.(y1 a))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(y1 a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188255/22063428. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 188256/22064094. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(a a)))) 7. ==[ beta ]==> (^y.(^z.(a a))) 8. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 188257/22064499. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(a z))) 3. ==[ eta ]==> (((^x.(x x))((^y.y) b)) a) 4. ==[ beta ]==> ((((^y.y) b)((^y.y) b)) a) 5. ==[ alpha ]==> ((((^x.x) b)((^y.y) b)) a) 6. ==[ beta ]==> ((b ((^y.y) b)) a) 7. ==[ alpha ]==> ((b ((^x.x) b)) a) 8. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 188258/22064688. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.(^x2.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188259/22064697. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(y1 b))) REDUCED to normal form. ------ 188260/22065243. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((^z.(^x1.x1)) b)(((^z.(^x1.x1)) b)(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.(^x1.x1)) b)(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) b)(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) b)(^x1.x1))) 7. ==[ beta ]==> (((^y.(^z.z)) b)(^x1.x1)) 8. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188261/22065642. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> (b (^x.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 188262/22065768. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188263/22065993. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(z (z z)))) REDUCED to normal form. ------ 188264/22066092. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 188265/22066116. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a)(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188266/22066245. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.x1)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.x1)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.z)) 5. ==[ beta ]==> (((^y.y) b)(^z.z)) 6. ==[ alpha ]==> (((^x.x) b)(^y.y)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188267/22066326. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.c)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.c)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.c)) REDUCED to normal form. ------ 188268/22066434. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.b)) 5. ==[ beta ]==> ((b (^y.y))(^z.b)) 6. ==[ alpha ]==> ((b (^x.x))(^y.b)) REDUCED to normal form. ------ 188269/22066533. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.b)) 3. ==[ beta ]==> ((b (^y.y))(^z.b)) 4. ==[ alpha ]==> ((b (^x.x))(^y.b)) REDUCED to normal form. ------ 188270/22066566. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188271/22066569. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 188272/22066578. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188273/22066608. ------ 1. ==[ start ]==> ((a (^a.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 188274/22066617. ------ 1. ==[ start ]==> (((^a.a) a)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (a (a ((^y.y)(^z.(^x1.x1))))) 4. ==[ alpha ]==> (a (a ((^x.x)(^y.(^z.z))))) 5. ==[ beta ]==> (a (a (^y.(^z.z)))) 6. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 188275/22066626. ------ 1. ==[ start ]==> ((a (a a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 188276/22066644. ------ 1. ==[ start ]==> (((a a) a)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a) a)((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 188277/22066653. ------ 1. ==[ start ]==> ((a b)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a b)((^x.(x (^y.y))) b)) 3. ==[ beta ]==> ((a b)(b (^y.y))) 4. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 188278/22066671. ------ 1. ==[ start ]==> (((a a)(^a.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 188279/22066698. ------ 1. ==[ start ]==> (((^a.a) b)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x) b)((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (b ((b (^y.y))((^z.z) a))) 4. ==[ alpha ]==> (b ((b (^x.x))((^y.y) a))) 5. ==[ beta ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 188280/22066725. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 188281/22066752. ------ 1. ==[ start ]==> (((a a) b)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.x) b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) b)(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a) b)(b (^y.y))) 6. ==[ alpha ]==> (((a a) b)(b (^x.x))) REDUCED to normal form. ------ 188282/22066779. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 188283/22066806. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b a)(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(a b))) REDUCED to normal form. ------ 188284/22066833. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 188285/22066887. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 188286/22066968. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 188287/22066995. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(a (b (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (b (^x.x)))) REDUCED to normal form. ------ 188288/22067022. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.a))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 188289/22067040. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(b (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(b (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 188290/22067049. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)(a (a (^x1.x1))))) REDUCED to normal form. ------ 188291/22067094. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a (^x.(x x)))((a a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 188292/22067112. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a) a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 188293/22067139. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 188294/22067166. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a (a a))(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 188295/22067193. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((a (a (a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 188296/22067202. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 11. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 12. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 13. ==[ beta ]==> ((^y.y)(^z.z)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188297/22067229. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188298/22067310. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 188299/22067337. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 188300/22067391. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 188301/22067418. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 188302/22067490. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 188303/22067517. ------ 1. ==[ start ]==> (((a (a a))(a a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(a a))((a (a (^x.x))) a)) REDUCED to normal form. ------ 188304/22067544. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> ((a (^x.x))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 188305/22067634. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188306/22067949. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((a a)((^y.(y (^z.z))) a)) 6. ==[ alpha ]==> ((a a)((^x.(x (^y.y))) a)) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 188307/22068102. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((b a)((a a) a))) 3. ==[ beta ]==> (((^y.y) b)((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.x) b)((b a)((a a) a))) 5. ==[ beta ]==> (b ((b a)((a a) a))) REDUCED to normal form. ------ 188308/22068129. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a) a)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 188309/22068183. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)((a a)(^x1.x1)))) REDUCED to normal form. ------ 188310/22068210. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((a a) a)(b a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a) a)(b a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a) a)(b a))) REDUCED to normal form. ------ 188311/22068237. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (a a))(^x.a))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (a a))(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 188312/22068264. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (a a))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188313/22068291. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(a ((a a)(a a)))) REDUCED to normal form. ------ 188314/22068309. ------ 1. ==[ start ]==> ((a (^a.b))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 188315/22068381. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.(^z.z)) a)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.(^y.y)) a)(^z.z))) 5. ==[ beta ]==> ((a (a (a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a (a a)))(^y.y)) 8. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 188316/22068408. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) a)((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 188317/22068435. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(a a))(^z.a))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(^z.a))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 188318/22068462. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(a a))(b (^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(b (^x.(x x)))) REDUCED to normal form. ------ 188319/22068489. ------ 1. ==[ start ]==> ((a (a b))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 188320/22068498. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 188321/22068579. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(a a))((^x1.x1)(a a)))) IRREDUCIBLE: cycle. ------ 188322/22068660. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188323/22068687. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((a b)((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> ((a b)((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> ((a b)(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> ((a b)(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> ((a b)(b ((^y.y) b))) 8. ==[ alpha ]==> ((a b)(b ((^x.x) b))) 9. ==[ beta ]==> ((a b)(b b)) REDUCED to normal form. ------ 188324/22068714. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)((a a)(a a))) 6. ==[ alpha ]==> ((^x.a)((a a)(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 188325/22068768. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z)) a)) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y)) a)) 7. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 8. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 188326/22068849. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 188327/22068876. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.(z z))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(y y))) REDUCED to normal form. ------ 188328/22069092. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((^y.(a a))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(^z.z))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 188329/22069119. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(a a))) 6. ==[ alpha ]==> ((^x.a)(^y.(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 188330/22069263. ------ 1. ==[ start ]==> (((a b) b)(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a b) b)(((^x.x) b)((^y.y) a))) 3. ==[ beta ]==> (((a b) b)(b ((^y.y) a))) 4. ==[ alpha ]==> (((a b) b)(b ((^x.x) a))) 5. ==[ beta ]==> (((a b) b)(b a)) REDUCED to normal form. ------ 188331/22069290. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 188332/22069317. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((b a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((b a)(^y.y))) REDUCED to normal form. ------ 188333/22069344. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(^z.z))((a a) a))) REDUCED to normal form. ------ 188334/22069398. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a b)(a a))) REDUCED to normal form. ------ 188335/22069425. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(y y))(((a a) a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.(x x))(((a a) a)((a a)(^y.y)))) 7. ==[ beta ]==> ((((a a) a)((a a)(^y.y)))(((a a) a)((a a)(^y.y)))) 8. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 188336/22069452. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((^z.z)(b a))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(b a))) 5. ==[ beta ]==> ((((a a) a)(^x.a))(b a)) REDUCED to normal form. ------ 188337/22069479. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 188338/22069506. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.x))(a ((^z.z) b))) 6. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) b))) 7. ==[ beta ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 188339/22069596. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((b (^y.y))(^z.z))) 3. ==[ beta ]==> ((a ((a a) a))((b (^y.y))(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 188340/22069623. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 188341/22069650. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) b)(^z.a))) 5. ==[ beta ]==> ((a (a a))(((^y.y) b)(^z.a))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) b)(^y.a))) 7. ==[ beta ]==> ((a (a a))(b (^y.a))) 8. ==[ alpha ]==> ((a (a a))(b (^x.a))) REDUCED to normal form. ------ 188342/22069677. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a) a)((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 188343/22069704. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 188344/22069758. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(^z.b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(^y.b))) REDUCED to normal form. ------ 188345/22069794. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 188346/22069929. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188347/22070037. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 188348/22070172. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 188349/22070406. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.b) c)) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.x) c)) 3. ==[ beta ]==> ((((a a) a)(a (a a))) c) REDUCED to normal form. ------ 188350/22070685. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(b (^z.(a a)))) 3. ==[ beta ]==> (b (b (^z.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 188351/22070793. ------ 1. ==[ start ]==> (((^a.a)(b a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 188352/22070874. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(a b))((^y.(a a))((a a) a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(a a))((a a) a))) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 188353/22070955. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188354/22071063. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 188355/22071081. ------ 1. ==[ start ]==> (((a a)(b a))(((a a)(a a)) a)) REDUCED to normal form. ------ 188356/22071108. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z) b) b)) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(b b)) REDUCED to normal form. ------ 188357/22071360. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188358/22071639. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(a a))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(a a))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 188359/22071666. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (a a))((a a)(^x1.x1)))) REDUCED to normal form. ------ 188360/22071738. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(b (^z.z))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(b (^z.z))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b (^z.z))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (^z.z))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (^y.y))) 7. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 8. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 188361/22071747. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a) b)) REDUCED to normal form. ------ 188362/22071819. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 188363/22071927. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.b)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188364/22071954. ------ 1. ==[ start ]==> ((a (^b.b))((^c.a)(a b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.a)(a b))) 3. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 188365/22071972. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.(a a))) 6. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(a a))) REDUCED to normal form. ------ 188366/22071999. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 188367/22072053. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a (^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a a))((a (^y.y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(a a))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 188368/22072080. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a a)(^z.z))) 3. ==[ beta ]==> (((^y.y)(a b))((a a)(^z.z))) 4. ==[ alpha ]==> (((^x.x)(a b))((a a)(^y.y))) 5. ==[ beta ]==> ((a b)((a a)(^y.y))) 6. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 188369/22072107. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) b) a)) 3. ==[ beta ]==> ((((a a) a)((a a) a))(b a)) REDUCED to normal form. ------ 188370/22072134. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 188371/22072161. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((b a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((b a) c)) 3. ==[ beta ]==> (((a a)(a (a a)))((b a) c)) REDUCED to normal form. ------ 188372/22072278. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.b))) 5. ==[ beta ]==> ((^y.a)(^z.b)) 6. ==[ alpha ]==> ((^x.a)(^y.b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 188373/22072305. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))(^y2.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188374/22072557. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((a b)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a b)(^z.z))) REDUCED to normal form. ------ 188375/22072584. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((a a) a)((a a) a))) 3. ==[ beta ]==> ((b a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 188376/22072611. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a b))) 5. ==[ beta ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 188377/22072638. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (a a))(a a))) REDUCED to normal form. ------ 188378/22072719. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.(a a))((a a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(a (^y.(^z.z))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 188379/22072764. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 188380/22072872. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188381/22072944. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (a a))(^y.(a a)))) 3. ==[ beta ]==> (((a a) b)((a (a a))(^y.(a a)))) 4. ==[ alpha ]==> (((a a) b)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 188382/22073025. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 188383/22073052. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1))) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z))) a)) 7. ==[ beta ]==> ((a a)((a (^y.(^z.z))) a)) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 188384/22073079. ------ 1. ==[ start ]==> ((((a a) a)(a b))((b a) b)) REDUCED to normal form. ------ 188385/22073106. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a)(^x.x)) c)) REDUCED to normal form. ------ 188386/22073583. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((b b)((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> ((b b)((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 188387/22073610. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a a)(b a))) REDUCED to normal form. ------ 188388/22073628. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 188389/22073709. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((b a)(b a))((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 188390/22073790. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (b ((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188391/22073898. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.y1)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188392/22074519. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y) a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 188393/22074627. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188394/22074735. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 188395/22074762. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.a))) 5. ==[ beta ]==> ((^y.b)(^z.a)) 6. ==[ alpha ]==> ((^x.b)(^y.a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 188396/22074816. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 188397/22074897. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188398/22074906. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(b (a a))) REDUCED to normal form. ------ 188399/22074933. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(a ((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^y.b))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.b))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 188400/22075014. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((a a) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(((a a) a) a)) REDUCED to normal form. ------ 188401/22075041. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b (^x.a))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((b (^x.a))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((b (^x.a))(a (a a))) REDUCED to normal form. ------ 188402/22075068. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 188403/22075185. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))(^z.z))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.y))) 7. ==[ beta ]==> ((a b)((a a)(^y.y))) 8. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 188404/22075212. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 188405/22075239. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((a a) a)(^z.a))) 3. ==[ beta ]==> (((^y.y)(b a))(((a a) a)(^z.a))) 4. ==[ alpha ]==> (((^x.x)(b a))(((a a) a)(^y.a))) 5. ==[ beta ]==> ((b a)(((a a) a)(^y.a))) 6. ==[ alpha ]==> ((b a)(((a a) a)(^x.a))) REDUCED to normal form. ------ 188406/22075266. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.(z z))) 6. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(y y))) REDUCED to normal form. ------ 188407/22075293. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 188408/22075320. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> (((a a)(a b))(a (^y.a))) 6. ==[ alpha ]==> (((a a)(a b))(a (^x.a))) REDUCED to normal form. ------ 188409/22075347. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 188410/22075401. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a a) a)) REDUCED to normal form. ------ 188411/22075428. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a b) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a b) b)) 3. ==[ beta ]==> ((b ((^y.y) a))((a b) b)) 4. ==[ alpha ]==> ((b ((^x.x) a))((a b) b)) 5. ==[ beta ]==> ((b a)((a b) b)) REDUCED to normal form. ------ 188412/22075599. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(a a)))) 7. ==[ beta ]==> ((^y.y)(^z.(a a))) 8. ==[ alpha ]==> ((^x.x)(^y.(a a))) 9. ==[ beta ]==> (^y.(a a)) 10. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 188413/22075788. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(b (^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188414/22075923. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(z z))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (a a)))) 7. ==[ beta ]==> ((^y.(y y))(a (a a))) 8. ==[ alpha ]==> ((^x.(x x))(a (a a))) 9. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 188415/22075950. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 188416/22076004. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)(a b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)(a b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.z)(a b))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.z)(a b))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.y)(a b))) 7. ==[ beta ]==> ((b b)((^y.y)(a b))) 8. ==[ alpha ]==> ((b b)((^x.x)(a b))) 9. ==[ beta ]==> ((b b)(a b)) REDUCED to normal form. ------ 188417/22076085. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188418/22076148. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(c (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (^z.z))) REDUCED to normal form. ------ 188419/22076193. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.z1)(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188420/22076202. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (a b))) REDUCED to normal form. ------ 188421/22076229. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((a a) a)(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))(((a a) a)(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((a a) a)(a a))) REDUCED to normal form. ------ 188422/22076256. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.y))) REDUCED to normal form. ------ 188423/22076310. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1) a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (a a)))) 7. ==[ beta ]==> (((^y.y) a)(a (a a))) 8. ==[ alpha ]==> (((^x.x) a)(a (a a))) 9. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 188424/22076400. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((a a) a)(^y.y))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((a a) a)(^x.x))) REDUCED to normal form. ------ 188425/22076427. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a)) b)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a (a a)) b)(^y.(^z.z))) 8. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.y))) REDUCED to normal form. ------ 188426/22076454. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (a a))(^x1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(^x1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.a))) REDUCED to normal form. ------ 188427/22076481. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) a)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(b a))(a (^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.(x x)))) REDUCED to normal form. ------ 188428/22076508. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 188429/22076562. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((a a) a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((a a) a) a)) REDUCED to normal form. ------ 188430/22076742. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 188431/22076751. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 188432/22077147. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (a ((^x.x)(^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 188433/22077174. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (a a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (a a))(a a))) REDUCED to normal form. ------ 188434/22077201. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a (a (^z.z)))) REDUCED to normal form. ------ 188435/22077273. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a (^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 188436/22077354. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188437/22077462. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188438/22077498. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (a (a a)))) REDUCED to normal form. ------ 188439/22077525. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((^y.y) a)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a (a a))) REDUCED to normal form. ------ 188440/22077579. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188441/22077597. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 188442/22077624. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(a a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 188443/22077642. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 188444/22077669. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.a))) REDUCED to normal form. ------ 188445/22077696. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(((^z.z) a) a)) 3. ==[ beta ]==> ((a (b (^y.y)))(((^z.z) a) a)) 4. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a) a)) 5. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 188446/22077723. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a (^x.x)) b)) REDUCED to normal form. ------ 188447/22077750. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a) c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a) c)) 5. ==[ beta ]==> (((^y.y) b)((a a) c)) 6. ==[ alpha ]==> (((^x.x) b)((a a) c)) 7. ==[ beta ]==> (b ((a a) c)) REDUCED to normal form. ------ 188448/22077777. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.a) a)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 188449/22077804. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y)) b)) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 188450/22077858. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 188451/22077912. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a (^z.z)) a)) REDUCED to normal form. ------ 188452/22077939. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a) b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a) b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a) b)) 5. ==[ beta ]==> ((b (^y.y))((a a) b)) 6. ==[ alpha ]==> ((b (^x.x))((a a) b)) REDUCED to normal form. ------ 188453/22077966. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.(^y.y)) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 188454/22078020. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(^z.z))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 188455/22078038. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a b)) 3. ==[ beta ]==> ((b (^y.y))(a b)) 4. ==[ alpha ]==> ((b (^x.x))(a b)) REDUCED to normal form. ------ 188456/22078047. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a a) a)) REDUCED to normal form. ------ 188457/22078074. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.x1) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 188458/22078083. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188459/22078100. ------ 1. ==[ start ]==> (^a.(b (a (a (^a.a))))) 2. ==[ alpha ]==> (^x.(b (x (x (^y.y))))) REDUCED to normal form. ------ 188460/22078101. ------ 1. ==[ start ]==> (a (b (a (a (^a.a))))) 2. ==[ alpha ]==> (a (b (a (a (^x.x))))) REDUCED to normal form. ------ 188461/22078131. ------ 1. ==[ start ]==> ((^a.(a a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.((^z.z)(^x1.(^y1.y1))))(^y.((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188462/22089579. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(y1 y1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188463/22089591. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a)))) c) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1)))) c) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1))) c) 4. ==[ alpha ]==> ((^x.(^y.(^z.z))) c) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188464/22089615. ------ 1. ==[ start ]==> ((^a.a)(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 3. ==[ beta ]==> (b (a (a (^y.y)))) 4. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 188465/22089636. ------ 1. ==[ start ]==> (((^a.a) a)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 188466/22089642. ------ 1. ==[ start ]==> ((^a.(a a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.(^x1.x1))))(a ((^y.y)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a ((^x1.x1)(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a ((^x1.x1)(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z)(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 188467/22089645. ------ 1. ==[ start ]==> ((a (a a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188468/22089669. ------ 1. ==[ start ]==> ((^a.b)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.b)((a (a (^y.y)))(a a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 188469/22089750. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 188470/22089939. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ eta ]==> ((^y.y)(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 188471/22090095. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 188472/22090110. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 188473/22090434. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188474/22090527. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((b b)(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((b b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 188475/22090968. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(y (y (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(y (y (^z.z))))) 6. ==[ alpha ]==> ((a a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 188476/22090992. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((((^y.(^z.z)) a)(a a))(((^y.(^z.z)) a)(a a)))(((^y.(^z.z)) a)(a a))) 4. ==[ alpha ]==> (((((^x.(^y.y)) a)(a a))(((^z.(^x1.x1)) a)(a a)))(((^y1.(^z1.z1)) a)(a a))) 5. ==[ beta ]==> ((((^y.y)(a a))(((^z.(^x1.x1)) a)(a a)))(((^y1.(^z1.z1)) a)(a a))) 6. ==[ alpha ]==> ((((^x.x)(a a))(((^y.(^z.z)) a)(a a)))(((^x1.(^y1.y1)) a)(a a))) 7. ==[ beta ]==> (((a a)(((^y.(^z.z)) a)(a a)))(((^x1.(^y1.y1)) a)(a a))) 8. ==[ alpha ]==> (((a a)(((^x.(^y.y)) a)(a a)))(((^z.(^x1.x1)) a)(a a))) 9. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.(^x1.x1)) a)(a a))) 10. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.(^z.z)) a)(a a))) 11. ==[ beta ]==> (((a a)(a a))(((^y.(^z.z)) a)(a a))) 12. ==[ alpha ]==> (((a a)(a a))(((^x.(^y.y)) a)(a a))) 13. ==[ beta ]==> (((a a)(a a))((^y.y)(a a))) 14. ==[ alpha ]==> (((a a)(a a))((^x.x)(a a))) 15. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 188477/22091796. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 188478/22092588. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(b (^z.z)))) REDUCED to normal form. ------ 188479/22092984. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.(y (^z.z)))) 3. ==[ beta ]==> (((a a) b)(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a a) b)(^x.(x (^y.y)))) REDUCED to normal form. ------ 188480/22093371. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 188481/22093530. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y)(a a))((a a) a))) 3. ==[ eta ]==> (b (((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> (b ((a a)((a a) a))) REDUCED to normal form. ------ 188482/22094793. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(^x1.(z z)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(z z)))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(y y)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 188483/22094970. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188484/22095765. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 188485/22096926. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(x1 a))) REDUCED to normal form. ------ 188486/22097205. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(^y.(b y))) 3. ==[ eta ]==> ((((^x.x)(a a))((a a) a)) b) 4. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 188487/22097364. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (a a))((a a) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188488/22097709. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 188489/22097952. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 188490/22099023. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.b))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.b))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.b))) 7. ==[ beta ]==> ((b b)(^y.(^z.b))) 8. ==[ alpha ]==> ((b b)(^x.(^y.b))) REDUCED to normal form. ------ 188491/22099032. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^b.(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(a y))) 3. ==[ eta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 188492/22099221. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.y1))) REDUCED to normal form. ------ 188493/22099392. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.((a a) a))) REDUCED to normal form. ------ 188494/22099743. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.((z z) z))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.((z z) z))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.((y y) y))) 5. ==[ beta ]==> ((a a)(^y.((y y) y))) 6. ==[ alpha ]==> ((a a)(^x.((x x) x))) REDUCED to normal form. ------ 188495/22099767. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((((^z.z)(^x1.x1))(a a))((((^z.z)(^x1.x1))(a a))(^y.y))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((((^z.z)(^x1.x1))(a a))(^y1.y1))) 5. ==[ beta ]==> (((^y.y)(a a))((((^z.z)(^x1.x1))(a a))(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(a a))((((^y.y)(^z.z))(a a))(^x1.x1))) 7. ==[ beta ]==> ((a a)((((^y.y)(^z.z))(a a))(^x1.x1))) 8. ==[ alpha ]==> ((a a)((((^x.x)(^y.y))(a a))(^z.z))) 9. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.z))) 10. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.y))) 11. ==[ beta ]==> ((a a)((a a)(^y.y))) 12. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 188496/22100166. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188497/22100517. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 188498/22100625. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 188499/22100640. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188500/22100796. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 188501/22100985. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 188502/22101057. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(a a))) 3. ==[ beta ]==> ((b (^y.y))(^z.(a a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(a a))) REDUCED to normal form. ------ 188503/22101066. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.b)) REDUCED to normal form. ------ 188504/22101090. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a (a a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188505/22101093. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(x1 x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 188506/22101102. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188507/22101132. ------ 1. ==[ start ]==> ((a a)(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((a a)(b (a (a (^x.x))))) REDUCED to normal form. ------ 188508/22101150. ------ 1. ==[ start ]==> (((^a.a) a)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a ((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188509/22101159. ------ 1. ==[ start ]==> ((a (a a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(a ((^x.x)(^y.(^z.z))))) 3. ==[ beta ]==> ((a (a a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 188510/22101168. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188511/22101186. ------ 1. ==[ start ]==> ((a b)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a b)((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 188512/22101195. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z))) b)) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y))) b)) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 188513/22101240. ------ 1. ==[ start ]==> (((a a)(a a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a a))((b (^x.x))((^y.y) a))) 3. ==[ beta ]==> (((a a)(a a))((b (^x.x)) a)) REDUCED to normal form. ------ 188514/22101267. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 188515/22101402. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 188516/22101429. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a b)(b a))) REDUCED to normal form. ------ 188517/22101456. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a a)(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a a)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 188518/22101582. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 188519/22101609. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 188520/22101627. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 188521/22101735. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((^y.y) b)(^z.(^x1.x1)))(((^y.y) b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((b (^x.(^y.y)))(b (^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 188522/22101762. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 188523/22101816. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 188524/22101852. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 188525/22101879. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.b)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a)) b) REDUCED to normal form. ------ 188526/22101924. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 188527/22101933. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 188528/22101951. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 188529/22102041. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((b b)((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> ((b b)((^x.x)(a (a (^y.y))))) 5. ==[ beta ]==> ((b b)(a (a (^y.y)))) 6. ==[ alpha ]==> ((b b)(a (a (^x.x)))) REDUCED to normal form. ------ 188530/22102086. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188531/22102113. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 5. ==[ beta ]==> ((b (^y.y)) c) 6. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 188532/22102176. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.y))) REDUCED to normal form. ------ 188533/22102284. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 188534/22102455. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(b (^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 188535/22102482. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(a (a (a (^z.z))))) 3. ==[ beta ]==> (((^y.y)(a a))(a (a (a (^z.z))))) 4. ==[ alpha ]==> (((^x.x)(a a))(a (a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (a (^y.y))))) 6. ==[ alpha ]==> ((a a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 188536/22102509. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> ((a ((a a) a))((^y.y)(a a))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(a a))) 5. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 188537/22102860. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 188538/22102887. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.z))) REDUCED to normal form. ------ 188539/22103013. ------ 1. ==[ start ]==> (((^a.b) a)((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b) a)((^y.y)(a (a a)))) 3. ==[ beta ]==> (b ((^y.y)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 188540/22103031. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 188541/22103112. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a))(^x1.(a a)))) IRREDUCIBLE: cycle. ------ 188542/22103175. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.a)(b a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.a)(b a))) 3. ==[ beta ]==> ((((a a) a) b) a) REDUCED to normal form. ------ 188543/22103193. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188544/22103202. ------ 1. ==[ start ]==> (((a b) a)((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 188545/22103220. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (a a))(^y.y))) 3. ==[ beta ]==> ((a b)((a (a a))(^y.y))) 4. ==[ alpha ]==> ((a b)((a (a a))(^x.x))) REDUCED to normal form. ------ 188546/22103229. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.b))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.b))(b ((^z.z) b))) 6. ==[ alpha ]==> (((a a)(^x.b))(b ((^y.y) b))) 7. ==[ beta ]==> (((a a)(^x.b))(b b)) REDUCED to normal form. ------ 188547/22103283. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 188548/22103310. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 188549/22103382. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(a a))(((a a)(a a)) c)) 3. ==[ beta ]==> (b (((a a)(a a)) c)) REDUCED to normal form. ------ 188550/22103391. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 188551/22103580. ------ 1. ==[ start ]==> (((^a.b) b)((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.a)(^z.a))) 3. ==[ beta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 188552/22103787. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a)) c)) 3. ==[ beta ]==> (b ((^x1.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 188553/22104075. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 188554/22104102. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a a)(b (^y.y)))) REDUCED to normal form. ------ 188555/22104228. ------ 1. ==[ start ]==> (((^a.b) c)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 188556/22104327. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(a a))) 6. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 188557/22104462. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 188558/22104471. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 188559/22104498. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a a) b)((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (((a a) b)(b (^y.y))) 6. ==[ alpha ]==> (((a a) b)(b (^x.x))) REDUCED to normal form. ------ 188560/22104543. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a)) b)) REDUCED to normal form. ------ 188561/22104570. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1) b) c)) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b) c)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) c)) 5. ==[ beta ]==> (((^y.y) b) c) 6. ==[ alpha ]==> (((^x.x) b) c) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 188562/22104579. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.a)) REDUCED to normal form. ------ 188563/22104606. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 188564/22104660. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188565/22104687. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 188566/22104714. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 188567/22104858. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(b ((a a)(a a)))) 3. ==[ beta ]==> ((a (a b))(b ((a a)(a a)))) REDUCED to normal form. ------ 188568/22104885. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(a (b (^x.x)))) REDUCED to normal form. ------ 188569/22104912. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a))(a a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(a a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(a a))) 7. ==[ beta ]==> ((^y.y)(((a a)(a a))(a a))) 8. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a a))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 188570/22104939. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((^x.x) b)(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(b (a (^y.y)))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(b (a (^x.x)))) REDUCED to normal form. ------ 188571/22104966. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a b) a)((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (((a b) a)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 188572/22104993. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((b a)(a (a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((b a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((b a)(a (a a)))) REDUCED to normal form. ------ 188573/22105020. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 188574/22105047. ------ 1. ==[ start ]==> ((a (b a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((a (b a))(((^x.x)(a a))((a a) a))) 3. ==[ beta ]==> ((a (b a))((a a)((a a) a))) REDUCED to normal form. ------ 188575/22105281. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 188576/22105326. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 188577/22105353. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((b a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(y y)))) 5. ==[ beta ]==> ((b a)(^y.(y y))) 6. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 188578/22105389. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 188579/22105407. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (((a b)(a b))((a a)(^y.a))) 6. ==[ alpha ]==> (((a b)(a b))((a a)(^x.a))) REDUCED to normal form. ------ 188580/22105416. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 188581/22105470. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 188582/22105488. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 188583/22105497. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 188584/22105524. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(y y))(b a))) 5. ==[ beta ]==> (((a a)(^x.a))((b a)(b a))) REDUCED to normal form. ------ 188585/22105551. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 188586/22105974. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(a a)) a)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(a a)) a)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a)) a)) 5. ==[ beta ]==> ((a a)((^z.(a a)) a)) 6. ==[ alpha ]==> ((a a)((^x.(a a)) a)) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 188587/22106280. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(b (^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(b (^y.y))) REDUCED to normal form. ------ 188588/22106307. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(a (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(a (^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(a (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(a (^z.(a a)))) 5. ==[ beta ]==> ((^y.b)(a (^z.(a a)))) 6. ==[ alpha ]==> ((^x.b)(a (^y.(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 188589/22106352. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 188590/22106361. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 188591/22106415. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 188592/22106460. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a b)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188593/22106469. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.b)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 188594/22106487. ------ 1. ==[ start ]==> ((a (^b.b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.b))) REDUCED to normal form. ------ 188595/22106766. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188596/22106973. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z) a)) 3. ==[ beta ]==> (b ((^z.z) a)) 4. ==[ alpha ]==> (b ((^x.x) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 188597/22107252. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(a a))(b (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(a a))(b (^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 188598/22107279. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(a (^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(a (^y.y))) REDUCED to normal form. ------ 188599/22107297. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a (^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 188600/22107306. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 188601/22107405. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188602/22107414. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 188603/22107441. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.a)((a a) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)((a a) a))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 188604/22108116. ------ 1. ==[ start ]==> ((((^a.a) b) b)(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(c (^y.(^z.z)))) 3. ==[ beta ]==> ((b b)(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((b b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 188605/22108188. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((b a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.y))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 188606/22108242. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (((b a)(b a))((a a)(^y.a))) 6. ==[ alpha ]==> (((b a)(b a))((a a)(^x.a))) REDUCED to normal form. ------ 188607/22108305. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) a) REDUCED to normal form. ------ 188608/22108323. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (b ((^y.y)(^z.a))) 6. ==[ alpha ]==> (b ((^x.x)(^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 188609/22108332. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 188610/22108386. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 188611/22108440. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(b a)) REDUCED to normal form. ------ 188612/22108692. ------ 1. ==[ start ]==> (((a b)(a b))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 188613/22108719. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(a (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(a (b a))) 3. ==[ beta ]==> (((a a)((a a) a))(a (b a))) REDUCED to normal form. ------ 188614/22108746. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 188615/22108800. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a b)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b) a)) REDUCED to normal form. ------ 188616/22108827. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 188617/22108854. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))(a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 188618/22108881. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a (a a))((a a) a))) REDUCED to normal form. ------ 188619/22109052. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a b)(^z.a))) 3. ==[ beta ]==> (b ((a b)(^z.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 188620/22109160. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1) a)(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188621/22109196. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 188622/22109223. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((a a)(^x.x))) REDUCED to normal form. ------ 188623/22109268. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((b (^x.x))((a a) b)) REDUCED to normal form. ------ 188624/22109295. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a b) c)) 3. ==[ beta ]==> ((^y.y)((a b) c)) 4. ==[ alpha ]==> ((^x.x)((a b) c)) 5. ==[ beta ]==> ((a b) c) REDUCED to normal form. ------ 188625/22109331. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 188626/22109358. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 188627/22109439. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 188628/22109466. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 188629/22109538. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188630/22109664. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (^y.y))(a b))) REDUCED to normal form. ------ 188631/22109691. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 188632/22110213. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a) c)) 3. ==[ beta ]==> (b ((^x1.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 188633/22110438. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (a ((^y.(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((^z.z) a))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 188634/22110456. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a (a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a (a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(y y)))) 7. ==[ beta ]==> ((a (a a))(^y.(y y))) 8. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 188635/22110483. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 188636/22110537. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)(^z.b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)(^z.b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)(^z.b))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)(^z.b))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)(^y.b))) 7. ==[ beta ]==> ((b b)((a a)(^y.b))) 8. ==[ alpha ]==> ((b b)((a a)(^x.b))) REDUCED to normal form. ------ 188637/22110546. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(a b))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a b)) REDUCED to normal form. ------ 188638/22110573. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b)(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.b)(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b)(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b)(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188639/22110618. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) c)) 5. ==[ beta ]==> (b ((^y.y) c)) 6. ==[ alpha ]==> (b ((^x.x) c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 188640/22110627. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 188641/22110654. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 188642/22110681. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 188643/22110735. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.b)) REDUCED to normal form. ------ 188644/22110879. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 188645/22110906. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 188646/22111257. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(a ((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))(a ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(a ((a a) a))) 5. ==[ beta ]==> ((a a)(a ((a a) a))) REDUCED to normal form. ------ 188647/22111284. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.z)(a a))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)(a a))) 5. ==[ beta ]==> ((a (a (a (^x.x))))(a a)) REDUCED to normal form. ------ 188648/22111293. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> (((^z.(^x1.x1)) b)(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188649/22111680. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 188650/22111698. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 7. ==[ beta ]==> ((^y.(^z.z)) a) 8. ==[ alpha ]==> ((^x.(^y.y)) a) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188651/22111725. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(z z)) b)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z)) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y)) b)) 5. ==[ beta ]==> ((a (a (^x.x)))(b b)) REDUCED to normal form. ------ 188652/22111752. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a) c)) 3. ==[ beta ]==> ((^y.y)((^y1.a) c)) 4. ==[ alpha ]==> ((^x.x)((^y.a) c)) 5. ==[ beta ]==> ((^y.a) c) 6. ==[ alpha ]==> ((^x.a) c) 7. ==[ beta ]==> a REDUCED to normal form. ------ 188653/22111842. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a a))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a a))) 7. ==[ beta ]==> ((^y.(y y))(a a)) 8. ==[ alpha ]==> ((^x.(x x))(a a)) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 188654/22111869. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 188655/22111887. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y))(^z.a))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 188656/22111950. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 188657/22112031. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 188658/22112112. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b (^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188659/22112139. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.(z z)))) REDUCED to normal form. ------ 188660/22112157. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 188661/22112202. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b c)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b c)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b c)) REDUCED to normal form. ------ 188662/22112283. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b (a (^z.z)))) 5. ==[ beta ]==> (((^y.y) b)(b (a (^z.z)))) 6. ==[ alpha ]==> (((^x.x) b)(b (a (^y.y)))) 7. ==[ beta ]==> (b (b (a (^y.y)))) 8. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 188663/22112310. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a ((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 188664/22112337. ------ 1. ==[ start ]==> (((a b)(b a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(b a))((a (^x.x))(a a))) REDUCED to normal form. ------ 188665/22112364. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 188666/22112472. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b (a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b (a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b (a a))) 5. ==[ beta ]==> ((b (^y.y))(b (a a))) 6. ==[ alpha ]==> ((b (^x.x))(b (a a))) REDUCED to normal form. ------ 188667/22112499. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 188668/22112553. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(b a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(b a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b a)) 5. ==[ beta ]==> ((a (^y.y))(b a)) 6. ==[ alpha ]==> ((a (^x.x))(b a)) REDUCED to normal form. ------ 188669/22112571. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z)(a a))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(a a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(a a))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 188670/22112580. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a b)) REDUCED to normal form. ------ 188671/22112607. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a (a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 188672/22112616. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188673/22112642. ------ 1. ==[ start ]==> (^a.((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^x.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188674/22112643. ------ 1. ==[ start ]==> (a ((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (a (^y.y)) 4. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 188675/22112673. ------ 1. ==[ start ]==> ((^a.(a a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188676/22124121. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188677/22124160. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a)))) a) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1)))) a) 3. ==[ beta ]==> ((^y.y) a) 4. ==[ alpha ]==> ((^x.x) a) 5. ==[ beta ]==> a REDUCED to normal form. ------ 188678/22124166. ------ 1. ==[ start ]==> ((^a.a)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188679/22124175. ------ 1. ==[ start ]==> ((^a.(^a.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (a (a (^z.z))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188680/22124193. ------ 1. ==[ start ]==> ((^a.(a a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188681/22124196. ------ 1. ==[ start ]==> ((a (a a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 188682/22124205. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188683/22124256. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188684/22124418. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (^x.(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (^x.(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 188685/22125078. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((b b)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((b b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 188686/22125087. ------ 1. ==[ start ]==> (((a (a a))(a a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 188687/22125111. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188688/22125519. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 188689/22125876. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 188690/22125951. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (a (a a)))(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 188691/22126056. ------ 1. ==[ start ]==> ((^a.(a b))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x b))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a))) b) 4. ==[ alpha ]==> (((^x.x)(a (a a))) b) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 188692/22126650. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2)))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.(^x3.(^y3.y3)))))) 5. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.(^x3.(^y3.y3))))) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3))))) 7. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3))))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 9. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188693/22127535. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188694/22128651. ------ 1. ==[ start ]==> (((a a)(b a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 188695/22129011. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.((z z)(z z)))) 5. ==[ beta ]==> ((a a)(^z.((z z)(z z)))) 6. ==[ alpha ]==> ((a a)(^x.((x x)(x x)))) REDUCED to normal form. ------ 188696/22129677. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.((^y.y) x))) 3. ==[ eta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 188697/22129836. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 188698/22130010. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (b (^z.((^x1.x1) b))) 4. ==[ alpha ]==> (b (^x.((^y.y) b))) 5. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 188699/22130622. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 188700/22130835. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((((^y.(y y))(^z.(a a)))((^y.(y y))(^z.(a a))))(((^y.(y y))(^z.(a a)))((^y.(y y))(^z.(a a))))) 4. ==[ alpha ]==> ((((^x.(x x))(^y.(a a)))((^z.(z z))(^x1.(a a))))(((^y1.(y1 y1))(^z1.(a a)))((^x2.(x2 x2))(^y2.(a a))))) 5. ==[ beta ]==> ((((^y.(a a))(^y.(a a)))((^z.(z z))(^x1.(a a))))(((^y1.(y1 y1))(^z1.(a a)))((^x2.(x2 x2))(^y2.(a a))))) 6. ==[ alpha ]==> ((((^x.(a a))(^y.(a a)))((^z.(z z))(^x1.(a a))))(((^y1.(y1 y1))(^z1.(a a)))((^x2.(x2 x2))(^y2.(a a))))) 7. ==[ beta ]==> (((a a)((^z.(z z))(^x1.(a a))))(((^y1.(y1 y1))(^z1.(a a)))((^x2.(x2 x2))(^y2.(a a))))) 8. ==[ alpha ]==> (((a a)((^x.(x x))(^y.(a a))))(((^z.(z z))(^x1.(a a)))((^y1.(y1 y1))(^z1.(a a))))) 9. ==[ beta ]==> (((a a)((^y.(a a))(^y.(a a))))(((^z.(z z))(^x1.(a a)))((^y1.(y1 y1))(^z1.(a a))))) 10. ==[ alpha ]==> (((a a)((^x.(a a))(^y.(a a))))(((^z.(z z))(^x1.(a a)))((^y1.(y1 y1))(^z1.(a a))))) 11. ==[ beta ]==> (((a a)(a a))(((^z.(z z))(^x1.(a a)))((^y1.(y1 y1))(^z1.(a a))))) 12. ==[ alpha ]==> (((a a)(a a))(((^x.(x x))(^y.(a a)))((^z.(z z))(^x1.(a a))))) 13. ==[ beta ]==> (((a a)(a a))(((^y.(a a))(^y.(a a)))((^z.(z z))(^x1.(a a))))) 14. ==[ alpha ]==> (((a a)(a a))(((^x.(a a))(^y.(a a)))((^z.(z z))(^x1.(a a))))) 15. ==[ beta ]==> (((a a)(a a))((a a)((^z.(z z))(^x1.(a a))))) 16. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(x x))(^y.(a a))))) 17. ==[ beta ]==> (((a a)(a a))((a a)((^y.(a a))(^y.(a a))))) 18. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a))(^y.(a a))))) 19. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 188701/22131477. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^c.(^d.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.a))) REDUCED to normal form. ------ 188702/22132260. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188703/22132755. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188704/22132971. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(a a))) REDUCED to normal form. ------ 188705/22133076. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188706/22133583. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 188707/22133895. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1) a)(a (a a)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 188708/22133970. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.(^z.b))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.b))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.b))) REDUCED to normal form. ------ 188709/22134132. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((a a) a))) REDUCED to normal form. ------ 188710/22134294. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.a))) 5. ==[ beta ]==> ((a a)(^y.(^z.a))) 6. ==[ alpha ]==> ((a a)(^x.(^y.a))) REDUCED to normal form. ------ 188711/22134735. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188712/22135068. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.d)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.d)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.d)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.d)) REDUCED to normal form. ------ 188713/22135266. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.((^z.z) a))) 5. ==[ beta ]==> ((a (b (^x.x)))(^y.a)) REDUCED to normal form. ------ 188714/22135347. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.a))) REDUCED to normal form. ------ 188715/22135428. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(^x1.z))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.y))) REDUCED to normal form. ------ 188716/22135482. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 188717/22135536. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188718/22135590. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 188719/22135608. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 188720/22135617. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(a a))) REDUCED to normal form. ------ 188721/22135641. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188722/22135644. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 188723/22135653. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(y1 y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188724/22135680. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^a.a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> ((^y.y)(^y1.y1)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188725/22135692. ------ 1. ==[ start ]==> ((a a)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.y)) 4. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 188726/22135701. ------ 1. ==[ start ]==> ((a (^a.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(b (a (a (^y.y))))) REDUCED to normal form. ------ 188727/22135719. ------ 1. ==[ start ]==> ((a (a a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188728/22135728. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 188729/22135737. ------ 1. ==[ start ]==> (((a a) a)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 188730/22135755. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(a a))((a (a (^y.y)))(a a))) 3. ==[ beta ]==> ((a a)((a (a (^y.y)))(a a))) 4. ==[ alpha ]==> ((a a)((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 188731/22135764. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 188732/22135782. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 188733/22135836. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188734/22135863. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188735/22135890. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 188736/22135917. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((b a)(a b))) 3. ==[ beta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 188737/22135944. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.a))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 188738/22136025. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.a)(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.a)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 188739/22136052. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2) b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))((^x2.x2) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 188740/22136106. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (a (((^y.y) a)(b (^z.z)))) 6. ==[ alpha ]==> (a (((^x.x) a)(b (^y.y)))) 7. ==[ beta ]==> (a (a (b (^y.y)))) 8. ==[ alpha ]==> (a (a (b (^x.x)))) REDUCED to normal form. ------ 188741/22136133. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 188742/22136205. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a a) a)((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 188743/22136277. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 188744/22136358. ------ 1. ==[ start ]==> ((((^a.a) a) b)((b a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a) b)((b a)(^y.b))) 3. ==[ beta ]==> ((a b)((b a)(^y.b))) 4. ==[ alpha ]==> ((a b)((b a)(^x.b))) REDUCED to normal form. ------ 188745/22136385. ------ 1. ==[ start ]==> (((a (a a)) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 188746/22136466. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 188747/22136493. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 188748/22136529. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 188749/22136556. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) a) a) REDUCED to normal form. ------ 188750/22136583. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 188751/22136601. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((b b)((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> ((b b)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 188752/22136610. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> (((a (a a))(a a))(a (a (^y.y)))) 4. ==[ alpha ]==> (((a (a a))(a a))(a (a (^x.x)))) REDUCED to normal form. ------ 188753/22136637. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))((^x1.x1)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 188754/22136934. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 188755/22137042. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(y (^z.z))))) 7. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 8. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 188756/22137105. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 188757/22137159. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> (a (((^z.z) b)(a (a a)))) 6. ==[ alpha ]==> (a (((^x.x) b)(a (a a)))) 7. ==[ beta ]==> (a (b (a (a a)))) REDUCED to normal form. ------ 188758/22137240. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(^y.y))(a b))) 3. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(a b))) 4. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 188759/22137267. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 7. ==[ beta ]==> ((a a)((^y.y)(a a))) 8. ==[ alpha ]==> ((a a)((^x.x)(a a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 188760/22137321. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((a a) a)(b a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a) a)(b a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a) a)(b a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a) a)(b a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a) a)(b a))) 7. ==[ beta ]==> ((a a)(((a a) a)(b a))) REDUCED to normal form. ------ 188761/22137402. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.b))(a ((a a)(a a)))) REDUCED to normal form. ------ 188762/22137474. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(a (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a (a (a a)))(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a (a (a a)))(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 188763/22137573. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (b (((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> (b (b (^y.(y y)))) 6. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 188764/22137582. ------ 1. ==[ start ]==> ((a (a b))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a (a b))((^x.x)(a (a a)))) 3. ==[ beta ]==> ((a (a b))(a (a a))) REDUCED to normal form. ------ 188765/22137762. ------ 1. ==[ start ]==> (((a b) a)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) a)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b) a)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a b) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188766/22137789. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(^y.y))) REDUCED to normal form. ------ 188767/22137897. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> ((^y.a)(((^z.(^x1.x1)) a) a)) 6. ==[ alpha ]==> ((^x.a)(((^y.(^z.z)) a) a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 188768/22137924. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b (^z.z)) b)) REDUCED to normal form. ------ 188769/22137951. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(a a)) c)) REDUCED to normal form. ------ 188770/22137987. ------ 1. ==[ start ]==> (((a a)(a b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(y y))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(x x))) REDUCED to normal form. ------ 188771/22138014. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(^z.z))) REDUCED to normal form. ------ 188772/22138095. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> (a ((^y.(a a))(^z.(a a)))) 8. ==[ alpha ]==> (a ((^x.(a a))(^y.(a a)))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 188773/22138122. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x))) b) REDUCED to normal form. ------ 188774/22138149. ------ 1. ==[ start ]==> (((a b)(a a))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.a))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 188775/22138176. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 188776/22138266. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(b (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (b (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(b (b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(b (b (^y.y)))) 7. ==[ beta ]==> (b (b (^y.y))) 8. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 188777/22138347. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 188778/22138356. ------ 1. ==[ start ]==> (((a b) b)((^c.(a a)) c)) 2. ==[ alpha ]==> (((a b) b)((^x.(a a)) c)) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 188779/22138401. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(a (a a)))) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 188780/22138428. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 188781/22138482. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1)(a a))(a b))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1)(a a))(a b))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(a a))(a b))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(a a))(a b))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(a b))) 9. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(a b))) 10. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a b))) 11. ==[ beta ]==> (((^y.y)(a a))(a b)) 12. ==[ alpha ]==> (((^x.x)(a a))(a b)) 13. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 188782/22138563. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (b ((^y.y)(b a))) 6. ==[ alpha ]==> (b ((^x.x)(b a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 188783/22138770. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a) a)((^y.y) a)) 6. ==[ alpha ]==> ((((a a) a) a)((^x.x) a)) 7. ==[ beta ]==> ((((a a) a) a) a) REDUCED to normal form. ------ 188784/22138788. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 188785/22138797. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 188786/22139031. ------ 1. ==[ start ]==> (((a b) c)((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 188787/22139085. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((b (^y.y)) a)) REDUCED to normal form. ------ 188788/22139139. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z) b) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(b c)) REDUCED to normal form. ------ 188789/22139364. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 188790/22139391. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 188791/22139418. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 188792/22139697. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (b (((^z.z)(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> (b ((^y.y)((a a)(^z.z)))) 8. ==[ alpha ]==> (b ((^x.x)((a a)(^y.y)))) 9. ==[ beta ]==> (b ((a a)(^y.y))) 10. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 188793/22139778. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (b ((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 188794/22139841. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 188795/22139949. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 188796/22139976. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a a)(^z.a))) 4. ==[ alpha ]==> (((a (a a))(^x.b))((a a)(^y.a))) REDUCED to normal form. ------ 188797/22140030. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a) a)(^z.(a a)))) REDUCED to normal form. ------ 188798/22140057. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 188799/22140111. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 188800/22140174. ------ 1. ==[ start ]==> (((a a)(b a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(b a))((a a)(a a))) REDUCED to normal form. ------ 188801/22140228. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 188802/22140255. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 188803/22140336. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 188804/22140363. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.b)(^x1.b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.b)(^z.b))) 5. ==[ beta ]==> (((a a) a)((^y.b)(^z.b))) 6. ==[ alpha ]==> (((a a) a)((^x.b)(^y.b))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 188805/22140534. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(a ((a a)(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(a ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(a ((a a)(a a)))) 5. ==[ beta ]==> ((a a)(a ((a a)(a a)))) REDUCED to normal form. ------ 188806/22140615. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b a)((^x1.x1) a))) 3. ==[ beta ]==> (b ((b a)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((b a)((^x.x) a))) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 188807/22140723. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((a a) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188808/22140750. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1)(a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a a))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 188809/22140777. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a))((a a)(^y.y))) 6. ==[ alpha ]==> ((a (a a))((a a)(^x.x))) REDUCED to normal form. ------ 188810/22140831. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a)(a a))((a (^y.y))(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 188811/22140921. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 188812/22140948. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((b a)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((b a)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((b a)(^y.a))) REDUCED to normal form. ------ 188813/22140975. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 188814/22141029. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a b)(^x1.a))) REDUCED to normal form. ------ 188815/22141092. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 188816/22141119. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(((a a)(^z.z))((a a)(^z.z)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 188817/22141146. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.a)(b a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.a)(b a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.a)(b a))) 5. ==[ beta ]==> (((a (a a))(a a)) a) REDUCED to normal form. ------ 188818/22141173. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 188819/22141200. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y) b)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x) b)) 5. ==[ beta ]==> ((((a a) a)((a a) a)) b) REDUCED to normal form. ------ 188820/22141227. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 188821/22141254. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 188822/22141335. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a a)) REDUCED to normal form. ------ 188823/22141362. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.b)(^z.a))) 3. ==[ beta ]==> ((a b)((^y.b)(^z.a))) 4. ==[ alpha ]==> ((a b)((^x.b)(^y.a))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 188824/22141533. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(a ((^z.z) b))) 3. ==[ beta ]==> (b (a ((^z.z) b))) 4. ==[ alpha ]==> (b (a ((^x.x) b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 188825/22141641. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188826/22141695. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((^y.y) b)(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x) b)(((a a) a)((a a) a))) 5. ==[ beta ]==> (b (((a a) a)((a a) a))) REDUCED to normal form. ------ 188827/22141722. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(a b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a b)) 7. ==[ beta ]==> ((^y.y)(a b)) 8. ==[ alpha ]==> ((^x.x)(a b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 188828/22141776. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a ((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 188829/22141866. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 188830/22141893. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 188831/22141920. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 188832/22141974. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 188833/22142001. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((b (^y.y))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 188834/22142037. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(a b))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 188835/22142064. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(((^y1.y1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 188836/22142091. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (b a))((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (b a))((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 188837/22142118. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 188838/22142145. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)((^y.y)(a (^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((^x.x)(a (^y.(^z.z))))) 9. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 10. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 188839/22142172. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 188840/22142253. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 188841/22142334. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 188842/22142361. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(a a))(^y.(a a)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 188843/22142397. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(c ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(c ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(c ((a a)(^y.y)))) 5. ==[ beta ]==> (c ((a a)(^y.y))) 6. ==[ alpha ]==> (c ((a a)(^x.x))) REDUCED to normal form. ------ 188844/22142532. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (b (((^z.z)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> (b ((a a)((^y.y) a))) 6. ==[ alpha ]==> (b ((a a)((^x.x) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 188845/22142640. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a (a a))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188846/22142721. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a a)(b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a a)(b a))) 3. ==[ beta ]==> (((a a)(a a))((a a)(b a))) REDUCED to normal form. ------ 188847/22142757. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)(^z.z))) REDUCED to normal form. ------ 188848/22142784. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 188849/22142865. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 188850/22142892. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.b))(^z.a)) 6. ==[ alpha ]==> (((a b)(^x.b))(^y.a)) REDUCED to normal form. ------ 188851/22142946. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.(a a)))) REDUCED to normal form. ------ 188852/22143027. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((b a) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((b a) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((b a) a)) REDUCED to normal form. ------ 188853/22143054. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 188854/22143090. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 188855/22143117. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)(^z.(z z)))) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 188856/22143171. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 188857/22143198. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(^x1.b))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.b))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.b)(^z.b))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.b))) 9. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 188858/22143225. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 188859/22143252. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 188860/22143531. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a a)((a a)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)((a a)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)((a a)(^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188861/22143756. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((b c)((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((b c)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 188862/22143783. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 188863/22143990. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(c (a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(c (a b))) 3. ==[ beta ]==> (b (c (a b))) REDUCED to normal form. ------ 188864/22144098. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a b)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188865/22144107. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.b) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 188866/22144134. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a) d)) 3. ==[ beta ]==> ((b (^y.a))((^z.a) d)) 4. ==[ alpha ]==> ((b (^x.a))((^y.a) d)) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 188867/22144224. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(c (^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(c (^y.b))) REDUCED to normal form. ------ 188868/22144251. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b (^y.(a a)))) REDUCED to normal form. ------ 188869/22144278. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(a (^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 188870/22144305. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(a a))(a a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 188871/22144332. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((b a)((^y.b)(a (^z.z)))) 6. ==[ alpha ]==> ((b a)((^x.b)(a (^y.y)))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 188872/22144386. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 188873/22144413. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a b))((^y.(y y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a b))(((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a b))((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a b))((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> (((a a)(a b))((^y.y)(^z.z))) 10. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.y))) 11. ==[ beta ]==> (((a a)(a b))(^y.y)) 12. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 188874/22144440. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.a)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 188875/22144494. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(a a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a a)) REDUCED to normal form. ------ 188876/22144521. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((b a)((^y.(a a))(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.(a a))(^y.y))) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 188877/22144548. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 188878/22144602. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 188879/22144692. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(b (a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b (a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (a b))) 5. ==[ beta ]==> ((^y.y)(b (a b))) 6. ==[ alpha ]==> ((^x.x)(b (a b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 188880/22144773. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(a (^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 188881/22144881. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.z1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188882/22144998. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(^x1.a))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.a))) 7. ==[ beta ]==> (a ((^y.y)(^z.a))) 8. ==[ alpha ]==> (a ((^x.x)(^y.a))) 9. ==[ beta ]==> (a (^y.a)) 10. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 188883/22145106. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 188884/22145133. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a b) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a b) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a b) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188885/22145187. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1) c)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) c)) 5. ==[ beta ]==> (((a b)(^x.(^y.y))) c) REDUCED to normal form. ------ 188886/22145286. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(b ((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188887/22145322. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.b) a)) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.b) a)) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.b) a)) 5. ==[ beta ]==> ((b (^x.(x x))) b) REDUCED to normal form. ------ 188888/22145349. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^c.a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 188889/22145421. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a (a (a a)))) REDUCED to normal form. ------ 188890/22145466. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b (^z.a))) REDUCED to normal form. ------ 188891/22145493. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(a (^y.b))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a (^y.b))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(a (^x.b))) REDUCED to normal form. ------ 188892/22145520. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^c.a)(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)(a a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)(a a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)(a a))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 188893/22145547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 188894/22145574. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(b a))(((^y.y) a)((^y.y) a))) 4. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(b a))(a ((^y.y) a))) 6. ==[ alpha ]==> ((((a a) a)(b a))(a ((^x.x) a))) 7. ==[ beta ]==> ((((a a) a)(b a))(a a)) REDUCED to normal form. ------ 188895/22145601. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 188896/22145628. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 188897/22145655. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((a a) a)) REDUCED to normal form. ------ 188898/22145709. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 188899/22145736. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y))(^z.a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x))(^y.a))) 5. ==[ beta ]==> ((b (a (a a)))((^y.a)(^y.a))) 6. ==[ alpha ]==> ((b (a (a a)))((^x.a)(^y.a))) 7. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 188900/22145763. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(^y.(y y)))) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 188901/22145853. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1)(^y1.y1))(a a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> ((((^z.z)(^x1.x1))(a a))(^y.y)) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.z)) 7. ==[ beta ]==> (((^y.y)(a a))(^z.z)) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.y)) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 188902/22146258. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> (a ((^y.y)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 188903/22146267. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 188904/22146285. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (a a))(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a a))(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))(a a))) REDUCED to normal form. ------ 188905/22146294. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(z z)) b)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(b b)) REDUCED to normal form. ------ 188906/22146312. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1) a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(a (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(a (^y.y))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 188907/22146366. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(a (a a)))) REDUCED to normal form. ------ 188908/22146402. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.z))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.z))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 188909/22146429. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 188910/22146447. ------ 1. ==[ start ]==> (((^a.b)(b a))(c c)) 2. ==[ alpha ]==> (((^x.b)(b a))(c c)) 3. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 188911/22146510. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (a a)) a)) REDUCED to normal form. ------ 188912/22146618. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(y y)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 188913/22146690. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 188914/22146735. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.a)(a a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 188915/22146762. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 188916/22146789. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a (b (^x.x)))((^z.z) a)) 6. ==[ alpha ]==> ((a (b (^x.x)))((^y.y) a)) 7. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 188917/22146816. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.a)(^y.y))) 3. ==[ beta ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 188918/22146843. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 188919/22146870. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.a)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.a)) REDUCED to normal form. ------ 188920/22146897. ------ 1. ==[ start ]==> (((a b)(b a))(c (^a.a))) 2. ==[ alpha ]==> (((a b)(b a))(c (^x.x))) REDUCED to normal form. ------ 188921/22146924. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 188922/22146951. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a (^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.a))) REDUCED to normal form. ------ 188923/22147005. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (^z.z))) REDUCED to normal form. ------ 188924/22147032. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 188925/22147059. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 188926/22147113. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 188927/22147131. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a)(^z.z))) 3. ==[ beta ]==> ((b (^y.y))((a a)(^z.z))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 188928/22147140. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y)(a a))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(a a)) REDUCED to normal form. ------ 188929/22147167. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 188930/22147176. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188931/22147203. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(a a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(a a)) 3. ==[ beta ]==> ((^y.y)(a a)) 4. ==[ alpha ]==> ((^x.x)(a a)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 188932/22147710. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 188933/22158240. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188934/22158729. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a)))) b) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1)))) b) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 188935/22158753. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188936/22158783. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 188937/22158792. ------ 1. ==[ start ]==> (((a a) a)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 188938/22158798. ------ 1. ==[ start ]==> ((^a.b)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 188939/22159239. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 188940/22159242. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 188941/22159338. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a))(^y.(y y)))((((a a)(a a))(^y.(y y)))(((a a)(a a))(^y.(y y))))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((((a a)(a a))(^y.(y y)))(((a a)(a a))(^z.(z z))))) REDUCED to normal form. ------ 188942/22159563. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188943/22159689. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188944/22160121. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((((^y.(y (^z.z))) a)((^y.(y (^z.z))) a))((^y.(y (^z.z))) a)) 4. ==[ alpha ]==> ((((^x.(x (^y.y))) a)((^z.(z (^x1.x1))) a))((^y1.(y1 (^z1.z1))) a)) 5. ==[ beta ]==> (((a (^y.y))((^z.(z (^x1.x1))) a))((^y1.(y1 (^z1.z1))) a)) 6. ==[ alpha ]==> (((a (^x.x))((^y.(y (^z.z))) a))((^x1.(x1 (^y1.y1))) a)) 7. ==[ beta ]==> (((a (^x.x))(a (^z.z)))((^x1.(x1 (^y1.y1))) a)) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z (^x1.x1))) a)) 9. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1))) 10. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 188945/22160634. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((((^y.y) b)(^z.(z z))) b) 4. ==[ alpha ]==> ((((^x.x) b)(^y.(y y))) b) 5. ==[ beta ]==> ((b (^y.(y y))) b) 6. ==[ alpha ]==> ((b (^x.(x x))) b) REDUCED to normal form. ------ 188946/22161021. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (^y.(((^z.(a a))(^x1.a))((^z.(a a))(^x1.a)))) 4. ==[ alpha ]==> (^x.(((^y.(a a))(^z.a))((^x1.(a a))(^y1.a)))) 5. ==[ beta ]==> (^x.((a a)((^x1.(a a))(^y1.a)))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a))(^z.a)))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 188947/22163208. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2) b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188948/22163229. ------ 1. ==[ start ]==> (((a a)(b a))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 188949/22163589. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(^x1.(a a)))) 5. ==[ beta ]==> ((a a)(^z.(^x1.(a a)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 188950/22163922. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.((^x1.x1) b))) 5. ==[ beta ]==> ((^y.b)(^z.((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.b)(^y.((^z.z) b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 188951/22164099. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188952/22164588. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.x1))) 3. ==[ beta ]==> (b (^z.(^x1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 188953/22164894. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 188954/22164912. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(^z.z))) 3. ==[ beta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 188955/22165803. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 188956/22168377. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(z b))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(z b))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(y b))) REDUCED to normal form. ------ 188957/22168710. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.a))) REDUCED to normal form. ------ 188958/22168890. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.((z z) z))) 3. ==[ beta ]==> ((a (^y.y))(^z.((z z) z))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((y y) y))) REDUCED to normal form. ------ 188959/22169313. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188960/22169322. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.z))) REDUCED to normal form. ------ 188961/22169673. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(y (y y)))) REDUCED to normal form. ------ 188962/22169769. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188963/22169772. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(y1 y1)))) REDUCED to normal form. ------ 188964/22169844. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.a))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 188965/22170006. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.c)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.c)) REDUCED to normal form. ------ 188966/22170168. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.x1)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.x1)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.z)) 5. ==[ beta ]==> ((a (^y.y))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 188967/22170219. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a a) a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188968/22170231. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188969/22170258. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 188970/22170288. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 188971/22170297. ------ 1. ==[ start ]==> (((^a.a) a)(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(b (a (a (^y.y))))) 3. ==[ beta ]==> (a (b (a (a (^y.y))))) 4. ==[ alpha ]==> (a (b (a (a (^x.x))))) REDUCED to normal form. ------ 188972/22170315. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 188973/22170324. ------ 1. ==[ start ]==> (((a a) a)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(a ((^x.x)(^y.(^z.z))))) 3. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 188974/22170333. ------ 1. ==[ start ]==> ((a b)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 188975/22170351. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 188976/22170378. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (b (((^y.(^z.z)) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a)(a (^z.z)))) 5. ==[ beta ]==> (b ((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 188977/22170405. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 188978/22170432. ------ 1. ==[ start ]==> (((a a) b)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 188979/22170459. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) a)(b (^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.y))) REDUCED to normal form. ------ 188980/22170486. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))((a a) a))) REDUCED to normal form. ------ 188981/22170513. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((b a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)(a b))) REDUCED to normal form. ------ 188982/22170567. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 188983/22170648. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z) b)) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y) b)) 7. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 188984/22170675. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 188985/22170702. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.a))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.a))(a (b (^y.y)))) REDUCED to normal form. ------ 188986/22170729. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 188987/22170756. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((a (^y.y))((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 188988/22170774. ------ 1. ==[ start ]==> ((a (^a.(a a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 188989/22170792. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a a) a)((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> (((a a) a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 188990/22170819. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 188991/22170846. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((a (a a))((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((a (a a))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 188992/22170873. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 188993/22170909. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188994/22171017. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 188995/22171098. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 188996/22171197. ------ 1. ==[ start ]==> (((a (a a))(a a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 188997/22171224. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a (^z.z))) a)) 3. ==[ beta ]==> ((a (^y.y))((a (a (^z.z))) a)) 4. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y))) a)) REDUCED to normal form. ------ 188998/22171233. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 188999/22171449. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 189000/22171656. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(x (^y.y))) a)) 3. ==[ beta ]==> ((a ((a a) a))(a (^y.y))) 4. ==[ alpha ]==> ((a ((a a) a))(a (^x.x))) REDUCED to normal form. ------ 189001/22171782. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (b ((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (b ((a (^x.(^y.y)))(^x1.x1))) 8. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 189002/22171809. ------ 1. ==[ start ]==> ((((a a) a) a)((b a)((a a) a))) REDUCED to normal form. ------ 189003/22171863. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)(a a))) REDUCED to normal form. ------ 189004/22171890. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 189005/22171917. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((a a) a)(b a))) REDUCED to normal form. ------ 189006/22171944. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189007/22171971. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((a (a a)) b)) REDUCED to normal form. ------ 189008/22172088. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.(^z.z)) a)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.(^y.y)) a)(^z.z))) 5. ==[ beta ]==> (((a (a a)) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a (a a)) a)(^y.y)) 8. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 189009/22172115. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((b (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 189010/22172142. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 189011/22172169. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> ((a (a b))(b (^y.(y y)))) 4. ==[ alpha ]==> ((a (a b))(b (^x.(x x)))) REDUCED to normal form. ------ 189012/22172178. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((^y.b)((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((^x.b)((^y.y)(a (a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 189013/22172340. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.a)(b a))) 3. ==[ beta ]==> (b ((^z.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189014/22172367. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 189015/22172394. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((^y.(y y))((^z.z) b)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) b)) 7. ==[ beta ]==> (((^y.y) b)((^y.y) b)) 8. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 9. ==[ beta ]==> (b ((^y.y) b)) 10. ==[ alpha ]==> (b ((^x.x) b)) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189016/22172448. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 189017/22172556. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 189018/22172772. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189019/22172799. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((^y.(y y))(^z.z)) 6. ==[ alpha ]==> ((^x.(x x))(^y.y)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189020/22172943. ------ 1. ==[ start ]==> (((a b) b)(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 189021/22172970. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a a) a)(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (((a a) a)(b ((^y.y) a))) 6. ==[ alpha ]==> (((a a) a)(b ((^x.x) a))) 7. ==[ beta ]==> (((a a) a)(b a)) REDUCED to normal form. ------ 189022/22172997. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 189023/22173024. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((b a)(^z.z))) REDUCED to normal form. ------ 189024/22173078. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 189025/22173105. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a b)((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((a b)((^y.y)(a a)))) 7. ==[ beta ]==> (((a b)((^y.y)(a a)))((a b)((^y.y)(a a)))) 8. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b)((^y.y)(a a)))) 9. ==[ beta ]==> (((a b)(a a))((a b)((^y.y)(a a)))) 10. ==[ alpha ]==> (((a b)(a a))((a b)((^x.x)(a a)))) 11. ==[ beta ]==> (((a b)(a a))((a b)(a a))) REDUCED to normal form. ------ 189026/22173132. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 189027/22173159. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(b a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(b a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 189028/22173186. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 189029/22173303. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^y.y))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 189030/22173330. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(((a a)(a a))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 189031/22173357. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y) b)(^z.a))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x) b)(^y.a))) 5. ==[ beta ]==> ((((a a) a) a)(b (^y.a))) 6. ==[ alpha ]==> ((((a a) a) a)(b (^x.a))) REDUCED to normal form. ------ 189032/22173384. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 189033/22173411. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 189034/22173474. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(a a))(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a b))) 5. ==[ beta ]==> ((^y.(a a))(a b)) 6. ==[ alpha ]==> ((^x.(a a))(a b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189035/22173609. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189036/22173771. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 189037/22173852. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 189038/22174113. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.b) c)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.y) c)) 3. ==[ beta ]==> (((a b) a)((^y.y) c)) 4. ==[ alpha ]==> (((a b) a)((^x.x) c)) 5. ==[ beta ]==> (((a b) a) c) REDUCED to normal form. ------ 189039/22174365. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(c (^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(c (^z.z))) 3. ==[ beta ]==> (b (c (^z.z))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 189040/22174473. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> ((b a)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((b a)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> ((b a)(a (^y.y))) 6. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 189041/22174500. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189042/22174554. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a b))(^y.y)) 6. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 189043/22174635. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (b ((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189044/22174743. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 189045/22174761. ------ 1. ==[ start ]==> (((a a)(b a))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((a a)(^x.(a a)))) REDUCED to normal form. ------ 189046/22174788. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 189047/22174815. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z) b) b)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z) b) b)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) b) b)) 5. ==[ beta ]==> ((a (a a))(((^y.y) b) b)) 6. ==[ alpha ]==> ((a (a a))(((^x.x) b) b)) 7. ==[ beta ]==> ((a (a a))(b b)) REDUCED to normal form. ------ 189048/22174842. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 189049/22175121. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((a a)((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(a a)))) 7. ==[ beta ]==> ((a a)(^y.(a a))) 8. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 189050/22175319. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a) a)(a b))) REDUCED to normal form. ------ 189051/22175346. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((^y1.y1)((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((^y1.y1)(a a))) 6. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1)(a a))) 7. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 189052/22175427. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 189053/22175454. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a a)((^z.z) b))) 5. ==[ beta ]==> ((^y.b)((a a)((^z.z) b))) 6. ==[ alpha ]==> ((^x.b)((a a)((^y.y) b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 189054/22175499. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.x1)(a a))) 3. ==[ beta ]==> (b ((^x1.x1)(a a))) 4. ==[ alpha ]==> (b ((^x.x)(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 189055/22175607. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189056/22175634. ------ 1. ==[ start ]==> ((a (^b.b))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.b)((a a) a))) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 189057/22175652. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a) a)(^z.b))) REDUCED to normal form. ------ 189058/22175679. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(b a))(^z.(a a))) 6. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(a a))) REDUCED to normal form. ------ 189059/22175760. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a b)((a (^y.y))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a b)((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189060/22175787. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)(^x.x))) REDUCED to normal form. ------ 189061/22175814. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z) b) a)) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z) b) a)) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) b) a)) 5. ==[ beta ]==> (((a b)(^x.x))(b a)) REDUCED to normal form. ------ 189062/22175841. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (^y.(^z.z))) b)) 3. ==[ beta ]==> (((a a)(a (a a)))((a (^y.(^z.z))) b)) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 189063/22175868. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((b a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((b a) c)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((b a) c)) REDUCED to normal form. ------ 189064/22175958. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.a))) 5. ==[ beta ]==> ((^y.b)(^z.a)) 6. ==[ alpha ]==> ((^x.b)(^y.a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 189065/22176120. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.x)(^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 189066/22176237. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((a a)(a (a a)))) REDUCED to normal form. ------ 189067/22176264. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b a)((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b a)((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b a)((a b)(^y.y))) 6. ==[ alpha ]==> ((b a)((a b)(^x.x))) REDUCED to normal form. ------ 189068/22176291. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 189069/22176318. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^z1.z1)(a b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1)(a b))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a b)) REDUCED to normal form. ------ 189070/22176399. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.z))(b a))) 5. ==[ beta ]==> ((^y.(a a))((a (^z.z))(b a))) 6. ==[ alpha ]==> ((^x.(a a))((a (^y.y))(b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189071/22176426. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 189072/22176444. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(a (^b.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(a (^y.y))) 3. ==[ beta ]==> (b (a (^y.y))) 4. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 189073/22176552. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189074/22176624. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a) b)((^y.y)(^z.b))) 6. ==[ alpha ]==> (((a a) b)((^x.x)(^y.b))) 7. ==[ beta ]==> (((a a) b)(^y.b)) 8. ==[ alpha ]==> (((a a) b)(^x.b)) REDUCED to normal form. ------ 189075/22176651. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (a a))(^x1.(a a)))) REDUCED to normal form. ------ 189076/22176678. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (b a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (b a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 189077/22176732. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)((a a)(^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 189078/22176759. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 189079/22176786. ------ 1. ==[ start ]==> (((a b)((a a) a))((b a) b)) REDUCED to normal form. ------ 189080/22176984. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 189081/22177263. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b b)(((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b b)(((^x.x) a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b b)(a ((^y.y)(a a)))) 6. ==[ alpha ]==> ((b b)(a ((^x.x)(a a)))) 7. ==[ beta ]==> ((b b)(a (a a))) REDUCED to normal form. ------ 189082/22177290. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 189083/22177335. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 189084/22177389. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 189085/22177470. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189086/22177578. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189087/22177947. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(a a)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(a a)) c)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a)) c)) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 189088/22178118. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(b (^x2.(^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x2.(^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189089/22178199. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 189090/22178307. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(y1 y1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189091/22178415. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 189092/22178442. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189093/22178577. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)(^x1.b))) 3. ==[ beta ]==> (b ((^z.a)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.a)(^y.b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189094/22178586. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(c (a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(c (a b))) REDUCED to normal form. ------ 189095/22178613. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))(b ((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(b (a a))) REDUCED to normal form. ------ 189096/22178694. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a b)(a (^x1.x1)))) REDUCED to normal form. ------ 189097/22178721. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((b (^y.a))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.a))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((b (^x.a))(((a a) a) a)) REDUCED to normal form. ------ 189098/22178748. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 189099/22178892. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 189100/22178919. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)((a b)(^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 189101/22178946. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((a a) a)(^y.a))) REDUCED to normal form. ------ 189102/22178973. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.(y y)))) 7. ==[ beta ]==> (((a b)(a a))(^y.(y y))) 8. ==[ alpha ]==> (((a b)(a a))(^x.(x x))) REDUCED to normal form. ------ 189103/22179000. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 189104/22179081. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 189105/22179108. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(a a)) a)) 5. ==[ beta ]==> ((b a)(((^y.y)(a a)) a)) 6. ==[ alpha ]==> ((b a)(((^x.x)(a a)) a)) 7. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 189106/22179135. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a b) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a b) b)) REDUCED to normal form. ------ 189107/22179279. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189108/22179468. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c (^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(c (^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(c (^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189109/22179603. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189110/22179630. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (a a)))) 5. ==[ beta ]==> ((^y.(y y))(a (a a))) 6. ==[ alpha ]==> ((^x.(x x))(a (a a))) 7. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 189111/22179684. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))((a a) a))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))((a a) a))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))((a a) a))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 189112/22179765. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189113/22179882. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b ((a a) a))) REDUCED to normal form. ------ 189114/22179909. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a (a b))) 3. ==[ beta ]==> ((b (^y.(y y)))(a (a b))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a (a b))) REDUCED to normal form. ------ 189115/22179936. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((a a) a)(a a))) REDUCED to normal form. ------ 189116/22179990. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) a))) 7. ==[ beta ]==> ((a (a a))((^y.y) a)) 8. ==[ alpha ]==> ((a (a a))((^x.x) a)) 9. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 189117/22180107. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((a a) a)(^y.y))) 3. ==[ beta ]==> (((a (a a)) b)(((a a) a)(^y.y))) 4. ==[ alpha ]==> (((a (a a)) b)(((a a) a)(^x.x))) REDUCED to normal form. ------ 189118/22180134. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 189119/22180161. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (a a))(^x.a))) REDUCED to normal form. ------ 189120/22180188. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 189121/22180215. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((a (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 189122/22180242. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)(^y.a))) REDUCED to normal form. ------ 189123/22180296. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1)(^z1.z1)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(^y1.y1)) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1) b)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1) b)) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 189124/22180323. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (a a)) c)) 3. ==[ beta ]==> ((b (a (a a)))((a (a a)) c)) REDUCED to normal form. ------ 189125/22180422. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a ((a a) a))) 3. ==[ beta ]==> ((a (^y.y))(a ((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))(a ((a a) a))) REDUCED to normal form. ------ 189126/22180827. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b (a (a a)))) 3. ==[ beta ]==> (((^y.y) b)(b (a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)(b (a (a a)))) 5. ==[ beta ]==> (b (b (a (a a)))) REDUCED to normal form. ------ 189127/22180845. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189128/22180854. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a (^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.y))) REDUCED to normal form. ------ 189129/22180881. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (a a))(a a))) REDUCED to normal form. ------ 189130/22180953. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (^y.(y y)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b (^x.(x x)))) REDUCED to normal form. ------ 189131/22181034. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.a)(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189132/22181142. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189133/22181178. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b ((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b ((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 189134/22181205. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (a (a a)))) REDUCED to normal form. ------ 189135/22181259. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189136/22181277. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b (^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b (^z.a))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.a))) REDUCED to normal form. ------ 189137/22181286. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a)((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))((a a) a)) REDUCED to normal form. ------ 189138/22181304. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(x1 x1)))) REDUCED to normal form. ------ 189139/22181322. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (^y.y))) REDUCED to normal form. ------ 189140/22181349. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 189141/22181376. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a)(^z.a))) 3. ==[ beta ]==> ((a (b (^y.y)))((a a)(^z.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 189142/22181403. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(((^x.x) a) a)) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 189143/22181430. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z)) b)) 5. ==[ beta ]==> (((^y.y) b)((a (^z.z)) b)) 6. ==[ alpha ]==> (((^x.x) b)((a (^y.y)) b)) 7. ==[ beta ]==> (b ((a (^y.y)) b)) 8. ==[ alpha ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 189144/22181484. ------ 1. ==[ start ]==> (((a b)(b a))((^b.a) a)) 2. ==[ alpha ]==> (((a b)(b a))((^x.a) a)) 3. ==[ beta ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 189145/22181511. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z)) b)) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 189146/22181592. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 189147/22181619. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a (^x1.x1)) a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a (^x1.x1)) a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a (^z.z)) a)) 5. ==[ beta ]==> ((b (^y.y))((a (^z.z)) a)) 6. ==[ alpha ]==> ((b (^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 189148/22181646. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a a) b)) REDUCED to normal form. ------ 189149/22181700. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((a (^y.y))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 189150/22181718. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(b a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(b a)) 3. ==[ beta ]==> ((b (^y.y))(b a)) 4. ==[ alpha ]==> ((b (^x.x))(b a)) REDUCED to normal form. ------ 189151/22181727. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a a)(^y.y))) REDUCED to normal form. ------ 189152/22181754. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a a) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 189153/22181763. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189154/22181790. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> ((^y.y)(a (^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(a (^y.y))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 189155/22181865. ------ 1. ==[ start ]==> ((^a.b)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 189156/22183188. ------ 1. ==[ start ]==> ((^a.((a a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> (((^y.(y (y (^z.z))))(^y.(y (y (^z.z)))))(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> (((^x.(x (x (^y.y))))(^z.(z (z (^x1.x1)))))(^y1.(y1 (y1 (^z1.z1))))) 5. ==[ beta ]==> (((^z.(z (z (^x1.x1))))((^z.(z (z (^x1.x1))))(^y.y)))(^y1.(y1 (y1 (^z1.z1))))) 6. ==[ alpha ]==> (((^x.(x (x (^y.y))))((^z.(z (z (^x1.x1))))(^y1.y1)))(^z1.(z1 (z1 (^x2.x2))))) 7. ==[ beta ]==> ((((^z.(z (z (^x1.x1))))(^y1.y1))(((^z.(z (z (^x1.x1))))(^y1.y1))(^y.y)))(^z1.(z1 (z1 (^x2.x2))))) 8. ==[ alpha ]==> ((((^x.(x (x (^y.y))))(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(^y2.(y2 (y2 (^z2.z2))))) 9. ==[ beta ]==> ((((^z.z)((^z.z)(^y.y)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(^y2.(y2 (y2 (^z2.z2))))) 10. ==[ alpha ]==> ((((^x.x)((^y.y)(^z.z)))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(^y2.(y2 (y2 (^z2.z2))))) 11. ==[ beta ]==> ((((^y.y)(^z.z))(((^x1.(x1 (x1 (^y1.y1))))(^z1.z1))(^x2.x2)))(^y2.(y2 (y2 (^z2.z2))))) 12. ==[ alpha ]==> ((((^x.x)(^y.y))(((^z.(z (z (^x1.x1))))(^y1.y1))(^z1.z1)))(^x2.(x2 (x2 (^y2.y2))))) 13. ==[ beta ]==> (((^y.y)(((^z.(z (z (^x1.x1))))(^y1.y1))(^z1.z1)))(^x2.(x2 (x2 (^y2.y2))))) 14. ==[ alpha ]==> (((^x.x)(((^y.(y (y (^z.z))))(^x1.x1))(^y1.y1)))(^z1.(z1 (z1 (^x2.x2))))) 15. ==[ beta ]==> ((((^y.(y (y (^z.z))))(^x1.x1))(^y1.y1))(^z1.(z1 (z1 (^x2.x2))))) 16. ==[ alpha ]==> ((((^x.(x (x (^y.y))))(^z.z))(^x1.x1))(^y1.(y1 (y1 (^z1.z1))))) 17. ==[ beta ]==> ((((^z.z)((^z.z)(^y.y)))(^x1.x1))(^y1.(y1 (y1 (^z1.z1))))) 18. ==[ alpha ]==> ((((^x.x)((^y.y)(^z.z)))(^x1.x1))(^y1.(y1 (y1 (^z1.z1))))) 19. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.x1))(^y1.(y1 (y1 (^z1.z1))))) 20. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(x1 (x1 (^y1.y1))))) 21. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 (x1 (^y1.y1))))) 22. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (z (^x1.x1))))) 23. ==[ beta ]==> ((^y.y)(^z.(z (z (^x1.x1))))) 24. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 25. ==[ beta ]==> (^y.(y (y (^z.z)))) 26. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 189157/22191963. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.((a a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.((z z) z))) 3. ==[ beta ]==> ((^z.((z z) z))((^z.((z z) z))(^y.y))) 4. ==[ alpha ]==> ((^x.((x x) x))((^y.((y y) y))(^z.z))) 5. ==[ beta ]==> ((((^y.((y y) y))(^z.z))((^y.((y y) y))(^z.z)))((^y.((y y) y))(^z.z))) 6. ==[ alpha ]==> ((((^x.((x x) x))(^y.y))((^z.((z z) z))(^x1.x1)))((^y1.((y1 y1) y1))(^z1.z1))) 7. ==[ beta ]==> (((((^y.y)(^y.y))(^y.y))((^z.((z z) z))(^x1.x1)))((^y1.((y1 y1) y1))(^z1.z1))) 8. ==[ alpha ]==> (((((^x.x)(^y.y))(^z.z))((^x1.((x1 x1) x1))(^y1.y1)))((^z1.((z1 z1) z1))(^x2.x2))) 9. ==[ beta ]==> ((((^y.y)(^z.z))((^x1.((x1 x1) x1))(^y1.y1)))((^z1.((z1 z1) z1))(^x2.x2))) 10. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.((z z) z))(^x1.x1)))((^y1.((y1 y1) y1))(^z1.z1))) 11. ==[ beta ]==> (((^y.y)((^z.((z z) z))(^x1.x1)))((^y1.((y1 y1) y1))(^z1.z1))) 12. ==[ alpha ]==> (((^x.x)((^y.((y y) y))(^z.z)))((^x1.((x1 x1) x1))(^y1.y1))) 13. ==[ beta ]==> (((^y.((y y) y))(^z.z))((^x1.((x1 x1) x1))(^y1.y1))) 14. ==[ alpha ]==> (((^x.((x x) x))(^y.y))((^z.((z z) z))(^x1.x1))) 15. ==[ beta ]==> ((((^y.y)(^y.y))(^y.y))((^z.((z z) z))(^x1.x1))) 16. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.((x1 x1) x1))(^y1.y1))) 17. ==[ beta ]==> (((^y.y)(^z.z))((^x1.((x1 x1) x1))(^y1.y1))) 18. ==[ alpha ]==> (((^x.x)(^y.y))((^z.((z z) z))(^x1.x1))) 19. ==[ beta ]==> ((^y.y)((^z.((z z) z))(^x1.x1))) 20. ==[ alpha ]==> ((^x.x)((^y.((y y) y))(^z.z))) 21. ==[ beta ]==> ((^y.((y y) y))(^z.z)) 22. ==[ alpha ]==> ((^x.((x x) x))(^y.y)) 23. ==[ beta ]==> (((^y.y)(^y.y))(^y.y)) 24. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 25. ==[ beta ]==> ((^y.y)(^z.z)) 26. ==[ alpha ]==> ((^x.x)(^y.y)) 27. ==[ beta ]==> (^y.y) 28. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189158/22193286. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.b)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189159/22193376. ------ 1. ==[ start ]==> ((^a.(a a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(b (a (a (^y.y))))) 3. ==[ beta ]==> ((b (a (a (^y.y))))(b (a (a (^y.y))))) 4. ==[ alpha ]==> ((b (a (a (^x.x))))(b (a (a (^y.y))))) REDUCED to normal form. ------ 189160/22193397. ------ 1. ==[ start ]==> (((a a) a)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189161/22193403. ------ 1. ==[ start ]==> ((^a.b)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 189162/22193406. ------ 1. ==[ start ]==> ((a b)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 189163/22193439. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 (^y1.y1))) b)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189164/22193484. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((b (^z.z))((^x1.x1) a))(^y.y)) 4. ==[ alpha ]==> (((b (^x.x))((^y.y) a))(^z.z)) 5. ==[ beta ]==> (((b (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((b (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 189165/22193673. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a b)(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a b)(b a))) 3. ==[ eta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 189166/22194168. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189167/22194726. ------ 1. ==[ start ]==> ((^a.((a a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))(a (a (a (^y.y))))) 3. ==[ beta ]==> (((a (a (a (^y.y))))(a (a (a (^y.y)))))(a (a (a (^y.y))))) 4. ==[ alpha ]==> (((a (a (a (^x.x))))(a (a (a (^y.y)))))(a (a (a (^z.z))))) REDUCED to normal form. ------ 189168/22194729. ------ 1. ==[ start ]==> ((a ((a a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 189169/22195557. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.a)(^z.((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((^x.a)(^y.((^z.(^x1.x1)) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 189170/22195626. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(a a)) c)) 3. ==[ beta ]==> (^y.((((a a)(a a)) c)(((a a)(a a)) c))) 4. ==[ alpha ]==> (^x.((((a a)(a a)) c)(((a a)(a a)) c))) REDUCED to normal form. ------ 189171/22196745. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(y (^z.z)))) REDUCED to normal form. ------ 189172/22197132. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(b (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(b (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(b (^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(^z.(b (^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 9. ==[ beta ]==> (^y.(b (^z.z))) 10. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 189173/22197264. ------ 1. ==[ start ]==> ((^a.(b a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ eta ]==> (b (((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 189174/22197813. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189175/22198704. ------ 1. ==[ start ]==> ((^a.(^b.b))((a b)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189176/22199526. ------ 1. ==[ start ]==> (((a b)(^c.a))(^a.(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 189177/22200417. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 189178/22200687. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(x1 a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(x1 a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(z a))) REDUCED to normal form. ------ 189179/22200966. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(^x1.(b x1))) 3. ==[ eta ]==> ((((a a)(^x.x))((^y.y)(^z.z))) b) 4. ==[ beta ]==> ((((a a)(^x.x))(^z.z)) b) 5. ==[ alpha ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 189180/22201098. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 189181/22201938. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((a b)(^y.((^z.z)(a a)))) 6. ==[ alpha ]==> ((a b)(^x.((^y.y)(a a)))) 7. ==[ beta ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 189182/22202793. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(a z1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) a) 4. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1)))) a) 5. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1)))) a) 6. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 7. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 8. ==[ beta ]==> (^y.(^z.z)) 9. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189183/22202982. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.z))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.z))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.y))) REDUCED to normal form. ------ 189184/22203495. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 189185/22203501. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a ((a a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a ((a a) a))) 3. ==[ beta ]==> ((a ((a a) a))((a ((a a) a))(^y.y))) 4. ==[ alpha ]==> ((a ((a a) a))((a ((a a) a))(^x.x))) REDUCED to normal form. ------ 189186/22203504. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.((a a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.((y y) y))) REDUCED to normal form. ------ 189187/22203927. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189188/22204062. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189189/22204170. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(a (a a)))) REDUCED to normal form. ------ 189190/22204278. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 189191/22204557. ------ 1. ==[ start ]==> (((a b)(b a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.((^y.y) x))) 3. ==[ eta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 189192/22204692. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.c)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.c)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.c)) 5. ==[ beta ]==> ((b (^y.y))(^z.c)) 6. ==[ alpha ]==> ((b (^x.x))(^y.c)) REDUCED to normal form. ------ 189193/22204791. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189194/22204824. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a b)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189195/22204827. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 189196/22204836. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^c.a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189197/22204863. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.a)) 3. ==[ beta ]==> ((^y.y)(^y1.a)) 4. ==[ alpha ]==> ((^x.x)(^y.a)) 5. ==[ beta ]==> (^y.a) 6. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 189198/22204911. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (a ((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 189199/22204920. ------ 1. ==[ start ]==> ((a (a a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))(b (a (a (^x.x))))) REDUCED to normal form. ------ 189200/22204938. ------ 1. ==[ start ]==> (((a a) a)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 189201/22204947. ------ 1. ==[ start ]==> ((a b)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(a ((^x.x)(^y.(^z.z))))) 3. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 189202/22204956. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 189203/22204983. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 189204/22205001. ------ 1. ==[ start ]==> (((a a)(a a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a a))(((^x.(^y.y)) a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 189205/22205028. ------ 1. ==[ start ]==> ((a (a (^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (a (^x.x)))((b (^y.y)) a)) REDUCED to normal form. ------ 189206/22205163. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 189207/22205190. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 189208/22205217. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a b)(b a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a b)(b a))) 3. ==[ beta ]==> ((a a)((a b)(b a))) REDUCED to normal form. ------ 189209/22205370. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 189210/22205496. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((^y.(y y))(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> ((((a a)(a a))(^y.(y y)))(((a a)(a a))(^y.(y y)))) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 189211/22205523. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 189212/22205559. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 189213/22205577. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((b a)(^z.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((b a)(^z.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.b))) 5. ==[ beta ]==> ((^y.y)((b a)(^z.b))) 6. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 7. ==[ beta ]==> ((b a)(^y.b)) 8. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 189214/22205604. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 189215/22205640. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 189216/22205667. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.b)(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(b a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 189217/22205685. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 189218/22205712. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 189219/22205802. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 189220/22205847. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a (^z.z))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189221/22205874. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((^y.(^z.z)) a) b) 6. ==[ alpha ]==> (((^x.(^y.y)) a) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 189222/22205937. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 189223/22205964. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 189224/22205991. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 189225/22206045. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 189226/22206072. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 189227/22206243. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y)(a a))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)(b ((^y.(^z.z)) a))) 6. ==[ alpha ]==> ((a a)(b ((^x.(^y.y)) a))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 189228/22206270. ------ 1. ==[ start ]==> ((a ((a a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))(a (a (a (^x.x))))) REDUCED to normal form. ------ 189229/22206360. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a)) d)) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a)) d)) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a)) d)) 5. ==[ beta ]==> (a ((^z.(a a)) d)) 6. ==[ alpha ]==> (a ((^x.(a a)) d)) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 189230/22206621. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(a ((a a)(a a)))) REDUCED to normal form. ------ 189231/22206648. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 189232/22206675. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a (a a)))((a a)((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((a (a (a a)))((a a)((^x.(^y.y)) a))) 5. ==[ beta ]==> ((a (a (a a)))((a a)(^y.y))) 6. ==[ alpha ]==> ((a (a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 189233/22206774. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) a)((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (b ((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 189234/22206792. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.b)(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 189235/22206873. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(^z.z))(^x1.b))) IRREDUCIBLE: cycle. ------ 189236/22206936. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a) b) b) REDUCED to normal form. ------ 189237/22206963. ------ 1. ==[ start ]==> (((a b) a)((^c.a)(b a))) 2. ==[ alpha ]==> (((a b) a)((^x.a)(b a))) 3. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 189238/22206981. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 189239/22206990. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 189240/22207008. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((a (a a))(^z.z))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.z))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 189241/22207044. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 189242/22207071. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 189243/22207098. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.a)((^z.z)((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((^x.a)((^y.y)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 189244/22207143. ------ 1. ==[ start ]==> (((^a.b)(a a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(a a))((b (^y.y)) b)) 3. ==[ beta ]==> (b ((b (^y.y)) b)) 4. ==[ alpha ]==> (b ((b (^x.x)) b)) REDUCED to normal form. ------ 189245/22207170. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(a a)) c)) REDUCED to normal form. ------ 189246/22207341. ------ 1. ==[ start ]==> (((^a.b) b)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189247/22207836. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (((a a)(a a))(a ((^y.y) b))) 6. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) b))) 7. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 189248/22207863. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 189249/22207890. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a a)(b (^y.y)))) 3. ==[ beta ]==> ((a ((a a) a))((a a)(b (^y.y)))) 4. ==[ alpha ]==> ((a ((a a) a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 189250/22207989. ------ 1. ==[ start ]==> (((^a.b) c)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.y)((^z.z) a))) 3. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189251/22208088. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.b)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.b)) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 189252/22208223. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 189253/22208232. ------ 1. ==[ start ]==> (((a b) c)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b) c)((^x.a)((^y.y) b))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 189254/22208259. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 189255/22208286. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.y))) REDUCED to normal form. ------ 189256/22208304. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b (^z.z)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 189257/22208331. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> ((^y.y)(((a a)(a a)) b)) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a)) b)) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 189258/22208340. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 189259/22208367. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((a (^y.b))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.a))) 5. ==[ beta ]==> ((a (^x.b))(^z.a)) 6. ==[ alpha ]==> ((a (^x.b))(^y.a)) REDUCED to normal form. ------ 189260/22208475. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 189261/22208502. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.b)(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 189262/22208619. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(c ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(c ((^y.y) b))) 3. ==[ beta ]==> ((a (a b))(c ((^y.y) b))) 4. ==[ alpha ]==> ((a (a b))(c ((^x.x) b))) 5. ==[ beta ]==> ((a (a b))(c b)) REDUCED to normal form. ------ 189263/22208646. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(b ((a a)(a a)))) REDUCED to normal form. ------ 189264/22208673. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(a (b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(a (b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a (b (^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (b (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (b (^z.z)))) 7. ==[ beta ]==> ((^y.y)(a (b (^z.z)))) 8. ==[ alpha ]==> ((^x.x)(a (b (^y.y)))) 9. ==[ beta ]==> (a (b (^y.y))) 10. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 189265/22208700. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 189266/22208727. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (((a b) a)(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> (((a b) a)(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (((a b) a)(b (a (^y.y)))) 6. ==[ alpha ]==> (((a b) a)(b (a (^x.x)))) REDUCED to normal form. ------ 189267/22208754. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 189268/22208781. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((b a)(a (a a)))) REDUCED to normal form. ------ 189269/22208808. ------ 1. ==[ start ]==> ((a (b a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (b a))(((a a)(^x.x))(^z.z))) 4. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 189270/22209087. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b a)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b a)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 189271/22209114. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 189272/22209168. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 189273/22209177. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.y)) REDUCED to normal form. ------ 189274/22209231. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 189275/22209249. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((a a) a)(^y.(a a)))) 3. ==[ beta ]==> (b (((a a) a)(^y.(a a)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 189276/22209258. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x))) a) REDUCED to normal form. ------ 189277/22209285. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 189278/22209312. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a)(b a))) REDUCED to normal form. ------ 189279/22209357. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 189280/22209636. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189281/22209816. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) c)) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1))) c)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 189282/22210041. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189283/22210068. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(b (^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.b))(b (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(b (^z.z))) 5. ==[ beta ]==> ((^y.b)(b (^z.z))) 6. ==[ alpha ]==> ((^x.b)(b (^y.y))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 189284/22210113. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> (b (((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.y))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 189285/22210122. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 189286/22210149. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 189287/22210221. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189288/22210230. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 189289/22210248. ------ 1. ==[ start ]==> ((a (^b.b))((a b)(^c.a))) 2. ==[ alpha ]==> ((a (^x.x))((a b)(^y.a))) REDUCED to normal form. ------ 189290/22210527. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189291/22211013. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(c (^d.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(c (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(c (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (^z.a))) 5. ==[ beta ]==> ((^y.(a a))(c (^z.a))) 6. ==[ alpha ]==> ((^x.(a a))(c (^y.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189292/22211040. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189293/22211067. ------ 1. ==[ start ]==> (((a b)(^c.a))(a (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 189294/22211094. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 189295/22211166. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^y1.y1)(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189296/22211175. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a a)) REDUCED to normal form. ------ 189297/22211202. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 189298/22211733. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 189299/22211958. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 189300/22212003. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 189301/22212066. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a))) b) REDUCED to normal form. ------ 189302/22212084. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (b (((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 189303/22212093. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b)) a) REDUCED to normal form. ------ 189304/22212147. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(a b))) REDUCED to normal form. ------ 189305/22212201. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 189306/22212228. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(b a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(b a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(b a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 189307/22212453. ------ 1. ==[ start ]==> (((a b)(a b))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(c ((^x.x)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(c (a a))) REDUCED to normal form. ------ 189308/22212480. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(b ((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)((a a) a))(b ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)((a a) a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 189309/22212507. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(a (b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(a (b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(a (b a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (b a))) REDUCED to normal form. ------ 189310/22212561. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1)(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1)(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(a (^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)(a (^z.z)))) REDUCED to normal form. ------ 189311/22212588. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a b)((^z.z) a))) 3. ==[ beta ]==> ((b (a (^y.y)))((a b)((^z.z) a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a b)((^y.y) a))) 5. ==[ beta ]==> ((b (a (^x.x)))((a b) a)) REDUCED to normal form. ------ 189312/22212615. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 189313/22212642. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (b (^x.x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 189314/22212813. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 189315/22212957. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(a b))) 3. ==[ beta ]==> ((b c)((^y.a)(a b))) 4. ==[ alpha ]==> ((b c)((^x.a)(a b))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 189316/22212984. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 189317/22213029. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((a a)(^z.z)) a)) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z)) a)) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 189318/22213056. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a)) b)) 5. ==[ beta ]==> (((^y.y)(a a)) b) 6. ==[ alpha ]==> (((^x.x)(a a)) b) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 189319/22213092. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 189320/22213200. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 189321/22213227. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 189322/22213299. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(a a)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189323/22213425. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 189324/22213452. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (^y.y))(a b))) REDUCED to normal form. ------ 189325/22213479. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> ((a b)((a a)((^x.x)(a a)))) 7. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 189326/22213974. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b) b)) 3. ==[ beta ]==> (b ((^x1.b) b)) 4. ==[ alpha ]==> (b ((^x.b) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189327/22214217. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 9. ==[ beta ]==> ((^y.y)(^z.a)) 10. ==[ alpha ]==> ((^x.x)(^y.a)) 11. ==[ beta ]==> (^y.a) 12. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 189328/22214244. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(y y)))) 5. ==[ beta ]==> ((a (a a))(^y.(y y))) 6. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 189329/22214298. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z))(^x1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y))(^z.a))) 7. ==[ beta ]==> ((b b)((a (^y.y))(^z.a))) 8. ==[ alpha ]==> ((b b)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 189330/22214307. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 189331/22214334. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(a b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(a b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189332/22214379. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((a a) a) b)) 3. ==[ beta ]==> (b (((a a) a) b)) REDUCED to normal form. ------ 189333/22214388. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 189334/22214415. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 189335/22214442. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 189336/22214496. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 189337/22214523. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.b))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.b)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.b)) REDUCED to normal form. ------ 189338/22214640. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (a (a a)))) REDUCED to normal form. ------ 189339/22214667. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 189340/22214694. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a a)((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a)((a a) a))) REDUCED to normal form. ------ 189341/22215018. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 189342/22215045. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a ((a a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a ((a a) a))) REDUCED to normal form. ------ 189343/22215441. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 189344/22215468. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.z))) REDUCED to normal form. ------ 189345/22215486. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 189346/22215513. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(y1 y1)) b)) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1)) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y y)) b)) 5. ==[ beta ]==> ((^y.(y y)) b) 6. ==[ alpha ]==> ((^x.(x x)) b) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189347/22215603. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 189348/22215630. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 189349/22215648. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 189350/22215711. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (a a))) REDUCED to normal form. ------ 189351/22215756. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(((^x1.x1) a) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189352/22215792. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 189353/22215819. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.(z z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(y y))) REDUCED to normal form. ------ 189354/22215900. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b (^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b (^z.a))) REDUCED to normal form. ------ 189355/22215990. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b c)) 3. ==[ beta ]==> ((a (b (^y.y)))(b c)) 4. ==[ alpha ]==> ((a (b (^x.x)))(b c)) REDUCED to normal form. ------ 189356/22216044. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(c (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(c (a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(c (a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(c (a a))) 5. ==[ beta ]==> (((^y.y) b)(c (a a))) 6. ==[ alpha ]==> (((^x.x) b)(c (a a))) 7. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 189357/22216071. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b (a (^z.z)))) REDUCED to normal form. ------ 189358/22216098. ------ 1. ==[ start ]==> (((a b)(b a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(b a))(a ((^x.x) a))) 3. ==[ beta ]==> (((a b)(b a))(a a)) REDUCED to normal form. ------ 189359/22216125. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a (^z.z))(a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a (^z.z))(a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.y))(a a))) REDUCED to normal form. ------ 189360/22216152. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a a)(a (^y.y)))) REDUCED to normal form. ------ 189361/22216206. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b b)) REDUCED to normal form. ------ 189362/22216233. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a c)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a c)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a c)) 5. ==[ beta ]==> ((b (^y.y))(a c)) 6. ==[ alpha ]==> ((b (^x.x))(a c)) REDUCED to normal form. ------ 189363/22216260. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(b (a a))) REDUCED to normal form. ------ 189364/22216314. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a a)(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(a a))) 5. ==[ beta ]==> ((a (^y.y))((a a)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 189365/22216332. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 189366/22216341. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(b a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(b a)) REDUCED to normal form. ------ 189367/22216368. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 189368/22216377. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189369/22216404. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> ((^y.y)((^y1.y1) a)) 4. ==[ alpha ]==> ((^x.x)((^y.y) a)) 5. ==[ beta ]==> ((^y.y) a) 6. ==[ alpha ]==> ((^x.x) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 189370/22216488. ------ 1. ==[ start ]==> ((^a.b)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 189371/22217379. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189372/22217811. ------ 1. ==[ start ]==> ((^a.((a a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.(^z.(z (^x1.x1))))(^y.(^z.(z (^x1.x1)))))(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.(^y.(y (^z.z))))(^x1.(^y1.(y1 (^z1.z1)))))(^x2.(^y2.(y2 (^z2.z2))))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^x2.(^y2.(y2 (^z2.z2))))) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 7. ==[ beta ]==> ((^z.(^x1.(x1 (^y1.y1))))(^y.y)) 8. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.x1)) 9. ==[ beta ]==> (^y.(y (^z.z))) 10. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 189373/22226586. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.a))) 3. ==[ beta ]==> ((^z.(^x1.a))((^z.(^x1.a))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.a))((^z.(^x1.a))(^y1.y1))) 5. ==[ beta ]==> (^y.a) 6. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 189374/22227459. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189375/22227909. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189376/22228008. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.(x1 (^y1.y1))))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.(^z1.z1))(^x2.(x2 (^y2.y2))))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(x2 (^y2.y2))))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189377/22228035. ------ 1. ==[ start ]==> ((^a.b)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 189378/22228038. ------ 1. ==[ start ]==> ((a b)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189379/22228047. ------ 1. ==[ start ]==> (((^a.a)(a a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(^x.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 189380/22228071. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a (^x1.x1)))(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189381/22228233. ------ 1. ==[ start ]==> ((^a.(^b.a))((b a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.x))((b a)(a b))) 3. ==[ beta ]==> (^y.((b a)(a b))) 4. ==[ alpha ]==> (^x.((b a)(a b))) REDUCED to normal form. ------ 189382/22228476. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 189383/22228497. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189384/22228926. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189385/22228929. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 189386/22229358. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((((^y.y)(^z.(z (^x1.x1))))((^y.y)(^z.(z (^x1.x1)))))((^y.y)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x)(^y.(y (^z.z))))((^x1.x1)(^y1.(y1 (^z1.z1)))))((^x2.x2)(^y2.(y2 (^z2.z2))))) 5. ==[ beta ]==> (((^y.(y (^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1)))))((^x2.x2)(^y2.(y2 (^z2.z2))))) 6. ==[ alpha ]==> (((^x.(x (^y.y)))((^z.z)(^x1.(x1 (^y1.y1)))))((^z1.z1)(^x2.(x2 (^y2.y2))))) 7. ==[ beta ]==> ((((^z.z)(^x1.(x1 (^y1.y1))))(^y.y))((^z1.z1)(^x2.(x2 (^y2.y2))))) 8. ==[ alpha ]==> ((((^x.x)(^y.(y (^z.z))))(^x1.x1))((^y1.y1)(^z1.(z1 (^x2.x2))))) 9. ==[ beta ]==> (((^y.(y (^z.z)))(^x1.x1))((^y1.y1)(^z1.(z1 (^x2.x2))))) 10. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)(^y1.(y1 (^z1.z1))))) 11. ==[ beta ]==> (((^z.z)(^y.y))((^x1.x1)(^y1.(y1 (^z1.z1))))) 12. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(x1 (^y1.y1))))) 13. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 (^y1.y1))))) 14. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z (^x1.x1))))) 15. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 16. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 17. ==[ beta ]==> (^y.(y (^z.z))) 18. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 189387/22229361. ------ 1. ==[ start ]==> ((a ((a a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 189388/22229691. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 189389/22229793. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (a a)) a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 189390/22229871. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((^y.(a a))((^z.z) a)) b) 4. ==[ alpha ]==> (((^x.(a a))((^y.y) a)) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 189391/22232493. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.((a a)(a a)))) REDUCED to normal form. ------ 189392/22232733. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^x1.(^y1.y1))(^z1.(^x2.x2)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.z1))) 5. ==[ beta ]==> ((^y.y)(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189393/22233519. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a b)((^x.x)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.z)) 5. ==[ beta ]==> (((a b)(^y.y))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 189394/22233651. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 189395/22233825. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^d.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 189396/22234149. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 189397/22234464. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 189398/22234650. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((^y.(^z.z))(^x1.b))((^y.(^z.z))(^x1.b)))(((^y.(^z.z))(^x1.b))((^y.(^z.z))(^x1.b)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.b)))(((^x2.(^y2.y2))(^z2.b))((^x3.(^y3.y3))(^z3.b)))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))(^z1.b)))(((^x2.(^y2.y2))(^z2.b))((^x3.(^y3.y3))(^z3.b)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.b)))(((^y1.(^z1.z1))(^x2.b))((^y2.(^z2.z2))(^x3.b)))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.b))(((^y1.(^z1.z1))(^x2.b))((^y2.(^z2.z2))(^x3.b)))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.(^y1.y1))(^z1.b))((^x2.(^y2.y2))(^z2.b)))) 9. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(^z1.b))((^x2.(^y2.y2))(^z2.b)))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.b))((^y1.(^z1.z1))(^x2.b)))) 11. ==[ beta ]==> (((^y.(^z.z))(^x1.b))((^y1.(^z1.z1))(^x2.b))) 12. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.b))) 13. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.b))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 15. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 16. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189399/22235040. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^c.(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(b a))) 3. ==[ beta ]==> ((^y.y)(^x1.(b a))) 4. ==[ alpha ]==> ((^x.x)(^y.(b a))) 5. ==[ beta ]==> (^y.(b a)) 6. ==[ alpha ]==> (^x.(b a)) REDUCED to normal form. ------ 189400/22235319. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 189401/22236813. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((b a)(^y.((^z.z)(a a)))) 6. ==[ alpha ]==> ((b a)(^x.((^y.y)(a a)))) 7. ==[ beta ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 189402/22237710. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (a a))((^x1.x1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 189403/22237812. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.b))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.b))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.b))) REDUCED to normal form. ------ 189404/22238136. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.a))) REDUCED to normal form. ------ 189405/22238145. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.((x1 x1) x1))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.((x1 x1) x1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.((z z) z))) 5. ==[ beta ]==> ((^z.((z z) z))(^y.y)) 6. ==[ alpha ]==> ((^x.((x x) x))(^y.y)) 7. ==[ beta ]==> (((^y.y)(^y.y))(^y.y)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189406/22238577. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 189407/22238802. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 189408/22239006. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189409/22239009. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 189410/22239027. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.(z z)))) REDUCED to normal form. ------ 189411/22239108. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.((^y.y) a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^x.a)) REDUCED to normal form. ------ 189412/22239189. ------ 1. ==[ start ]==> (((a b)(b a))(^b.(^b.a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 189413/22239324. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(a (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(a (^z.z)))) REDUCED to normal form. ------ 189414/22239423. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.z)) 3. ==[ beta ]==> ((b (^y.y))(^z.z)) 4. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 189415/22239432. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189416/22239456. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.y1)(a a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189417/22239459. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 189418/22239468. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189419/22239495. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(y1 y1))) 3. ==[ beta ]==> ((^y.y)(^y1.(y1 y1))) 4. ==[ alpha ]==> ((^x.x)(^y.(y y))) 5. ==[ beta ]==> (^y.(y y)) 6. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 189420/22239561. ------ 1. ==[ start ]==> ((a (a a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(^y.y)) 4. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 189421/22239570. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(b (a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)(b (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 189422/22239588. ------ 1. ==[ start ]==> ((a b)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 189423/22239597. ------ 1. ==[ start ]==> (((^a.a)(a a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(a ((^y.y)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(a ((^x.x)(^y.(^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 189424/22239606. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 189425/22239624. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a (^z.z)))(a a))) REDUCED to normal form. ------ 189426/22239633. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x) b)((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (b ((^y.(y (^z.z))) b)) 4. ==[ alpha ]==> (b ((^x.(x (^y.y))) b)) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 189427/22239678. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189428/22239705. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 189429/22239732. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(b ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(b ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 189430/22239759. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 189431/22239786. ------ 1. ==[ start ]==> ((a (^b.a))((b a)(a b))) 2. ==[ alpha ]==> ((a (^x.a))((b a)(a b))) REDUCED to normal form. ------ 189432/22239867. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a b)(b a))) 3. ==[ beta ]==> ((^y.a)((a b)(b a))) 4. ==[ alpha ]==> ((^x.a)((a b)(b a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 189433/22239894. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 189434/22239948. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> (a ((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 189435/22239975. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 189436/22240029. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 189437/22240047. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 189438/22240074. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 189439/22240119. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((a a)((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((a a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 189440/22240200. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 189441/22240227. ------ 1. ==[ start ]==> (((a (a a)) a)((b a)(^a.b))) 2. ==[ alpha ]==> (((a (a a)) a)((b a)(^x.b))) REDUCED to normal form. ------ 189442/22240254. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 189443/22240281. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 189444/22240335. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189445/22240371. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 189446/22240398. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 189447/22240425. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 189448/22240452. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 189449/22240479. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((a (^x.x))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 189450/22240803. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 189451/22240911. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 189452/22240947. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(a a))) 3. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a)(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a a)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a a)) 7. ==[ beta ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189453/22241001. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> (a (((a a)(a a))((^z.z) a))) 6. ==[ alpha ]==> (a (((a a)(a a))((^x.x) a))) 7. ==[ beta ]==> (a (((a a)(a a)) a)) REDUCED to normal form. ------ 189454/22241082. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((b a)((a a) a))) 3. ==[ beta ]==> (((a a) a)((b a)((a a) a))) REDUCED to normal form. ------ 189455/22241109. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))(a b)) 6. ==[ alpha ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 189456/22241163. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a b)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a b)((a a)(^y.y)))) 7. ==[ beta ]==> ((a a)((a b)((a a)(^y.y)))) 8. ==[ alpha ]==> ((a a)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 189457/22241244. ------ 1. ==[ start ]==> ((a (^a.b))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.b))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((a (^x.b))((a (a a)) b)) REDUCED to normal form. ------ 189458/22241343. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(a (^y.(y (^z.z))))) 3. ==[ beta ]==> (((a (a a)) a)(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a (a a)) a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 189459/22241415. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b) a)(((a a)(a a))(^y.a))) 3. ==[ beta ]==> (b (((a a)(a a))(^y.a))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.a))) REDUCED to normal form. ------ 189460/22241424. ------ 1. ==[ start ]==> ((a (a b))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a b))((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 189461/22241577. ------ 1. ==[ start ]==> ((((a a) a) b)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 189462/22241631. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189463/22241685. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 189464/22241766. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z) a)) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 189465/22241793. ------ 1. ==[ start ]==> (((a b)(^a.a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a b)(^x.x))((b (^y.y)) b)) REDUCED to normal form. ------ 189466/22241829. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 189467/22241856. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.(z z))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(y y))) REDUCED to normal form. ------ 189468/22241883. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 189469/22241964. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 189470/22241991. ------ 1. ==[ start ]==> (((a b)(a a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 189471/22242108. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(c ((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(c ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c ((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)(c ((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)(c ((a a)(a a)))) 7. ==[ beta ]==> (c ((a a)(a a))) REDUCED to normal form. ------ 189472/22242189. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b (^x1.x1))(a a))) 3. ==[ beta ]==> (b ((b (^x1.x1))(a a))) 4. ==[ alpha ]==> (b ((b (^x.x))(a a))) REDUCED to normal form. ------ 189473/22242243. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> ((a a)(((^y.y) b)((^z.z) a))) 6. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y) a))) 7. ==[ beta ]==> ((a a)(b ((^y.y) a))) 8. ==[ alpha ]==> ((a a)(b ((^x.x) a))) 9. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 189474/22242270. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a (a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 189475/22242324. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(^y1.y1))((a a) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(^y1.y1))((a a) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))((a a) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))((a a) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((a a) a))) 9. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((a a) a))) 10. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((a a) a))) 11. ==[ beta ]==> (((a a)(^y.y))((a a) a)) 12. ==[ alpha ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 189476/22242405. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (b (((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (b (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 189477/22242504. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(c (^y.(a a)))) REDUCED to normal form. ------ 189478/22242630. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (b (((^y.y) b)(^z.a))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.a))) 5. ==[ beta ]==> (b (b (^y.a))) 6. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 189479/22242639. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((^z.z) a)) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y) a)) 5. ==[ beta ]==> (((a b)(a (^x.x))) a) REDUCED to normal form. ------ 189480/22242666. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 189481/22242873. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) a)(^y.y))) 3. ==[ beta ]==> (((a b) c)(a (^y.y))) 4. ==[ alpha ]==> (((a b) c)(a (^x.x))) REDUCED to normal form. ------ 189482/22242900. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 189483/22242981. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(a a)) b)) REDUCED to normal form. ------ 189484/22243008. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) b) c)) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) b) c)) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) b) c)) 5. ==[ beta ]==> ((a (^x.b))(b c)) REDUCED to normal form. ------ 189485/22243233. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 189486/22243260. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a (a b))((^y.a)(^z.z))) 4. ==[ alpha ]==> ((a (a b))((^x.a)(^y.y))) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 189487/22243539. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a) a)((^z.z)(a a)))) 5. ==[ beta ]==> (b (((a a) a)((^z.z)(a a)))) 6. ==[ alpha ]==> (b (((a a) a)((^x.x)(a a)))) 7. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 189488/22243620. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (a (^y.(^z.z))))) 6. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 189489/22243791. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((b a)(^z.(z z)))) 3. ==[ beta ]==> ((a (^y.(a a)))((b a)(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 189490/22243818. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 189491/22243872. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)(^z.b))) REDUCED to normal form. ------ 189492/22243899. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 189493/22243926. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 189494/22244016. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 189495/22244043. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 189496/22244097. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 189497/22244124. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(^y1.a))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 189498/22244178. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 189499/22244205. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((a a) a)((^y.(a a))(^z.a))) 6. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 189500/22244232. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 189501/22244286. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 189502/22244376. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(b ((^z.z) b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(b ((^z.z) b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(b ((^z.z) b))) 5. ==[ beta ]==> ((a a)(b ((^z.z) b))) 6. ==[ alpha ]==> ((a a)(b ((^x.x) b))) 7. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 189503/22244457. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 189504/22244565. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a b)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189505/22244592. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a) a)(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(a b))) REDUCED to normal form. ------ 189506/22244619. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> ((^y.y)((^z.z)(a a))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(a a))) 9. ==[ beta ]==> ((^y.y)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189507/22244673. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z) a)(b a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) a)(b a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) a)(b a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)(b a))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(b a))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(b a))) 9. ==[ beta ]==> (((a a)(a a))(a (b a))) REDUCED to normal form. ------ 189508/22244763. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 189509/22244790. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 189510/22244817. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((b a)(^z.a))) REDUCED to normal form. ------ 189511/22244871. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 189512/22244907. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 189513/22244934. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.a)(a b))) 3. ==[ beta ]==> (((a (^x.x))(b a)) a) REDUCED to normal form. ------ 189514/22244961. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 189515/22244988. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(y y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (((a (a a))(a a))(((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (((a (a a))(a a))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 189516/22245015. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)(b a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)(b a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(b a))) 5. ==[ beta ]==> ((a b)((^y.a)(b a))) 6. ==[ alpha ]==> ((a b)((^x.a)(b a))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 189517/22245042. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 189518/22245069. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.z) b)) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.y) b)) 7. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 189519/22245096. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 189520/22245123. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 189521/22245204. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 189522/22245375. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (b (a (^x.(^y.y))))) REDUCED to normal form. ------ 189523/22245483. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a)(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189524/22245492. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 189525/22245537. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((a b)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b ((a b)((^x.x)(^y.y)))) 7. ==[ beta ]==> (b ((a b)(^y.y))) 8. ==[ alpha ]==> (b ((a b)(^x.x))) REDUCED to normal form. ------ 189526/22245564. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((a a) a))) 5. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 189527/22245618. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (a a))(a a))) REDUCED to normal form. ------ 189528/22245699. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (b ((a a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> (b ((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 189529/22245735. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 189530/22245762. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 189531/22245816. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.(y1 y1)))) REDUCED to normal form. ------ 189532/22245843. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 189533/22245879. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.a)((a a) a))) 3. ==[ beta ]==> (((a a) b)((^y.a)((a a) a))) 4. ==[ alpha ]==> (((a a) b)((^x.a)((a a) a))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 189534/22245906. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 189535/22245933. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (b a))((^y.(y y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a (b a))(((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> ((a (b a))(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((a (b a))((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> ((a (b a))((a a)((^x.x)(a a)))) 9. ==[ beta ]==> ((a (b a))((a a)(a a))) REDUCED to normal form. ------ 189536/22245960. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) a) REDUCED to normal form. ------ 189537/22245987. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(b a))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(b a))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(b a))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 189538/22246014. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.x)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((((a a) a)(a b))(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 189539/22246041. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 189540/22246149. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 189541/22246176. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)(^z.a))) 3. ==[ beta ]==> ((b (a a))((^y.a)(^z.a))) 4. ==[ alpha ]==> ((b (a a))((^x.a)(^y.a))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 189542/22246203. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 189543/22246374. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 189544/22246482. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1)(^z1.z1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189545/22246563. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 189546/22246590. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a a)(b a))) 3. ==[ beta ]==> ((^y.y)((a a)(b a))) 4. ==[ alpha ]==> ((^x.x)((a a)(b a))) 5. ==[ beta ]==> ((a a)(b a)) REDUCED to normal form. ------ 189547/22246626. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((b a)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((b a)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a)(^x1.x1))) REDUCED to normal form. ------ 189548/22246707. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b)(^y.(y y)))) REDUCED to normal form. ------ 189549/22246734. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 189550/22246788. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (a a))(^x1.b))) REDUCED to normal form. ------ 189551/22246842. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 189552/22246896. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((b a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((b a) a)) REDUCED to normal form. ------ 189553/22246959. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))(^z.a))) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 189554/22246986. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 189555/22247013. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 189556/22247040. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 189557/22247067. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> ((((a a) a)(a a))((^y.b)(^y.b))) 6. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)(^y.b))) 7. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 189558/22247094. ------ 1. ==[ start ]==> (((a b)(a b))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 189559/22247373. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (^x2.x2))((^y2.y2)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x2.x2))((^y2.y2)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189560/22247598. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) a)(^z.b))) 3. ==[ beta ]==> ((b c)(((^y.y) a)(^z.b))) 4. ==[ alpha ]==> ((b c)(((^x.x) a)(^y.b))) 5. ==[ beta ]==> ((b c)(a (^y.b))) 6. ==[ alpha ]==> ((b c)(a (^x.b))) REDUCED to normal form. ------ 189561/22247625. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 189562/22247733. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b) c)) 3. ==[ beta ]==> ((a (^y.y))((a b) c)) 4. ==[ alpha ]==> ((a (^x.x))((a b) c)) REDUCED to normal form. ------ 189563/22247940. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1)(a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189564/22247949. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a a)) REDUCED to normal form. ------ 189565/22247976. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.b) c)) 3. ==[ beta ]==> ((b (^y.a))((^z.b) c)) 4. ==[ alpha ]==> ((b (^x.a))((^y.b) c)) 5. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 189566/22248120. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b (^z.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(b (^z.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b (^y.(a a)))) 5. ==[ beta ]==> ((a b)(b (^y.(a a)))) 6. ==[ alpha ]==> ((a b)(b (^x.(a a)))) REDUCED to normal form. ------ 189567/22248174. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(a a))(a a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a))(a a))) 5. ==[ beta ]==> ((b a)((^y.(a a))(a a))) 6. ==[ alpha ]==> ((b a)((^x.(a a))(a a))) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 189568/22248201. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 189569/22248228. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)((^y.y) a))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 189570/22248255. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 189571/22248282. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(^z.z))) 9. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 10. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 189572/22248336. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 189573/22248363. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((b a)((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> ((b a)((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> ((b a)((^y.y)(a a))) 8. ==[ alpha ]==> ((b a)((^x.x)(a a))) 9. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 189574/22248390. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(a a))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 189575/22248534. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(c ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(c ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c ((a a) a))) 5. ==[ beta ]==> ((^y.y)(c ((a a) a))) 6. ==[ alpha ]==> ((^x.x)(c ((a a) a))) 7. ==[ beta ]==> (c ((a a) a)) REDUCED to normal form. ------ 189576/22248615. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)(a a))) 3. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 189577/22248723. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) a)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189578/22248840. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> (a (((a a) a)(^y.(^z.z)))) 6. ==[ alpha ]==> (a (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 189579/22248948. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 189580/22248975. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a a)(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a a)(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(^y1.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(^y1.b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189581/22249029. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a) b)) REDUCED to normal form. ------ 189582/22249056. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) c)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) c)) 7. ==[ beta ]==> (((a a)(^x.(a a))) c) REDUCED to normal form. ------ 189583/22249191. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.b) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.b) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) b) REDUCED to normal form. ------ 189584/22249245. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 7. ==[ beta ]==> ((^y.(^z.z)) c) 8. ==[ alpha ]==> ((^x.(^y.y)) c) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189585/22249263. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((a (a a)) a)) REDUCED to normal form. ------ 189586/22249308. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 189587/22249335. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(b (^y.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(b (^y.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(b (^x.a))) REDUCED to normal form. ------ 189588/22249362. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a (^y.b))) 3. ==[ beta ]==> (((a (a a)) b)(a (^y.b))) 4. ==[ alpha ]==> (((a (a a)) b)(a (^x.b))) REDUCED to normal form. ------ 189589/22249416. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 189590/22249443. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(a ((^z.z) a))) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a ((^y.y) a))) 7. ==[ beta ]==> (((a b)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 189591/22249470. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))((^y.a)(a (a a)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.a)(a (a a)))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 189592/22249497. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 189593/22249578. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 189594/22249605. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y))(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(^y.a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.a)(^y.a))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(^y.a))) 7. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 189595/22249659. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 189596/22249695. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(a ((a a) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(a ((a a) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a ((a a) a))) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 189597/22250100. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b (a (a a)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(b (a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (a (a a)))) 5. ==[ beta ]==> ((^y.y)(b (a (a a)))) 6. ==[ alpha ]==> ((^x.x)(b (a (a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 189598/22250127. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 189599/22250136. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 189600/22250154. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (a a))(a a))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a a))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 189601/22250208. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x)) a)) REDUCED to normal form. ------ 189602/22250271. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (a a))(^x1.x1))) REDUCED to normal form. ------ 189603/22250352. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 189604/22250433. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z)) c)) REDUCED to normal form. ------ 189605/22250514. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.a) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189606/22250532. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 189607/22250559. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 189608/22250577. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (^y.(y y)))) REDUCED to normal form. ------ 189609/22250604. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^b.a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 189610/22250631. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 189611/22250658. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))((^y.y) a)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x) a)) 5. ==[ beta ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 189612/22250685. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.z))) 7. ==[ beta ]==> (b ((^y.a)(^z.z))) 8. ==[ alpha ]==> (b ((^x.a)(^y.y))) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189613/22250712. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 189614/22250739. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.x)(^y.a))) 3. ==[ beta ]==> (((a b)(b a))(^y.a)) 4. ==[ alpha ]==> (((a b)(b a))(^x.a)) REDUCED to normal form. ------ 189615/22250793. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 189616/22250847. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 189617/22250874. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> ((b (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 189618/22250901. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 189619/22250955. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(b (^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.z))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 189620/22250973. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z) b)) 3. ==[ beta ]==> ((b (^y.y))((^z.z) b)) 4. ==[ alpha ]==> ((b (^x.x))((^y.y) b)) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 189621/22250982. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 189622/22251009. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.x1)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 189623/22251018. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189624/22251045. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(a (a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(a (a a))) 3. ==[ beta ]==> ((^y.y)(a (a a))) 4. ==[ alpha ]==> ((^x.x)(a (a a))) 5. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 189625/22262706. ------ 1. ==[ start ]==> (((^a.a)(a a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189626/22262715. ------ 1. ==[ start ]==> (((a a)(^a.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.x))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189627/22263135. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 189628/22263234. ------ 1. ==[ start ]==> ((^a.(a (a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((b (^y.y))(^z.a))) 3. ==[ beta ]==> (((b (^y.y))(^z.a))(((b (^y.y))(^z.a))((b (^y.y))(^z.a)))) 4. ==[ alpha ]==> (((b (^x.x))(^y.a))(((b (^z.z))(^x1.a))((b (^y1.y1))(^z1.a)))) REDUCED to normal form. ------ 189629/22263459. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189630/22263585. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189631/22263597. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (a (^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189632/22264530. ------ 1. ==[ start ]==> ((^a.(a b))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x b))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> ((((a a)(a a))(^y.a)) b) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a)) b) REDUCED to normal form. ------ 189633/22265799. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((b a)(^z.(^x1.x1)))((b a)(^z.(^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((((b a)(^x.(^y.y)))((b a)(^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 189634/22266054. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 189635/22266792. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.((a a)(a a)))) REDUCED to normal form. ------ 189636/22267104. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189637/22267863. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (b (^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 189638/22267995. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189639/22268178. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^c.(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 189640/22268817. ------ 1. ==[ start ]==> (((a b)(^c.a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 189641/22269123. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189642/22269708. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^c.(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(b a))) REDUCED to normal form. ------ 189643/22270779. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 189644/22271472. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^c.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.(a a)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(a a)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 189645/22272300. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(y b))) REDUCED to normal form. ------ 189646/22272804. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.(^y1.a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.a))) 5. ==[ beta ]==> ((^z.(^x1.a))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.a))(^z.z)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 189647/22273236. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189648/22273245. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 189649/22273353. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(a (a a)))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (a a)))) 7. ==[ beta ]==> (^y.(a (a a))) 8. ==[ alpha ]==> (^x.(a (a a))) REDUCED to normal form. ------ 189650/22273665. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b (^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (^y1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189651/22273848. ------ 1. ==[ start ]==> (((a b)(b a))(^c.c)) 2. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 189652/22273983. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189653/22274082. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(a a))) 3. ==[ beta ]==> ((b (^y.y))(^z.(a a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(a a))) REDUCED to normal form. ------ 189654/22274091. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 189655/22274115. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189656/22274127. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189657/22274154. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189658/22274238. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189659/22274247. ------ 1. ==[ start ]==> (((a a) a)(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)(b (a (a (^x.x))))) REDUCED to normal form. ------ 189660/22274265. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 189661/22274274. ------ 1. ==[ start ]==> (((a a)(^a.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^x.x))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 189662/22274301. ------ 1. ==[ start ]==> (((^a.a) b)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x) b)((a (a (^y.y)))(a a))) 3. ==[ beta ]==> (b ((a (a (^y.y)))(a a))) 4. ==[ alpha ]==> (b ((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 189663/22274310. ------ 1. ==[ start ]==> (((a a)(a a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a a)(a a))((^x.(x (^y.y))) b)) 3. ==[ beta ]==> (((a a)(a a))(b (^y.y))) 4. ==[ alpha ]==> (((a a)(a a))(b (^x.x))) REDUCED to normal form. ------ 189664/22274328. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 189665/22274355. ------ 1. ==[ start ]==> (((a a) b)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a) b)((b (^x.x))((^y.y) a))) 3. ==[ beta ]==> (((a a) b)((b (^x.x)) a)) REDUCED to normal form. ------ 189666/22274382. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 189667/22274409. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 189668/22274436. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))((a a) a))) REDUCED to normal form. ------ 189669/22274490. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 189670/22274571. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 189671/22274598. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a a)((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a a)((^y.y) b)) 8. ==[ alpha ]==> ((a a)((^x.x) b)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 189672/22274625. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 189673/22274652. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (b (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (b (^x1.x1)))) REDUCED to normal form. ------ 189674/22274679. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 189675/22274697. ------ 1. ==[ start ]==> ((a (^a.(a a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 189676/22274742. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 189677/22274769. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 189678/22274796. ------ 1. ==[ start ]==> ((a (a (a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (a (a a)))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 189679/22274832. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))(a (a a))) 6. ==[ alpha ]==> ((^x.(a a))(a (a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189680/22274886. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189681/22274994. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.b)(b a))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(b a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(b a))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 189682/22275021. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 189683/22275039. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 189684/22275147. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 189685/22275156. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (a (^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189686/22275183. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 7. ==[ beta ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189687/22275291. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189688/22275705. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (b (((^y.y) b)(a (a a)))) 6. ==[ alpha ]==> (b (((^x.x) b)(a (a a)))) 7. ==[ beta ]==> (b (b (a (a a)))) REDUCED to normal form. ------ 189689/22275732. ------ 1. ==[ start ]==> ((((a a) a) a)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a) a)((a (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 189690/22275786. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(a b))) REDUCED to normal form. ------ 189691/22275813. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((a (^x.(x x)))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a (^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 189692/22275840. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 189693/22275867. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(b a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189694/22275894. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 189695/22276038. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.(^x1.x1)) a)(^y1.y1))) 5. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 189696/22276065. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 189697/22276092. ------ 1. ==[ start ]==> ((a (a b))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a (a b))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 189698/22276101. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.b)((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.b)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 189699/22276263. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189700/22276290. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(b a))) 3. ==[ beta ]==> ((a b)((^y.a)(b a))) 4. ==[ alpha ]==> ((a b)((^x.a)(b a))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 189701/22276317. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189702/22276371. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a)((a a)(a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 189703/22276497. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(a a)) c)) REDUCED to normal form. ------ 189704/22276695. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189705/22276722. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189706/22276776. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(a a)))) 7. ==[ beta ]==> ((^y.a)(^z.(a a))) 8. ==[ alpha ]==> ((^x.a)(^y.(a a))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 189707/22276866. ------ 1. ==[ start ]==> (((a b) b)((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a b) b)((b (^x.x))(a a))) REDUCED to normal form. ------ 189708/22276893. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a a) a)(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> (((a a) a)(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 189709/22276920. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b ((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(b a)) REDUCED to normal form. ------ 189710/22276947. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 189711/22277001. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(^z.z))((a a) a))) REDUCED to normal form. ------ 189712/22277028. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(a a))(a b))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z)(a a))(a b))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))(a b))) 7. ==[ beta ]==> ((((^y.y)(a a))(a b))(((^y.y)(a a))(a b))) 8. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(a a))(a b))) 9. ==[ beta ]==> (((a a)(a b))(((^y.y)(a a))(a b))) 10. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a))(a b))) 11. ==[ beta ]==> (((a a)(a b))((a a)(a b))) REDUCED to normal form. ------ 189713/22277055. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a b)(a a))) REDUCED to normal form. ------ 189714/22277082. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)((a a)(^z.z)))) REDUCED to normal form. ------ 189715/22277109. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(b a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(b a))) 7. ==[ beta ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 189716/22277253. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((a (a a))((b (^y.y))(^z.z))) 6. ==[ alpha ]==> ((a (a a))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 189717/22277280. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a) a)(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 189718/22277307. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(b (^z.a))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 189719/22277334. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 189720/22277361. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 189721/22277397. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189722/22277532. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 189723/22277613. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 189724/22277694. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(^y.a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.a)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.a)) REDUCED to normal form. ------ 189725/22277775. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 189726/22278036. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a)) b)) 3. ==[ beta ]==> (((a b) a)((^y.(a a)) b)) 4. ==[ alpha ]==> (((a b) a)((^x.(a a)) b)) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 189727/22278063. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.z) c)) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.z) c)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y) c)) 5. ==[ beta ]==> (((a a)(a (^x.x))) c) REDUCED to normal form. ------ 189728/22278351. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a a)((a a)(a a)))) REDUCED to normal form. ------ 189729/22278396. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a))(a a))) 3. ==[ beta ]==> ((b a)((^y.(a a))(a a))) 4. ==[ alpha ]==> ((b a)((^x.(a a))(a a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 189730/22278423. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(a (^z.z))) 6. ==[ alpha ]==> ((^x.x)(a (^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 189731/22278558. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.b)(a b))) 3. ==[ beta ]==> (b ((^y.b)(a b))) 4. ==[ alpha ]==> (b ((^x.b)(a b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189732/22278666. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 189733/22278684. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 189734/22278738. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((a a)(a a)) a)) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a)(a a)) a)) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(a a)) a)) 5. ==[ beta ]==> ((a (a a))(((a a)(a a)) a)) REDUCED to normal form. ------ 189735/22278765. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x) b) b)) 3. ==[ beta ]==> (((a (a a))(a b))(b b)) REDUCED to normal form. ------ 189736/22278963. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189737/22279044. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 189738/22279242. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a b)((a a) a))) REDUCED to normal form. ------ 189739/22279269. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((a a) a)(a b))) REDUCED to normal form. ------ 189740/22279350. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a (b a))) REDUCED to normal form. ------ 189741/22279377. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)((a (^z.z))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.b)((a (^y.y))(a (^z.(^x1.x1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 189742/22279422. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(a (^x1.(a a)))) 3. ==[ beta ]==> (b (a (^x1.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 189743/22279557. ------ 1. ==[ start ]==> ((a (^b.b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 189744/22279575. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a b)(^z.a))) REDUCED to normal form. ------ 189745/22279602. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a) a)(^y.b))) REDUCED to normal form. ------ 189746/22279629. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(^z.(a a)))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(a a))) 8. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(a a))) REDUCED to normal form. ------ 189747/22279710. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189748/22279737. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a a)(^z.z))) 3. ==[ beta ]==> (((a b)(^y.y))((a a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 189749/22279764. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y) b) a)) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y) b) a)) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x) b) a)) 5. ==[ beta ]==> (((a a)(a (a a)))(b a)) REDUCED to normal form. ------ 189750/22279791. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 189751/22279881. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189752/22279908. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b)(^x2.a))) 3. ==[ beta ]==> ((^y.y)((^z1.b)(^x2.a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.a))) 5. ==[ beta ]==> ((^y.b)(^z.a)) 6. ==[ alpha ]==> ((^x.b)(^y.a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 189753/22280043. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 189754/22280160. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(((a a)(^z.z)) a)) REDUCED to normal form. ------ 189755/22280187. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> ((b a)(((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> ((b a)(((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> ((b a)((a a)(a (a a)))) REDUCED to normal form. ------ 189756/22280214. ------ 1. ==[ start ]==> (((a a)(^b.b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.x))((a b)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 189757/22280241. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((a a) a)((a a) a))) REDUCED to normal form. ------ 189758/22280322. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z) a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)((a a)(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189759/22280349. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (^y.y))(b a))) REDUCED to normal form. ------ 189760/22280367. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (b (b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 189761/22280376. ------ 1. ==[ start ]==> (((a b)(^c.a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 189762/22280547. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a) a)(^y.a))) 3. ==[ beta ]==> (((a a) b)(((a a) a)(^y.a))) 4. ==[ alpha ]==> (((a a) b)(((a a) a)(^x.a))) REDUCED to normal form. ------ 189763/22280574. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.y1)(^z1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)(^y1.b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.b)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.b)) REDUCED to normal form. ------ 189764/22280601. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (a a))(^y.(a a)))) 3. ==[ beta ]==> ((a (b a))((a (a a))(^y.(a a)))) 4. ==[ alpha ]==> ((a (b a))((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 189765/22280682. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 189766/22280709. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)((a a) a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 189767/22280736. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((b a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((b a) b)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((b a) b)) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b a) b)) 5. ==[ beta ]==> (((a a)(^y.y))((b a) b)) 6. ==[ alpha ]==> (((a a)(^x.x))((b a) b)) REDUCED to normal form. ------ 189768/22280907. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(a a))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(a a))) 7. ==[ beta ]==> ((^y.(a a))(^y.(a a))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189769/22281186. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a (a a))(a b))) 3. ==[ beta ]==> ((b b)((a (a a))(a b))) REDUCED to normal form. ------ 189770/22281213. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a ((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(a ((^x.x)(a a)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a (a a))) REDUCED to normal form. ------ 189771/22281267. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(b a))) REDUCED to normal form. ------ 189772/22281393. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.b)(a (a a)))) 3. ==[ beta ]==> (b ((^y.b)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.b)(a (a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189773/22281501. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.a)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189774/22281600. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 189775/22281627. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(a a)) c)) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(a a)) c)) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a)) c)) 5. ==[ beta ]==> (((a (^x.x)) b)((a a) c)) REDUCED to normal form. ------ 189776/22281897. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(a a)) c)) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(a a)) c)) 5. ==[ beta ]==> ((b (a (^x.x)))(a a)) REDUCED to normal form. ------ 189777/22282122. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 189778/22282230. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189779/22282338. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((b (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 189780/22282419. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b)(^z1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 189781/22282500. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.a))) 5. ==[ beta ]==> (b ((^y.a)(^y.a))) 6. ==[ alpha ]==> (b ((^x.a)(^y.a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189782/22282536. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(c (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(c (a b))) 3. ==[ beta ]==> (((a a)(^y.b))(c (a b))) 4. ==[ alpha ]==> (((a a)(^x.b))(c (a b))) REDUCED to normal form. ------ 189783/22282617. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(a a))) REDUCED to normal form. ------ 189784/22282644. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.a))((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.a))((a b)(a (^y.y)))) REDUCED to normal form. ------ 189785/22282671. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(((a a) a) a)) REDUCED to normal form. ------ 189786/22282842. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> ((b a)(((^y.y)(a a))(^z.z))) 6. ==[ alpha ]==> ((b a)(((^x.x)(a a))(^y.y))) 7. ==[ beta ]==> ((b a)((a a)(^y.y))) 8. ==[ alpha ]==> ((b a)((a a)(^x.x))) REDUCED to normal form. ------ 189787/22282869. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 189788/22282896. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((a a) a)(^y.a))) 3. ==[ beta ]==> (((a b)(a a))(((a a) a)(^y.a))) 4. ==[ alpha ]==> (((a b)(a a))(((a a) a)(^x.a))) REDUCED to normal form. ------ 189789/22282923. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a b))((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.(y y)))) 7. ==[ beta ]==> (((a a)(a b))(^y.(y y))) 8. ==[ alpha ]==> (((a a)(a b))(^x.(x x))) REDUCED to normal form. ------ 189790/22282950. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 189791/22283004. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (^z.z))(^x1.b))) REDUCED to normal form. ------ 189792/22283031. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a a)(^y.(a a)))) 5. ==[ beta ]==> ((b a)((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((b a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 189793/22283058. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y)(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((a a) a)) REDUCED to normal form. ------ 189794/22283202. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 7. ==[ beta ]==> ((^y.a)(^z.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 189795/22283553. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189796/22283607. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b b)((^y.a)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b b)((^x.a)((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 189797/22283688. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.b)(^y.y))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189798/22283796. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189799/22283805. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (^y1.y1))) REDUCED to normal form. ------ 189800/22283832. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b ((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))(b ((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b ((a a) a))) REDUCED to normal form. ------ 189801/22283859. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a (a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (a b))) REDUCED to normal form. ------ 189802/22283913. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.z))) 9. ==[ beta ]==> ((^y.y)(a (^z.z))) 10. ==[ alpha ]==> ((^x.x)(a (^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 189803/22284057. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((a a) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a) a)(^x1.x1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 189804/22284084. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(b a))(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 189805/22284111. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (a a))(^y.a))) REDUCED to normal form. ------ 189806/22284138. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(^y.(y y)))) 7. ==[ beta ]==> (((a a)(a a))(a (^y.(y y)))) 8. ==[ alpha ]==> (((a a)(a a))(a (^x.(x x)))) REDUCED to normal form. ------ 189807/22284165. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 189808/22284219. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((a a) a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((a a) a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((a a) a) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a) a) a)) REDUCED to normal form. ------ 189809/22284246. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y)(^z.z)) b)) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x)(^y.y)) b)) 5. ==[ beta ]==> ((b (a (a a)))((^y.y) b)) 6. ==[ alpha ]==> ((b (a (a a)))((^x.x) b)) 7. ==[ beta ]==> ((b (a (a a))) b) REDUCED to normal form. ------ 189810/22284345. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 189811/22284750. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c ((^z.z) a))) 3. ==[ beta ]==> (((^y.y) b)(c ((^z.z) a))) 4. ==[ alpha ]==> (((^x.x) b)(c ((^y.y) a))) 5. ==[ beta ]==> (b (c ((^y.y) a))) 6. ==[ alpha ]==> (b (c ((^x.x) a))) 7. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 189812/22284768. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189813/22284777. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b (a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b (a (a a)))) REDUCED to normal form. ------ 189814/22284795. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 189815/22284804. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a (^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a (^z.z))) REDUCED to normal form. ------ 189816/22284912. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a a)(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a a)(a (a a)))) 7. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 189817/22284957. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(y y))(a a))) 3. ==[ beta ]==> (b ((^y.(y y))(a a))) 4. ==[ alpha ]==> (b ((^x.(x x))(a a))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 189818/22285065. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189819/22285101. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (a (^z.z)))) REDUCED to normal form. ------ 189820/22285128. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b ((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(b a)) REDUCED to normal form. ------ 189821/22285182. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.y1) a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189822/22285209. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 189823/22285227. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b (^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.a))) REDUCED to normal form. ------ 189824/22285272. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 189825/22285299. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 189826/22285326. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a a)(^x.a))) REDUCED to normal form. ------ 189827/22285353. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(((^x1.x1) a) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(((^x1.x1) a) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a) a)) 5. ==[ beta ]==> (((^y.y) b)(((^z.z) a) a)) 6. ==[ alpha ]==> (((^x.x) b)(((^y.y) a) a)) 7. ==[ beta ]==> (b (((^y.y) a) a)) 8. ==[ alpha ]==> (b (((^x.x) a) a)) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 189828/22285380. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a (^z.z)) b)) REDUCED to normal form. ------ 189829/22285407. ------ 1. ==[ start ]==> (((a b)(b a))((a a) c)) REDUCED to normal form. ------ 189830/22285434. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.a) a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.a) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a) a)) 5. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 189831/22285461. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 189832/22285515. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 189833/22285542. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 189834/22285569. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a (^x.x)) a)) REDUCED to normal form. ------ 189835/22285623. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 189836/22285641. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a)(a a))) 3. ==[ beta ]==> ((b (^y.y))((a a)(a a))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(a a))) REDUCED to normal form. ------ 189837/22285650. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.a) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y) b)) 3. ==[ beta ]==> (((a (a (^x.x)))(a a)) b) REDUCED to normal form. ------ 189838/22285677. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 189839/22285686. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189840/22285713. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189841/22297380. ------ 1. ==[ start ]==> ((^a.b)(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)(b (a (a (^y.y))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 189842/22297401. ------ 1. ==[ start ]==> (((a a)(^a.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 189843/22297416. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189844/22297461. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((((^z.(^x1.x1)) a)(a (^y1.y1)))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.x1)) 5. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.z)) 7. ==[ beta ]==> ((a (^y.y))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 189845/22297650. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ eta ]==> ((^y.y)(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 189846/22298145. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189847/22298283. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189848/22298703. ------ 1. ==[ start ]==> ((^a.((a a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((x x) x))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((b ((^y.(^z.z)) a))(b ((^y.(^z.z)) a)))(b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((b ((^x.(^y.y)) a))(b ((^z.(^x1.x1)) a)))(b ((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> (((b (^y.y))(b ((^z.(^x1.x1)) a)))(b ((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> (((b (^x.x))(b ((^y.(^z.z)) a)))(b ((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> (((b (^x.x))(b (^z.z)))(b ((^x1.(^y1.y1)) a))) 8. ==[ alpha ]==> (((b (^x.x))(b (^y.y)))(b ((^z.(^x1.x1)) a))) 9. ==[ beta ]==> (((b (^x.x))(b (^y.y)))(b (^x1.x1))) 10. ==[ alpha ]==> (((b (^x.x))(b (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 189849/22299561. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 189850/22299603. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b (^z.z)) b)) 3. ==[ beta ]==> (^y.(((b (^z.z)) b)((b (^z.z)) b))) 4. ==[ alpha ]==> (^x.(((b (^y.y)) b)((b (^z.z)) b))) REDUCED to normal form. ------ 189851/22301136. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(b (^y.y)))) REDUCED to normal form. ------ 189852/22301241. ------ 1. ==[ start ]==> ((^a.(b a))((b a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(b x))((b a)(a (a a)))) 3. ==[ eta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 189853/22301790. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189854/22302558. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 189855/22302681. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189856/22303503. ------ 1. ==[ start ]==> (((a b)(^c.a))(^d.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 189857/22303530. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 189858/22304421. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 189859/22304691. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(^b.(b a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.(y a))) REDUCED to normal form. ------ 189860/22305075. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 189861/22305465. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189862/22306986. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.y))) REDUCED to normal form. ------ 189863/22307055. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 189864/22307157. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.((a a) a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.((a a) a))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.((a a) a))) REDUCED to normal form. ------ 189865/22307478. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b ((^z.z)(^x1.x1)))((b ((^z.z)(^x1.x1)))(^y.y))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((b ((^z.z)(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((b (^y.y))((b ((^z.z)(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((b (^x.x))((b ((^y.y)(^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((b (^x.x))((b (^z.z))(^x1.x1))) 8. ==[ alpha ]==> ((b (^x.x))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 189866/22307931. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 189867/22308066. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 189868/22308351. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189869/22308561. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((^x.x)(a a))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.z)) 5. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 189870/22308750. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(z (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 189871/22308801. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(b a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(b a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189872/22308813. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^c.(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 189873/22308942. ------ 1. ==[ start ]==> (((a a) a)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(^y.y)) 4. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 189874/22308951. ------ 1. ==[ start ]==> ((a b)(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((a b)(b (a (a (^x.x))))) REDUCED to normal form. ------ 189875/22308969. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 189876/22308987. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 189877/22309005. ------ 1. ==[ start ]==> (((a a)(a a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(a a))((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 189878/22309032. ------ 1. ==[ start ]==> ((a (a (^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 189879/22309167. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((b a)(a b))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((b a)(a b))) REDUCED to normal form. ------ 189880/22309194. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 189881/22309221. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a a)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 189882/22309410. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> (((a a) a)((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> (((a a) a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 189883/22309500. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((^y.(y y))((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((^x.(x x))((b (^y.y))(^z.a))) 5. ==[ beta ]==> (((b (^y.y))(^z.a))((b (^y.y))(^z.a))) 6. ==[ alpha ]==> (((b (^x.x))(^y.a))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 189884/22309527. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 189885/22309563. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 189886/22309590. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a (a a)) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 189887/22309608. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((b a)(^y.b))) 3. ==[ beta ]==> ((a (a a))((b a)(^y.b))) 4. ==[ alpha ]==> ((a (a a))((b a)(^x.b))) REDUCED to normal form. ------ 189888/22309635. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 189889/22309644. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 189890/22309671. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 189891/22309698. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(b a))) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 189892/22309716. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 189893/22309806. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.a)(b (^z.z)))) 3. ==[ beta ]==> ((b b)((^y.a)(b (^z.z)))) 4. ==[ alpha ]==> ((b b)((^x.a)(b (^y.y)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 189894/22309851. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189895/22309878. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 5. ==[ beta ]==> ((a (a (^y.y))) a) 6. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 189896/22309932. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b (^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1)) c)) 5. ==[ beta ]==> ((^y.y)((b (^y1.y1)) c)) 6. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 7. ==[ beta ]==> ((b (^y.y)) c) 8. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 189897/22309995. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 189898/22310103. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 189899/22310274. ------ 1. ==[ start ]==> ((a ((a a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((a a) a))(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((a ((a a) a))(b (^y.y))) 4. ==[ alpha ]==> ((a ((a a) a))(b (^x.x))) REDUCED to normal form. ------ 189900/22310310. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 (^z1.z1))) a)) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 (^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((^y.(y (^z.z))) a) 6. ==[ alpha ]==> ((^x.(x (^y.y))) a) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 189901/22310625. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (a a))((^x.x) b))) 3. ==[ beta ]==> (((a a)((a a) a))((a (a a)) b)) REDUCED to normal form. ------ 189902/22310652. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a ((a a)(a a)))) REDUCED to normal form. ------ 189903/22310679. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))((a (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> ((a (a (a a)))((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 189904/22310706. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a)) a)((a a)((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a (a a)) a)((a a)((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a (a a)) a)((a a)(^y.y))) 6. ==[ alpha ]==> (((a (a a)) a)((a a)(^x.x))) REDUCED to normal form. ------ 189905/22310796. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((^y.b)(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((^x.b)(((a a)(a a))(^y.a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 189906/22310877. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b a)(^z.a))) IRREDUCIBLE: cycle. ------ 189907/22310940. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 189908/22310958. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 189909/22310967. ------ 1. ==[ start ]==> (((a b) a)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 189910/22310994. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.a)(b a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(b a))) 3. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 189911/22311012. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 9. ==[ beta ]==> (^y.(^z.(^x1.x1))) 10. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 189912/22311048. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(((^x1.x1) b)((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)((^x1.x1) b))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(b ((^x1.x1) b))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.z) b))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 189913/22311075. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x))) a) REDUCED to normal form. ------ 189914/22311102. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(b (^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 189915/22311129. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 189916/22311147. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (b (((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 189917/22311174. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a (^x.(a a)))((b (^y.y)) b)) REDUCED to normal form. ------ 189918/22311345. ------ 1. ==[ start ]==> (((^a.b) b)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 189919/22311840. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 189920/22311867. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(a ((^y.y) b))) 5. ==[ beta ]==> (((a (^x.x))(a b))(a b)) REDUCED to normal form. ------ 189921/22311894. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 189922/22311921. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a a)(b (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a a)(b (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(b (^y.y)))) REDUCED to normal form. ------ 189923/22311993. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 189924/22312092. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.a)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 189925/22312227. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 189926/22312236. ------ 1. ==[ start ]==> (((a b) c)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)((^x.(x x))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b) c)((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 189927/22312263. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a a) b)((^y.a)((^z.z) b))) 4. ==[ alpha ]==> (((a a) b)((^x.a)((^y.y) b))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 189928/22312290. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 189929/22312335. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((b (^x1.x1)) a)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) a)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) a)) 5. ==[ beta ]==> ((b (^y.y)) a) 6. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 189930/22312371. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 189931/22312389. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) b) c)) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) b) c)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) b) c)) 5. ==[ beta ]==> ((((a a) a)((a a) a))(b c)) REDUCED to normal form. ------ 189932/22312425. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189933/22312479. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 189934/22312506. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(a a))(^y1.b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(a a))(^y1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 189935/22312533. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 189936/22312677. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b ((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b ((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b ((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b ((a a)(a a)))) 7. ==[ beta ]==> ((^y.y)(b ((a a)(a a)))) 8. ==[ alpha ]==> ((^x.x)(b ((a a)(a a)))) 9. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 189937/22312704. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(a (b (^x.x)))) REDUCED to normal form. ------ 189938/22312731. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((a b) a)(((a a)(a a))(a a))) REDUCED to normal form. ------ 189939/22312758. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(b (a (^z.z)))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(b (a (^y.y)))) REDUCED to normal form. ------ 189940/22312785. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 189941/22312812. ------ 1. ==[ start ]==> ((a (b a))((b a)(a (a a)))) REDUCED to normal form. ------ 189942/22313046. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(b (^y.(a a)))) REDUCED to normal form. ------ 189943/22313091. ------ 1. ==[ start ]==> (((^a.a)(b a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b a))(((a a)(a a))(^y.y))) 3. ==[ beta ]==> ((b a)(((a a)(a a))(^y.y))) 4. ==[ alpha ]==> ((b a)(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 189944/22313118. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 189945/22313154. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 189946/22313172. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((b a)(^y.(y y)))) 3. ==[ beta ]==> (((a b)(a b))((b a)(^y.(y y)))) 4. ==[ alpha ]==> (((a b)(a b))((b a)(^x.(x x)))) REDUCED to normal form. ------ 189947/22313235. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 189948/22313253. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a b)(^y.b))) 3. ==[ beta ]==> (b ((a b)(^y.b))) 4. ==[ alpha ]==> (b ((a b)(^x.b))) REDUCED to normal form. ------ 189949/22313262. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.b)(a b))) 3. ==[ beta ]==> (((a b)(^x.(x x))) b) REDUCED to normal form. ------ 189950/22313289. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.a)) a) REDUCED to normal form. ------ 189951/22313316. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 189952/22313361. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 189953/22313820. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> (b ((^x1.x1) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 189954/22314072. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(c (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(c (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(c (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(c (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.b)(c (^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 189955/22314126. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 189956/22314153. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.z)(a a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.z)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(a a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 189957/22314180. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 189958/22314225. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189959/22314252. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 189960/22315044. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(c (^d.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(c (^y.a))) REDUCED to normal form. ------ 189961/22315071. ------ 1. ==[ start ]==> (((a b)(^c.a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 189962/22315098. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(a (^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 189963/22315125. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 189964/22315170. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((a a)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189965/22315206. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 189966/22315989. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(a (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 189967/22316007. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((b a)(^y.y))) 3. ==[ beta ]==> (((b a)(b a))((b a)(^y.y))) 4. ==[ alpha ]==> (((b a)(b a))((b a)(^x.x))) REDUCED to normal form. ------ 189968/22316070. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 189969/22316088. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((a b)(^y.(y y)))) 3. ==[ beta ]==> (b ((a b)(^y.(y y)))) 4. ==[ alpha ]==> (b ((a b)(^x.(x x)))) REDUCED to normal form. ------ 189970/22316097. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.b)) b) REDUCED to normal form. ------ 189971/22316151. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 189972/22316196. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1) a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189973/22316205. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 189974/22316232. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 189975/22316259. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.y)(b a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(b a)) REDUCED to normal form. ------ 189976/22316511. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b ((a a)(^z.z)))) REDUCED to normal form. ------ 189977/22316565. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((a a)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 189978/22316592. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((b (a (^x.x)))((a a)(a (^z.z)))) 6. ==[ alpha ]==> ((b (a (^x.x)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 189979/22316619. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((a b)((^x.x) a))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a b) a)) REDUCED to normal form. ------ 189980/22316646. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 189981/22316817. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 189982/22316925. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 189983/22316961. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(y y))((a a) a))) 3. ==[ beta ]==> ((b c)((^y.(y y))((a a) a))) 4. ==[ alpha ]==> ((b c)((^x.(x x))((a a) a))) 5. ==[ beta ]==> ((b c)(((a a) a)((a a) a))) REDUCED to normal form. ------ 189984/22316988. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)(a b))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 189985/22317033. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 189986/22317060. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((a a)(^z.z)) a)) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z)) a)) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y)) a)) 5. ==[ beta ]==> (((a a)(^y.y)) a) 6. ==[ alpha ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 189987/22317096. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 189988/22317114. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a b) c)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a b) c)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a b) c)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a b) c)) REDUCED to normal form. ------ 189989/22317123. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 189990/22317204. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.a)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 189991/22317231. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 189992/22317429. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a (a a))(^z.z))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 189993/22317456. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a ((a a) a))) REDUCED to normal form. ------ 189994/22317483. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (^z.z))(a b))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (^z.z))(a b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.y))(a b))) 5. ==[ beta ]==> ((a b)((a (^y.y))(a b))) 6. ==[ alpha ]==> ((a b)((a (^x.x))(a b))) REDUCED to normal form. ------ 189995/22317510. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 189996/22317978. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> (b ((^x1.(a a)) a)) 4. ==[ alpha ]==> (b ((^x.(a a)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 189997/22318203. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.b)(a a))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)(a a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)(a a))) 5. ==[ beta ]==> (a ((^y.b)(a a))) 6. ==[ alpha ]==> (a ((^x.b)(a a))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 189998/22318221. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 189999/22318248. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 7. ==[ beta ]==> ((^y.y)(^z.a)) 8. ==[ alpha ]==> ((^x.x)(^y.a)) 9. ==[ beta ]==> (^y.a) 10. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 190000/22318302. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b b)(((^y.y) a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)(^y.(^z.z)))) 9. ==[ beta ]==> ((b b)(a (^y.(^z.z)))) 10. ==[ alpha ]==> ((b b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 190001/22318311. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 190002/22318338. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190003/22318383. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a b) a)) 3. ==[ beta ]==> (b ((a b) a)) REDUCED to normal form. ------ 190004/22318392. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 190005/22318419. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 190006/22318446. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 190007/22318500. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 190008/22318527. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 190009/22318554. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.b)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.b)) REDUCED to normal form. ------ 190010/22318626. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 190011/22318644. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a (a a)) a)) REDUCED to normal form. ------ 190012/22318671. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a (a (a a)))) REDUCED to normal form. ------ 190013/22318698. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a (^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a (^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 190014/22318725. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a a)((a a) a))) 3. ==[ beta ]==> (((a (a a)) b)((a a)((a a) a))) REDUCED to normal form. ------ 190015/22319040. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 190016/22319049. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(b (^z.z))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(b (^y.y))) REDUCED to normal form. ------ 190017/22319445. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.a))) 5. ==[ beta ]==> (b ((^y.a)(^z.a))) 6. ==[ alpha ]==> (b ((^x.a)(^y.a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 190018/22319472. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 190019/22319499. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 190020/22319517. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 5. ==[ beta ]==> ((^y.(^z.z)) a) 6. ==[ alpha ]==> ((^x.(^y.y)) a) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190021/22319571. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a) c)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a) c)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a) c)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 190022/22319607. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(y y)))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 190023/22319634. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 190024/22319652. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (a a))(^y.y))) 3. ==[ beta ]==> (b ((a (a a))(^y.y))) 4. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 190025/22319715. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 190026/22319760. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190027/22319796. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 190028/22319823. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 190029/22319895. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^b.a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.a) b)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a) b)) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 190030/22319922. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 190031/22319940. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)((^y.y) a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))((a a) a)) REDUCED to normal form. ------ 190032/22319994. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(c b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(c b)) 3. ==[ beta ]==> ((a (b (^y.y)))(c b)) 4. ==[ alpha ]==> ((a (b (^x.x)))(c b)) REDUCED to normal form. ------ 190033/22320021. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b c)) REDUCED to normal form. ------ 190034/22320102. ------ 1. ==[ start ]==> (((a b)(b a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(b (a (^x.x)))) REDUCED to normal form. ------ 190035/22320129. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a ((^z.z) a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a ((^z.z) a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a ((^y.y) a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 190036/22320156. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a (^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^z.z))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))(a a))) REDUCED to normal form. ------ 190037/22320237. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b b)) 5. ==[ beta ]==> ((b (^y.y))(b b)) 6. ==[ alpha ]==> ((b (^x.x))(b b)) REDUCED to normal form. ------ 190038/22320318. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (a (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 190039/22320336. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(b (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(b (^z.z))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.z))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 190040/22320345. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a a)(a a))) REDUCED to normal form. ------ 190041/22320372. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(b a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(b a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b a)) REDUCED to normal form. ------ 190042/22320381. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190043/22320408. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a a) a)) 3. ==[ beta ]==> ((^y.y)((a a) a)) 4. ==[ alpha ]==> ((^x.x)((a a) a)) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 190044/22320555. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((^y1.y1)(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190045/22331940. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190046/22332093. ------ 1. ==[ start ]==> ((^a.b)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 190047/22332129. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a ((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190048/22332132. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^z.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 190049/22332291. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (^y.((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> (^x.((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 190050/22332534. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 190051/22332582. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 190052/22332984. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190053/22333455. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(y1 (y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^y1.(y1 (y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 5. ==[ beta ]==> (^y.(y (y (^z.z)))) 6. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 190054/22333749. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 190055/22333878. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 190056/22334523. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.b)(^x1.(^y1.y1)))((^z.b)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.b)(^z.(^x1.x1)))((^y1.b)(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.b)(^z.(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (b ((^x1.b)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 190057/22334697. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> (((^x.b)(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (b (^x1.(^y1.y1))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 190058/22335198. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((((^z.(^x1.(^y1.y1)))(a (a a)))((^z.(^x1.(^y1.y1)))(a (a a))))(^y.y)) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.(^z1.z1)))(a (a a))))(^x2.x2)) 5. ==[ beta ]==> (((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a (a a))))(^x2.x2)) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (a a))))(^z1.z1)) 7. ==[ beta ]==> ((^y.y)(^z1.z1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190059/22336578. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(^z.((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(^z.((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.((a a)(a a)))) 6. ==[ alpha ]==> ((a (a a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 190060/22337262. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> (b (^x1.((^y1.y1) b))) 4. ==[ alpha ]==> (b (^x.((^y.y) b))) 5. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 190061/22337604. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(^y.((^z.z) y))) 3. ==[ eta ]==> ((((^x.x)(a a))(a (a a)))(^z.z)) 4. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(^y.y)) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 190062/22337709. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 190063/22338549. ------ 1. ==[ start ]==> (((a b)((a a) a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 190064/22340448. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.((x1 x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((x1 x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190065/22340682. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 190066/22340898. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^y.(a a))) REDUCED to normal form. ------ 190067/22340949. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190068/22341123. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> (b (^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(x x)))) 5. ==[ beta ]==> (b (^x.(x x))) REDUCED to normal form. ------ 190069/22341768. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 190070/22341897. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.(^z1.b))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.b))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 190071/22342059. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.((a a) a))) REDUCED to normal form. ------ 190072/22342191. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y1.(^z1.z1)))(((^z.(^x1.x1))(^y1.(^z1.z1)))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1))(^x2.(^y2.y2)))(^z2.z2))) 5. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1))(^x2.(^y2.y2)))(^z2.z2))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.(^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1)))(^z1.z1)) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 9. ==[ beta ]==> ((^y.y)(^y1.y1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190073/22342662. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190074/22343064. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190075/22343112. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 190076/22343193. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1) a))) 6. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) a))) 7. ==[ beta ]==> (b (^y.((^z.z) a))) 8. ==[ alpha ]==> (b (^x.((^y.y) a))) 9. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 190077/22343274. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(^x1.a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(^x1.a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 190078/22343355. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.z))) REDUCED to normal form. ------ 190079/22343409. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(a (^y.y)))) REDUCED to normal form. ------ 190080/22343463. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 190081/22343514. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190082/22343517. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 190083/22343553. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^a.b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.b)) 3. ==[ beta ]==> ((^y.y)(^y1.b)) 4. ==[ alpha ]==> ((^x.x)(^y.b)) 5. ==[ beta ]==> (^y.b) 6. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 190084/22343673. ------ 1. ==[ start ]==> ((a b)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 190085/22343682. ------ 1. ==[ start ]==> (((^a.a)(a a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))(b (a (a (^y.y))))) 3. ==[ beta ]==> ((a a)(b (a (a (^y.y))))) 4. ==[ alpha ]==> ((a a)(b (a (a (^x.x))))) REDUCED to normal form. ------ 190086/22343709. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 190087/22343718. ------ 1. ==[ start ]==> (((^a.a) b)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 190088/22343745. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((^y.(y (^z.z))) b) 6. ==[ alpha ]==> ((^x.(x (^y.y))) b) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190089/22343763. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190090/22343790. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 190091/22343817. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 190092/22343844. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190093/22343871. ------ 1. ==[ start ]==> ((a (^b.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.a))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 190094/22343952. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.a)(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 190095/22343979. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 190096/22344033. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))((^z.z) b))) 7. ==[ beta ]==> (a ((^y.y)((^z.z) b))) 8. ==[ alpha ]==> (a ((^x.x)((^y.y) b))) 9. ==[ beta ]==> (a ((^y.y) b)) 10. ==[ alpha ]==> (a ((^x.x) b)) 11. ==[ beta ]==> (a b) REDUCED to normal form. ------ 190097/22344060. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 190098/22344114. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.(x x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 190099/22344132. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(b (^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a) a)(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a a) a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 190100/22344159. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 190101/22344186. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a (a a))((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a a))((a a)(^y.y))) 6. ==[ alpha ]==> ((a (a a))((a a)(^x.x))) REDUCED to normal form. ------ 190102/22344204. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 190103/22344285. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 190104/22344339. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((b a)(^y.b))) REDUCED to normal form. ------ 190105/22344366. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 190106/22344483. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 190107/22344510. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((a (a (^x.x)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 190108/22344537. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.a)(b (^y.y)))) 3. ==[ beta ]==> (((a (a a))(a a)) a) REDUCED to normal form. ------ 190109/22344564. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 190110/22344663. ------ 1. ==[ start ]==> (((a (a a)) b)((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (a a)) b)((b (^x.x)) c)) REDUCED to normal form. ------ 190111/22344915. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 190112/22345032. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a (a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a (a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (a (a (^y.y))))) 5. ==[ beta ]==> (a (a (a (^y.y)))) 6. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 190113/22345086. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((b (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (a ((b (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (a ((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 190114/22345122. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(a a)) d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a)) d)) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a)) d)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a)) d)) 5. ==[ beta ]==> (b ((^y.(a a)) d)) 6. ==[ alpha ]==> (b ((^x.(a a)) d)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 190115/22345167. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((a (^x.(^y.y)))(^x1.x1))) 6. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 190116/22345194. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.y)((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((b a)((a a) a))) 5. ==[ beta ]==> ((b a)((a a) a)) REDUCED to normal form. ------ 190117/22345248. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))((^z.z)(a a)))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(a a)))) 9. ==[ beta ]==> ((a a)((a a)((^y.y)(a a)))) 10. ==[ alpha ]==> ((a a)((a a)((^x.x)(a a)))) 11. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 190118/22345329. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.b))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 190119/22345455. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(a (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 190120/22345500. ------ 1. ==[ start ]==> (((^a.b) a)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 190121/22345662. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a) b)((a a)(^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a) b)((a a)(^x.(a a)))) REDUCED to normal form. ------ 190122/22345689. ------ 1. ==[ start ]==> (((a b) a)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 190123/22345770. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (a a))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 190124/22345878. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a b)(^x.x))((^z.z) a)) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y) a)) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 190125/22345968. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 190126/22345995. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 190127/22346076. ------ 1. ==[ start ]==> (((a b)(a a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 190128/22346103. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 190129/22346274. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (b (a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (b (a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 190130/22346328. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a)(a a))(a (^y.y)))) 5. ==[ beta ]==> ((a a)(((a a)(a a))(a (^y.y)))) 6. ==[ alpha ]==> ((a a)(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 190131/22346337. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a)) c)) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 190132/22346355. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> (((^y.y) b)((^z.z) a)) 6. ==[ alpha ]==> (((^x.x) b)((^y.y) a)) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 190133/22346409. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b a)((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b a)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((b a)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((b a)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)((b a)((^z.z)(^x1.x1)))) 10. ==[ alpha ]==> ((^x.x)((b a)((^y.y)(^z.z)))) 11. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 12. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 13. ==[ beta ]==> ((b a)(^y.y)) 14. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 190134/22346490. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (b ((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 190135/22346715. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (b (((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 190136/22346724. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 190137/22346751. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 190138/22346778. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 190139/22346958. ------ 1. ==[ start ]==> (((a b) c)((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 190140/22346985. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)(^y.y))) 5. ==[ beta ]==> (((a a) b)(a (^y.y))) 6. ==[ alpha ]==> (((a a) b)(a (^x.x))) REDUCED to normal form. ------ 190141/22347066. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((b (^z.z)) a)) REDUCED to normal form. ------ 190142/22347093. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(a a)) b)) 3. ==[ beta ]==> ((a (^y.b))(((a a)(a a)) b)) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(a a)) b)) REDUCED to normal form. ------ 190143/22347345. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a b))((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a b))((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a b))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 190144/22347372. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.a)(^y.y))) 3. ==[ beta ]==> (((a (a a))((a a) a)) a) REDUCED to normal form. ------ 190145/22347624. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a b)(a b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a b)(a b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a b)(a b))) 5. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 190146/22347705. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 190147/22347876. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 190148/22347903. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((b a)(^y.(y y)))) REDUCED to normal form. ------ 190149/22347957. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 190150/22347984. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a b)(^y.b))) REDUCED to normal form. ------ 190151/22348011. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 190152/22348101. ------ 1. ==[ start ]==> (((a a)(b a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 190153/22348128. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 190154/22348155. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((^y.y)((a a)(a a)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)((a a)(a a)))) 7. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 190155/22348182. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(a a))(^y.y))) 3. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 190156/22348209. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 190157/22348236. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 190158/22348317. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 190159/22348461. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(c (a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(c (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a a)(c (a (^x.(^y.y))))) REDUCED to normal form. ------ 190160/22348542. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> (b (((^x1.x1) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 190161/22348650. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1)(a a))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190162/22348677. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a b)((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)((a a) a))) REDUCED to normal form. ------ 190163/22348704. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((a a) a)(a b))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a b))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a b))) 5. ==[ beta ]==> (((a a) a)(a b)) REDUCED to normal form. ------ 190164/22348758. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (a a))((a a)(^z.z)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a))((a a)(^y.y)))) 7. ==[ beta ]==> (((a a)(a a))((a (a a))((a a)(^y.y)))) 8. ==[ alpha ]==> (((a a)(a a))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 190165/22348839. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a a)((^x1.x1) b))) 3. ==[ beta ]==> (b ((a a)((^x1.x1) b))) 4. ==[ alpha ]==> (b ((a a)((^x.x) b))) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 190166/22348875. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 190167/22348902. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 190168/22348956. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a)(^x1.x1))(^y1.(y1 y1)))) REDUCED to normal form. ------ 190169/22348992. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 190170/22349019. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.b)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(b a)) b) REDUCED to normal form. ------ 190171/22349073. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 190172/22349100. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.(y y))((a a)(^z.z)))) 6. ==[ alpha ]==> ((a b)((^x.(x x))((a a)(^y.y)))) 7. ==[ beta ]==> ((a b)(((a a)(^y.y))((a a)(^y.y)))) 8. ==[ alpha ]==> ((a b)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 190173/22349127. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.a)(b a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.a)(b a))) 3. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 190174/22349154. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 190175/22349181. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.y)((^z.z) b))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)((^y.y) b))) 5. ==[ beta ]==> (((a a)(a (a a)))((^y.y) b)) 6. ==[ alpha ]==> (((a a)(a (a a)))((^x.x) b)) 7. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 190176/22349208. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 190177/22349253. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((b a) c)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190178/22349289. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 190179/22349460. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(c (b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c (b a))) 3. ==[ beta ]==> (b (c (b a))) REDUCED to normal form. ------ 190180/22349568. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((b a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190181/22349604. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z)) d)) 3. ==[ beta ]==> ((b a)((^y.(^z.z)) d)) 4. ==[ alpha ]==> ((b a)((^x.(^y.y)) d)) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 190182/22349622. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (b (((^y.y)(a a))(a (a a)))) 6. ==[ alpha ]==> (b (((^x.x)(a a))(a (a a)))) 7. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 190183/22349649. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 190184/22349703. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((^x1.x1)(a b))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)(a b))) 7. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a b)) REDUCED to normal form. ------ 190185/22349784. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a (^y.y))(b a))) 3. ==[ beta ]==> (b ((a (^y.y))(b a))) 4. ==[ alpha ]==> (b ((a (^x.x))(b a))) REDUCED to normal form. ------ 190186/22349847. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 190187/22349901. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.a))) REDUCED to normal form. ------ 190188/22349928. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.x))((a a)(^z.(z z)))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 190189/22349964. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 190190/22350018. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 190191/22350045. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a)(a a))) REDUCED to normal form. ------ 190192/22350072. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.a)((a a)(^z.z)))) 7. ==[ beta ]==> ((a a)((^y.a)((a a)(^z.z)))) 8. ==[ alpha ]==> ((a a)((^x.a)((a a)(^y.y)))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 190193/22350099. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y))(b a))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.x)) REDUCED to normal form. ------ 190194/22350126. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.x)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b)((a a) a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)((a a) a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 190195/22350153. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.z1))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.y1))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 190196/22350234. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a a)) REDUCED to normal form. ------ 190197/22350261. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 190198/22350459. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((b a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((b a)(a a))) 3. ==[ beta ]==> (b ((b a)(a a))) REDUCED to normal form. ------ 190199/22350567. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((a a) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190200/22350648. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a a))(a ((^y.y)(a a)))) 6. ==[ alpha ]==> (((a a)(a a))(a ((^x.x)(a a)))) 7. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 190201/22350675. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 190202/22350792. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)(^y.a))) REDUCED to normal form. ------ 190203/22350819. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a b)(^y.(y y)))) REDUCED to normal form. ------ 190204/22350873. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.a)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.a)) REDUCED to normal form. ------ 190205/22350927. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a (^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a (^x1.(a a)))) REDUCED to normal form. ------ 190206/22350954. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 190207/22351044. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 190208/22351071. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 190209/22351098. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b)(^y.(y y)))) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 190210/22351152. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 190211/22351179. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(x x))(^y.b))) 3. ==[ beta ]==> (((a b)(a b))((^y.b)(^y.b))) 4. ==[ alpha ]==> (((a b)(a b))((^x.b)(^y.b))) 5. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 190212/22351206. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 190213/22351458. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2) a)(a b))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2) a)(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190214/22351683. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (a a))(^y.a))) 3. ==[ beta ]==> ((b c)((a (a a))(^y.a))) 4. ==[ alpha ]==> ((b c)((a (a a))(^x.a))) REDUCED to normal form. ------ 190215/22351710. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x) a)(^y.b))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a (^y.b))) 4. ==[ alpha ]==> ((((a a)(a a)) b)(a (^x.b))) REDUCED to normal form. ------ 190216/22351818. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((a (^x.x))((a a) b)) REDUCED to normal form. ------ 190217/22351845. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a b) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a b) c)) REDUCED to normal form. ------ 190218/22352025. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(a ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190219/22352061. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(a a)) b)) 3. ==[ beta ]==> ((b (^y.a))((^z.(a a)) b)) 4. ==[ alpha ]==> ((b (^x.a))((^y.(a a)) b)) 5. ==[ beta ]==> ((b (^x.a))(a a)) REDUCED to normal form. ------ 190220/22352088. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.b) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 190221/22352205. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(c (^z.b))) 3. ==[ beta ]==> ((a ((^y.y) b))(c (^z.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))(c (^y.b))) 5. ==[ beta ]==> ((a b)(c (^y.b))) 6. ==[ alpha ]==> ((a b)(c (^x.b))) REDUCED to normal form. ------ 190222/22352232. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b (^z.(a a)))) REDUCED to normal form. ------ 190223/22352259. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(a (^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 190224/22352286. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(a a))(a a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 190225/22352313. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(a a))((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 190226/22352340. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(a b))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 190227/22352367. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 190228/22352421. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) a) REDUCED to normal form. ------ 190229/22352448. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(a b))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(a b))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 190230/22352475. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 190231/22352529. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 190232/22352700. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> (b (a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b (a ((^x.x)(a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 190233/22352808. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190234/22352925. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a b)(^z.z))) 3. ==[ beta ]==> (((^y.y) a)((a b)(^z.z))) 4. ==[ alpha ]==> (((^x.x) a)((a b)(^y.y))) 5. ==[ beta ]==> (a ((a b)(^y.y))) 6. ==[ alpha ]==> (a ((a b)(^x.x))) REDUCED to normal form. ------ 190235/22353033. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 190236/22353114. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b) a)) REDUCED to normal form. ------ 190237/22353141. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((a a) a) b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((a a) a) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a) b)) REDUCED to normal form. ------ 190238/22353168. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1) c)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z) c)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) c) REDUCED to normal form. ------ 190239/22353348. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.z))) REDUCED to normal form. ------ 190240/22353447. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b (^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b (^y.a))) 3. ==[ beta ]==> (((a (a a)) b)(b (^y.a))) 4. ==[ alpha ]==> (((a (a a)) b)(b (^x.a))) REDUCED to normal form. ------ 190241/22353474. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(a (^y1.b))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(a (^y1.b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(a (^x1.b))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.b))) REDUCED to normal form. ------ 190242/22353501. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^c.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(a a))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 190243/22353528. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 190244/22353555. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> (((a a)(a a))(a ((^y.y) a))) 10. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) a))) 11. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 190245/22353582. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 190246/22353636. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.y1)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a) a)) REDUCED to normal form. ------ 190247/22353663. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^c.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)(^z.z))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)(^z.z))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)(^y.y))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 190248/22353690. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 190249/22353744. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((a a)((^y.a)(^z.(z z)))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.(y y)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 190250/22353771. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 190251/22353780. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(b ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(b ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b ((^z.z)(^x1.x1)))(^y.y)) 6. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.z)) 7. ==[ beta ]==> ((b (^y.y))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 190252/22354167. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a) c)) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a) c)) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a) c)) 5. ==[ beta ]==> (b (((^y.y) a) c)) 6. ==[ alpha ]==> (b (((^x.x) a) c)) 7. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 190253/22354212. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b (a (a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))(b (a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (a (a a)))) REDUCED to normal form. ------ 190254/22354239. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(a ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (a ((^y.y)(^z.z))) 6. ==[ alpha ]==> (a ((^x.x)(^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 190255/22354293. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y) a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x) a)(a (^y.y)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (a (^y.y)))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (a (^x.x)))) REDUCED to normal form. ------ 190256/22354437. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 190257/22354518. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a) b)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 190258/22354599. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(y1 y1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1)) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190259/22354617. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(((^z.z) a)(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(a a))) 5. ==[ beta ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 190260/22354626. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^b.a) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.a) b)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 190261/22354644. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 190262/22354662. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b (^b.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b (^y.a))) REDUCED to normal form. ------ 190263/22354689. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(z z)))) REDUCED to normal form. ------ 190264/22354716. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.a)(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.a)(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(a a))) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 190265/22354743. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 190266/22354770. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)((^z.z) a))) 7. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 8. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 9. ==[ beta ]==> (b ((^y.y) a)) 10. ==[ alpha ]==> (b ((^x.x) a)) 11. ==[ beta ]==> (b a) REDUCED to normal form. ------ 190267/22354797. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 190268/22354824. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 190269/22354851. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.a)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 190270/22354932. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a (^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (^z.a))) REDUCED to normal form. ------ 190271/22354959. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(a a))) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 190272/22354986. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(a (^y.y))) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 190273/22355040. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 190274/22355058. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 190275/22355067. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(b (^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(b (^y.y))) REDUCED to normal form. ------ 190276/22355094. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 190277/22355103. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(b a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190278/22355130. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(a b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(a b)) 3. ==[ beta ]==> ((^y.y)(a b)) 4. ==[ alpha ]==> ((^x.x)(a b)) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 190279/22355286. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190280/22366671. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190281/22366869. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190282/22366872. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 190283/22366881. ------ 1. ==[ start ]==> (((^a.a) b)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^y.((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^x.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 190284/22366914. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> (((^z.(z (^x1.x1))) b)(^y.y)) 4. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.z)) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 190285/22367373. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((^y.(^z.z)) a)(^x1.(^y1.y1)))((((^y.(^z.z)) a)(^x1.(^y1.y1)))(((^y.(^z.z)) a)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))(((^z2.(^x3.x3)) a)(^y3.(^z3.z3))))) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))(((^z2.(^x3.x3)) a)(^y3.(^z3.z3))))) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))(((^y2.(^z2.z2)) a)(^x3.(^y3.y3))))) 7. ==[ beta ]==> ((^y.(^z.z))((((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))(((^y2.(^z2.z2)) a)(^x3.(^y3.y3))))) 8. ==[ alpha ]==> ((^x.(^y.y))((((^z.(^x1.x1)) a)(^y1.(^z1.z1)))(((^x2.(^y2.y2)) a)(^z2.(^x3.x3))))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190286/22367598. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(b a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190287/22367763. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 190288/22368195. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 190289/22368669. ------ 1. ==[ start ]==> ((^a.(a b))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b (^y.y))(^z.(^x1.x1))) b) 4. ==[ alpha ]==> (((b (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 190290/22369032. ------ 1. ==[ start ]==> (((^a.b)(a a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b (^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b (^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 190291/22369446. ------ 1. ==[ start ]==> (((a b) b)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) b)(^x.((^y.(^z.z)) x))) 3. ==[ eta ]==> (((a b) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) b)(^x.(^y.y))) REDUCED to normal form. ------ 190292/22369938. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a (^z.(^x1.x1)))(^y1.(y1 y1)))((a (^z.(^x1.x1)))(^y1.(y1 y1))))(^y.y)) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))(^z.(z z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1))))(^x2.x2)) REDUCED to normal form. ------ 190293/22370220. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 190294/22371243. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(b a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190295/22372011. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 190296/22372134. ------ 1. ==[ start ]==> ((^a.(^b.b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190297/22372983. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 190298/22373289. ------ 1. ==[ start ]==> (((a b)((a a) a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 190299/22373892. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((b a)(b a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 190300/22374945. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.((a a)(^z.z)))) 5. ==[ beta ]==> (^y.((a a)(^z.z))) 6. ==[ alpha ]==> (^x.((a a)(^y.y))) REDUCED to normal form. ------ 190301/22375188. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190302/22375197. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.((x1 x1)(^y1.y1)))) REDUCED to normal form. ------ 190303/22375689. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a b) b)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a b) b)) 3. ==[ eta ]==> ((^y.(^z.z))((a b) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190304/22375863. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (b (^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 190305/22376268. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(a z))) 3. ==[ eta ]==> (((^x.b)((a a)(^y.y))) a) 4. ==[ beta ]==> (b a) REDUCED to normal form. ------ 190306/22377402. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190307/22377537. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 190308/22377645. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190309/22377762. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(y1 (y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(y1 (y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 (x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190310/22377804. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(c (^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190311/22377933. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.a))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.a))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.a))) 7. ==[ beta ]==> (b (^y.(^z.a))) 8. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 190312/22378095. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.c)) REDUCED to normal form. ------ 190313/22378221. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 190314/22378254. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.y1) b)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190315/22378257. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.x1)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 190316/22378266. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190317/22378293. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> ((^y.y)(^y1.(a a))) 4. ==[ alpha ]==> ((^x.x)(^y.(a a))) 5. ==[ beta ]==> (^y.(a a)) 6. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 190318/22378431. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 190319/22378440. ------ 1. ==[ start ]==> (((a a)(^a.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(b (a (a (^y.y))))) REDUCED to normal form. ------ 190320/22378458. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 190321/22378467. ------ 1. ==[ start ]==> (((^a.a) b)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (b (a ((^y.y)(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (a ((^x.x)(^y.(^z.z))))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 190322/22378476. ------ 1. ==[ start ]==> (((a a)(a a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 190323/22378494. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((a (a (^z.z)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a (^y.y)))(a a)) 6. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 190324/22378503. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> ((a (a (^x.x)))(b (^z.z))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 190325/22378521. ------ 1. ==[ start ]==> (((a a) b)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a) b)(((^x.(^y.y)) a)(a (^z.z)))) 3. ==[ beta ]==> (((a a) b)((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (((a a) b)((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (((a a) b)(a (^y.y))) 6. ==[ alpha ]==> (((a a) b)(a (^x.x))) REDUCED to normal form. ------ 190326/22378548. ------ 1. ==[ start ]==> (((a (^a.a)) a)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x)) a)((b (^y.y)) a)) REDUCED to normal form. ------ 190327/22378575. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 190328/22378602. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(b ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(b (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.z))) REDUCED to normal form. ------ 190329/22378656. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((b a)(a b))) 3. ==[ beta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 190330/22378737. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a b)(b a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a b)(b a))) REDUCED to normal form. ------ 190331/22378764. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a a)(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a a)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 190332/22378791. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 190333/22378818. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 190334/22378845. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a (b (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 190335/22378935. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a (a a))((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> ((a (a a))((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 190336/22378962. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 190337/22379052. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190338/22379079. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 190339/22379160. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 190340/22379187. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 190341/22379205. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 190342/22379232. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.z))) 7. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 8. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 190343/22379322. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190344/22379349. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 190345/22379484. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190346/22379781. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 7. ==[ beta ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 190347/22379871. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (b (((a a)(a a))((^y.y) a))) 6. ==[ alpha ]==> (b (((a a)(a a))((^x.x) a))) 7. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 190348/22379898. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> ((((a a) a) a)(b (a (a a)))) REDUCED to normal form. ------ 190349/22379952. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)((a a) a))) REDUCED to normal form. ------ 190350/22379979. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 190351/22380006. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.a))((a a)(a a))) REDUCED to normal form. ------ 190352/22380033. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)((a a)(^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190353/22380060. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a) a)(b a))) REDUCED to normal form. ------ 190354/22380231. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.(^y.y)) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 190355/22380258. ------ 1. ==[ start ]==> ((a (a b))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 190356/22380348. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) IRREDUCIBLE: cycle. ------ 190357/22380429. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 190358/22380456. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a b)((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 190359/22380537. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(b ((^y.y) b))) 8. ==[ alpha ]==> (((a (a a))(a (a a)))(b ((^x.x) b))) 9. ==[ beta ]==> (((a (a a))(a (a a)))(b b)) REDUCED to normal form. ------ 190360/22380618. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b ((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190361/22380663. ------ 1. ==[ start ]==> (((a a)(a b))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a a)(a b))((b (^x.x)) b)) REDUCED to normal form. ------ 190362/22380861. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 190363/22380888. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 190364/22380942. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 7. ==[ beta ]==> ((^y.(y y))(^z.z)) 8. ==[ alpha ]==> ((^x.(x x))(^y.y)) 9. ==[ beta ]==> ((^y.y)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190365/22381032. ------ 1. ==[ start ]==> (((a b) b)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) b)(a ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a b) b)(a (^y.y))) 4. ==[ alpha ]==> (((a b) b)(a (^x.x))) REDUCED to normal form. ------ 190366/22381059. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((b (^y.y))(a a))) 3. ==[ beta ]==> (((a a) a)((b (^y.y))(a a))) 4. ==[ alpha ]==> (((a a) a)((b (^x.x))(a a))) REDUCED to normal form. ------ 190367/22381086. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 190368/22381113. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(b ((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.b))(b a)) REDUCED to normal form. ------ 190369/22381167. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 190370/22381194. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.(y y))(((a a)(^z.z))((a a) a))) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))((a a) a))) 7. ==[ beta ]==> ((((a a)(^y.y))((a a) a))(((a a)(^y.y))((a a) a))) 8. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 190371/22381221. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((a a)(a b))) REDUCED to normal form. ------ 190372/22381248. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a b)(a a))) REDUCED to normal form. ------ 190373/22381275. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 190374/22381446. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((b (^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a) a) a)((b (^y.y))(^z.z))) 4. ==[ alpha ]==> ((((a a) a) a)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 190375/22381473. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 190376/22381500. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) b)(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.a))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.a))) REDUCED to normal form. ------ 190377/22381527. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 190378/22381698. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190379/22381779. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 190380/22381806. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(b (^z.z)))) 5. ==[ beta ]==> ((^y.y)(b (^z.z))) 6. ==[ alpha ]==> ((^x.x)(b (^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190381/22382256. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) c) REDUCED to normal form. ------ 190382/22382517. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((a (^y.y)) b)) REDUCED to normal form. ------ 190383/22382643. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a b)(a b))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (((a b)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 190384/22382724. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (b ((^y.(a a))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((a a) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 190385/22382832. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((b a)(b a))) REDUCED to normal form. ------ 190386/22382850. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(b a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(b a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 190387/22382877. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 190388/22382931. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a)(a a)) a)) REDUCED to normal form. ------ 190389/22382958. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z) b) b)) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z) b) b)) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) b) b)) 5. ==[ beta ]==> (((a a) a)(((^y.y) b) b)) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b) b)) 7. ==[ beta ]==> (((a a) a)(b b)) REDUCED to normal form. ------ 190390/22383210. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a a)((^z.a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 190391/22383408. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a a)(^z.z))) REDUCED to normal form. ------ 190392/22383435. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a b)((a a) a))) REDUCED to normal form. ------ 190393/22383516. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 190394/22383543. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)(b a))) 5. ==[ beta ]==> ((^y.b)(((^z.z) a)(b a))) 6. ==[ alpha ]==> ((^x.b)(((^y.y) a)(b a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 190395/22383588. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(b (^x1.x1))) 3. ==[ beta ]==> (b (b (^x1.x1))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 190396/22383597. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 190397/22383723. ------ 1. ==[ start ]==> ((a (^b.b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 190398/22383741. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 190399/22383768. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a b)(^y.a))) REDUCED to normal form. ------ 190400/22383795. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((a a) a)(^z.b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((a a) a)(^z.b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a) a)(^y.b))) REDUCED to normal form. ------ 190401/22383822. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))(a a))((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (((a (a a))(a a))(^y.(a a))) 8. ==[ alpha ]==> (((a (a a))(a a))(^x.(a a))) REDUCED to normal form. ------ 190402/22383849. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a b))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)((a (a a))(^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 190403/22383903. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 190404/22383930. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a a)(^y.y))) 3. ==[ beta ]==> (((a a)(a (a a)))((a a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 190405/22383957. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a) b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z) b) a)) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z) b) a)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) b) a)) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(b a)) REDUCED to normal form. ------ 190406/22384011. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((b a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((b a) c)) REDUCED to normal form. ------ 190407/22384047. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190408/22384074. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(a a))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^z1.(a a))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 190409/22384209. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.a)(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b ((^z.a)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 190410/22384326. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((b a)(a (^z.z)))) REDUCED to normal form. ------ 190411/22384353. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((b a)(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((b a)(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> ((b a)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 190412/22384380. ------ 1. ==[ start ]==> (((a a)(^b.b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.x))((a a)(a (a a)))) REDUCED to normal form. ------ 190413/22384407. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a b)(^y1.y1))) REDUCED to normal form. ------ 190414/22384488. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.(a a))((a (a a))((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.(a a))((a (a a))((^y.y)(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 190415/22384515. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 190416/22384533. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(c (^d.a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(c (^y.a))) 3. ==[ beta ]==> (b (c (^y.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 190417/22384542. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))(b a))) REDUCED to normal form. ------ 190418/22384569. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 190419/22384713. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 190420/22384767. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> ((a (b a))((^y.y)(^z.b))) 6. ==[ alpha ]==> ((a (b a))((^x.x)(^y.b))) 7. ==[ beta ]==> ((a (b a))(^y.b)) 8. ==[ alpha ]==> ((a (b a))(^x.b)) REDUCED to normal form. ------ 190421/22384794. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 190422/22384875. ------ 1. ==[ start ]==> (((a b)((a a) a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 190423/22384902. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a (^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.(^x1.x1))) a)) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1))) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 190424/22384929. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((b a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((b a) b)) REDUCED to normal form. ------ 190425/22385073. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190426/22385352. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((b b)(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> ((b b)((^y.y)((a a) a))) 6. ==[ alpha ]==> ((b b)((^x.x)((a a) a))) 7. ==[ beta ]==> ((b b)((a a) a)) REDUCED to normal form. ------ 190427/22385379. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a (a a))(a b))) REDUCED to normal form. ------ 190428/22385424. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(^z.z)))) 5. ==[ beta ]==> (c (^y.(^z.z))) 6. ==[ alpha ]==> (c (^x.(^y.y))) REDUCED to normal form. ------ 190429/22385433. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 190430/22385460. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a a)(b a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a a)(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(b a))) REDUCED to normal form. ------ 190431/22385478. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((b a)(b a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((b a)(b a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 190432/22385559. ------ 1. ==[ start ]==> (((^a.b)(a b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (b ((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 190433/22385667. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(y1 y1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190434/22385766. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((b a) a)) REDUCED to normal form. ------ 190435/22385793. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a)(^z.z)) b)) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(^z.z)) b)) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y)) b)) REDUCED to normal form. ------ 190436/22386063. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 190437/22386090. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(a a)) c)) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a a)) REDUCED to normal form. ------ 190438/22386504. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 190439/22386531. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 190440/22386585. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(a a))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 190441/22386666. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190442/22386783. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 190443/22386810. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((b (^x.a))((a a)(a a))) REDUCED to normal form. ------ 190444/22386837. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a b)(a (^z.z)))) REDUCED to normal form. ------ 190445/22387035. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 190446/22387062. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 190447/22387089. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((a a) a)(^y.a))) 3. ==[ beta ]==> (((a a)(a b))(((a a) a)(^y.a))) 4. ==[ alpha ]==> (((a a)(a b))(((a a) a)(^x.a))) REDUCED to normal form. ------ 190448/22387116. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.(z z))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(y y))) REDUCED to normal form. ------ 190449/22387197. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (^y.y))(^z.b))) 5. ==[ beta ]==> ((b a)((a (^y.y))(^z.b))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(^y.b))) REDUCED to normal form. ------ 190450/22387224. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 190451/22387278. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a b) b)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a b) b)) 3. ==[ beta ]==> ((a (^y.y))((a b) b)) 4. ==[ alpha ]==> ((a (^x.x))((a b) b)) REDUCED to normal form. ------ 190452/22387368. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 9. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190453/22387449. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 190454/22387692. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.b)(a a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.b)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.b)(a a))) 5. ==[ beta ]==> ((^y.y)((^z.b)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 7. ==[ beta ]==> ((^y.b)(a a)) 8. ==[ alpha ]==> ((^x.b)(a a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 190455/22387719. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.a)(a (^z.z))) 6. ==[ alpha ]==> ((^x.a)(a (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 190456/22387773. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))(a (a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))(a (a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))(a (a a)))) 7. ==[ beta ]==> ((b b)((^y.(y y))(a (a a)))) 8. ==[ alpha ]==> ((b b)((^x.(x x))(a (a a)))) 9. ==[ beta ]==> ((b b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 190457/22387854. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.z)(a b))) 3. ==[ beta ]==> (b ((^z.z)(a b))) 4. ==[ alpha ]==> (b ((^x.x)(a b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 190458/22387962. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(z1 z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190459/22387998. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(c ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x)))(c (^z.z))) 6. ==[ alpha ]==> ((b (^x.(x x)))(c (^y.y))) REDUCED to normal form. ------ 190460/22388025. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b ((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b ((a a) a))) REDUCED to normal form. ------ 190461/22388079. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((a a) a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(a a))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(a a))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 190462/22388115. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 190463/22388250. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 190464/22388277. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 190465/22388304. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a))(^z.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a))(^y.a))) 5. ==[ beta ]==> (((a a)(a a))((a (a a))(^y.a))) 6. ==[ alpha ]==> (((a a)(a a))((a (a a))(^x.a))) REDUCED to normal form. ------ 190466/22388331. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a (^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.(y y)))) REDUCED to normal form. ------ 190467/22388412. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((a a) a) a)) 3. ==[ beta ]==> ((b (a (a a)))(((a a) a) a)) REDUCED to normal form. ------ 190468/22388439. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y)(^z.z)) b)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(^y.y)) b)) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.y) b)) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x) b)) 7. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 190469/22388529. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^z.(^x1.x1))(^y1.(^z1.z1)))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 7. ==[ beta ]==> ((^y.y)(^y1.y1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190470/22388934. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 7. ==[ beta ]==> ((^y.a)(^z.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 190471/22388961. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 190472/22388970. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b (a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b (a (a a)))) REDUCED to normal form. ------ 190473/22388988. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190474/22389078. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z) a))) 7. ==[ beta ]==> ((a (^y.y))((^z.z) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 190475/22389105. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(a (a a)))) REDUCED to normal form. ------ 190476/22389123. ------ 1. ==[ start ]==> (((^a.b)(b a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(a (^y.(^z.z)))) 3. ==[ beta ]==> (b (a (^y.(^z.z)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 190477/22389186. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c c)) REDUCED to normal form. ------ 190478/22389231. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190479/22389348. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190480/22389375. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(((^z.z) a)(a a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a (a a))) REDUCED to normal form. ------ 190481/22389393. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(c (^x1.(^y1.y1)))) REDUCED to normal form. ------ 190482/22389465. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((a (b (^y.y)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((a (b (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 190483/22389492. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 190484/22389519. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(^z.a))) 5. ==[ beta ]==> (((^y.y) b)((a a)(^z.a))) 6. ==[ alpha ]==> (((^x.x) b)((a a)(^y.a))) 7. ==[ beta ]==> (b ((a a)(^y.a))) 8. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 190485/22389546. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(((^z.z) a) a)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 190486/22389573. ------ 1. ==[ start ]==> (((a b)(b a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a b)(b a))((a (^x.x)) b)) REDUCED to normal form. ------ 190487/22389627. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^b.a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.a) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 190488/22389708. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 190489/22389735. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 190490/22389789. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a a) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a) b)) 5. ==[ beta ]==> ((a (^y.y))((a a) b)) 6. ==[ alpha ]==> ((a (^x.x))((a a) b)) REDUCED to normal form. ------ 190491/22389807. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a (a (^z.z)))) 3. ==[ beta ]==> ((b (^y.y))(a (a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 190492/22389816. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 190493/22389843. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.x1) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 190494/22389852. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190495/22389879. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.y1)(a a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a a))) 5. ==[ beta ]==> ((^y.y)(a a)) 6. ==[ alpha ]==> ((^x.x)(a a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 190496/22401600. ------ 1. ==[ start ]==> ((^a.b)(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.b)(c ((^y.(^z.z)) a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 190497/22401648. ------ 1. ==[ start ]==> (((^a.a) b)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 190498/22401657. ------ 1. ==[ start ]==> (((a a)(a a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))(^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 190499/22401681. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> (((a (a (^z.z)))(a a))(^y.y)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 190500/22401870. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ eta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 190501/22403808. ------ 1. ==[ start ]==> (((a b)(^a.a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(^x.x))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a b)(^x.x))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 190502/22403823. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> (^y.((((^z.(^x1.x1)) a) a)(((^z.(^x1.x1)) a) a))) 4. ==[ alpha ]==> (^x.((((^y.(^z.z)) a) a)(((^x1.(^y1.y1)) a) a))) 5. ==[ beta ]==> (^x.(((^z.z) a)(((^x1.(^y1.y1)) a) a))) 6. ==[ alpha ]==> (^x.(((^y.y) a)(((^z.(^x1.x1)) a) a))) 7. ==[ beta ]==> (^x.(a (((^z.(^x1.x1)) a) a))) 8. ==[ alpha ]==> (^x.(a (((^y.(^z.z)) a) a))) 9. ==[ beta ]==> (^x.(a ((^z.z) a))) 10. ==[ alpha ]==> (^x.(a ((^y.y) a))) 11. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 190503/22404996. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 190504/22405383. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(b (^z.z)))) 3. ==[ beta ]==> (((a b) a)(^y.(b (^z.z)))) 4. ==[ alpha ]==> (((a b) a)(^x.(b (^y.y)))) REDUCED to normal form. ------ 190505/22405461. ------ 1. ==[ start ]==> ((^a.(b a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b x))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ eta ]==> (b ((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 190506/22406901. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190507/22407777. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 190508/22409217. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^a.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.(b x1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))((^z.z) a)) b) 4. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 190509/22409295. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a b)((^z.z) a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190510/22409964. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 190511/22410189. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((b a)(^y.((^z.z)(a a)))) 6. ==[ alpha ]==> ((b a)(^x.((^y.y)(a a)))) 7. ==[ beta ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 190512/22410855. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(y y)))) 5. ==[ beta ]==> (a (^y.(^z.(y y)))) 6. ==[ alpha ]==> (a (^x.(^y.(x x)))) REDUCED to normal form. ------ 190513/22411035. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.b))) 3. ==[ beta ]==> (b (^z.(^x1.b))) 4. ==[ alpha ]==> (b (^x.(^y.b))) REDUCED to normal form. ------ 190514/22411044. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a z))) 3. ==[ eta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 190515/22412529. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190516/22412571. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^b.a) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190517/22412808. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a)(^x.x))((^y.y)(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.z)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 190518/22412988. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 190519/22412997. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 190520/22413021. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a a)(a a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190521/22413033. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190522/22413198. ------ 1. ==[ start ]==> ((a b)(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a b)(c ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((a b)(c (^y.y))) 4. ==[ alpha ]==> ((a b)(c (^x.x))) REDUCED to normal form. ------ 190523/22413216. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 190524/22413243. ------ 1. ==[ start ]==> (((^a.a) b)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 190525/22413252. ------ 1. ==[ start ]==> (((a a)(a a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))(a ((^x.x)(^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(a a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 190526/22413279. ------ 1. ==[ start ]==> ((a (a (^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 190527/22413288. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 (^y1.y1))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 (^y1.y1))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190528/22413414. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 190529/22413441. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b a)(a b))) REDUCED to normal form. ------ 190530/22413468. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 190531/22413657. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a) a)((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a a) a)((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a a) a)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 190532/22413684. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(a (a (^z.z))))) REDUCED to normal form. ------ 190533/22413729. ------ 1. ==[ start ]==> (((^a.(a a)) a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((a a)((a a)(^y.y))) 6. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 190534/22413747. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((^y.(^z.z)) a)(^x1.(^y1.y1)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))) 7. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(^x2.(^y2.y2)))) 8. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 9. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 10. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190535/22413774. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 190536/22413810. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((a b)((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))(a (a a)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 190537/22413828. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 9. ==[ beta ]==> (b (^y.(^z.z))) 10. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 190538/22413837. ------ 1. ==[ start ]==> (((a (a a)) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a)) a)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 190539/22413864. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 190540/22413882. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 190541/22413945. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 190542/22414053. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> ((b b)((^y.(y y))((a a)(a a)))) 4. ==[ alpha ]==> ((b b)((^x.(x x))((a a)(a a)))) 5. ==[ beta ]==> ((b b)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 190543/22414125. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 190544/22414179. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a) b)) 5. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a) b)) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 7. ==[ beta ]==> (((^y.(^z.z)) a) b) 8. ==[ alpha ]==> (((^x.(^y.y)) a) b) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 190545/22414242. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 190546/22414269. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 190547/22414296. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 190548/22414872. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a)((a a) a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)((a a) a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 190549/22414899. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a))((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a (a a)) b)) REDUCED to normal form. ------ 190550/22414926. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (a (a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 190551/22414953. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)((a (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> (((a (a a)) a)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 190552/22414980. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((a a)((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 8. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 190553/22415043. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.b)((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 190554/22415124. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) IRREDUCIBLE: cycle. ------ 190555/22415187. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.y))(a b))) 3. ==[ beta ]==> ((((a a) a) b)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 190556/22415205. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> (b ((a a)(^y.(a a)))) 6. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 190557/22415214. ------ 1. ==[ start ]==> (((a b) a)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 190558/22415232. ------ 1. ==[ start ]==> (((^a.a)(a b))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 190559/22415241. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 190560/22415295. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 190561/22415313. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a (a a))(^y.y))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (a a))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (a a))(^x.x))) REDUCED to normal form. ------ 190562/22415322. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(b ((^z.z) b))) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))(b ((^y.y) b))) 7. ==[ beta ]==> (((a (a a))(^x.(x x)))(b b)) REDUCED to normal form. ------ 190563/22415349. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.a)((a a)(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 190564/22415376. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 190565/22415403. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a b)(^x.x))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 190566/22415421. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.z) a)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y) a)) 5. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 190567/22415592. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190568/22415880. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(a a)) c)) 3. ==[ beta ]==> ((^y.y)((^z.(a a)) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(a a)) c)) 5. ==[ beta ]==> ((^y.(a a)) c) 6. ==[ alpha ]==> ((^x.(a a)) c) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 190569/22416087. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(b a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(b a))) 7. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 190570/22416114. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 190571/22416141. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> ((a ((a a) a))(a ((^y.y) b))) 6. ==[ alpha ]==> ((a ((a a) a))(a ((^x.x) b))) 7. ==[ beta ]==> ((a ((a a) a))(a b)) REDUCED to normal form. ------ 190572/22416168. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 190573/22416195. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a a)(b (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a a)(b (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a (a a))((a a)(b (^y.y)))) 6. ==[ alpha ]==> ((a (a a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 190574/22416240. ------ 1. ==[ start ]==> (((^a.b) c)((^d.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z))(a a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190575/22416339. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 190576/22416483. ------ 1. ==[ start ]==> (((a b) c)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))(b a))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 190577/22416510. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) b)((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 190578/22416537. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 190579/22416591. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(b (^z.z))) REDUCED to normal form. ------ 190580/22416636. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((a a)(a a)) b)) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)(a a)) b)) REDUCED to normal form. ------ 190581/22416672. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190582/22416699. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 190583/22416780. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 190584/22416951. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(b ((a a)(a a)))) REDUCED to normal form. ------ 190585/22416978. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(a (b (^y.y)))) 3. ==[ beta ]==> (((a b) a)(a (b (^y.y)))) 4. ==[ alpha ]==> (((a b) a)(a (b (^x.x)))) REDUCED to normal form. ------ 190586/22417005. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(a a))(a a))) REDUCED to normal form. ------ 190587/22417032. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b (a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (a (^y.y)))) REDUCED to normal form. ------ 190588/22417059. ------ 1. ==[ start ]==> ((a (b a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((a (b a))((a (^x.(^y.y)))((^z.z) a))) 3. ==[ beta ]==> ((a (b a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 190589/22417293. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(c (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(c (^y.y))) REDUCED to normal form. ------ 190590/22417365. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((a a)(a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.y))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 190591/22417401. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.(a a)))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 190592/22417419. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 190593/22417428. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 190594/22417482. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 190595/22417500. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (b ((a a)(^y.a))) 6. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 190596/22417509. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 190597/22417536. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.b)(a b))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.b)(a b))) 5. ==[ beta ]==> (((a a)(^x.a)) b) REDUCED to normal form. ------ 190598/22417887. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.b)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190599/22418067. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> (b ((^x1.(a a)) a)) 4. ==[ alpha ]==> (b ((^x.(a a)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 190600/22418373. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 190601/22418427. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 190602/22418472. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190603/22418499. ------ 1. ==[ start ]==> ((a (^b.b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 190604/22418778. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190605/22419093. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.(^y2.y2))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190606/22419147. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) d)) 5. ==[ beta ]==> (b ((^y.(^z.z)) d)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) d)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190607/22419318. ------ 1. ==[ start ]==> (((a b)(^c.a))(c (^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(c (^y.a))) REDUCED to normal form. ------ 190608/22419345. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 190609/22419372. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(a (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a (^z.z))) REDUCED to normal form. ------ 190610/22419417. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((b a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190611/22419453. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 190612/22419984. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 190613/22420209. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 190614/22420317. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 190615/22420335. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> (b ((a a)(^y.a))) 6. ==[ alpha ]==> (b ((a a)(^x.a))) REDUCED to normal form. ------ 190616/22420344. ------ 1. ==[ start ]==> (((a b)(^a.b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.b))(a a)) REDUCED to normal form. ------ 190617/22420398. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 190618/22420443. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a (a a))(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190619/22420452. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a b)(a b))) REDUCED to normal form. ------ 190620/22420479. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 190621/22420506. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 190622/22420812. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(a (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(a (b a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (b a))) REDUCED to normal form. ------ 190623/22420839. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((a a)(^z.z))(a a))) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a)(^z.z))(a a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 190624/22420866. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((^x.x)(a a))(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((a a)(a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))((a a)(a (^x.x)))) REDUCED to normal form. ------ 190625/22420893. ------ 1. ==[ start ]==> ((a (b (^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((a b)((^y.y) a))) 3. ==[ beta ]==> ((a (b (^x.x)))((a b) a)) REDUCED to normal form. ------ 190626/22421172. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((a a) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190627/22421208. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 190628/22421235. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(x x))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 190629/22421280. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 190630/22421343. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 190631/22421361. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(a a)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(a a)) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a) b)) REDUCED to normal form. ------ 190632/22421370. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 190633/22421451. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 190634/22421478. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))(^z.a))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.a)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 190635/22421676. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(a (a a)))) 5. ==[ beta ]==> (((a a)(b (^x.x)))(a (a a))) REDUCED to normal form. ------ 190636/22421703. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a (a a))(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a (a a))(^y.y))) REDUCED to normal form. ------ 190637/22421730. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((a b)(((^y.y) a)((a a) a))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)((a a) a))) 7. ==[ beta ]==> ((a b)(a ((a a) a))) REDUCED to normal form. ------ 190638/22421757. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (^z.z))(a b))) REDUCED to normal form. ------ 190639/22421784. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> ((b a)((a a)((^x.x)(a a)))) 7. ==[ beta ]==> ((b a)((a a)(a a))) REDUCED to normal form. ------ 190640/22422450. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(a (^z.(a a)))) 3. ==[ beta ]==> (((^y.y) a)(a (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(a (^y.(a a)))) 5. ==[ beta ]==> (a (a (^y.(a a)))) 6. ==[ alpha ]==> (a (a (^x.(a a)))) REDUCED to normal form. ------ 190641/22422468. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a b)(^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a b)(^z.z))) 5. ==[ beta ]==> ((^y.y)((a b)(^z.z))) 6. ==[ alpha ]==> ((^x.x)((a b)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 190642/22422495. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 190643/22422549. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (a a))(^z.(z z)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (a a))(^z.(z z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (a a))(^y.(y y)))) 7. ==[ beta ]==> ((b b)((a (a a))(^y.(y y)))) 8. ==[ alpha ]==> ((b b)((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 190644/22422558. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a (a a))(a (a a)))) REDUCED to normal form. ------ 190645/22422585. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.a)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.a)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190646/22422630. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a)(^z.b))) 3. ==[ beta ]==> (b ((a a)(^z.b))) 4. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 190647/22422639. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 190648/22422666. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 190649/22422693. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 190650/22422747. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.(z1 z1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(z1 z1)))) IRREDUCIBLE: cycle. ------ 190651/22422774. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 190652/22422801. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 190653/22422891. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 190654/22422918. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 190655/22422945. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)(a (a a)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)(a (a a)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a (a (a a)))) REDUCED to normal form. ------ 190656/22422972. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a)) b)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 190657/22422999. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a)((a a) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 190658/22423287. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 190659/22423692. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> (b ((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190660/22423719. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 190661/22423746. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 190662/22423818. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(y y)) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(y y)) b)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(x x)) b)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b b)) REDUCED to normal form. ------ 190663/22423854. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(c (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c (^z.a))) 5. ==[ beta ]==> ((^y.y)(c (^z.a))) 6. ==[ alpha ]==> ((^x.x)(c (^y.a))) 7. ==[ beta ]==> (c (^y.a)) 8. ==[ alpha ]==> (c (^x.a)) REDUCED to normal form. ------ 190664/22423881. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b (^x1.(x1 x1)))) REDUCED to normal form. ------ 190665/22423962. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 190666/22424007. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190667/22424043. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 190668/22424070. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 190669/22424124. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190670/22424142. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(z z)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y)) a)) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 190671/22424169. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^b.a) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a) b)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 190672/22424187. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 190673/22424214. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a) a)) REDUCED to normal form. ------ 190674/22424295. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b c)) 5. ==[ beta ]==> (((^y.y) b)(b c)) 6. ==[ alpha ]==> (((^x.x) b)(b c)) 7. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 190675/22424349. ------ 1. ==[ start ]==> (((a b)(b a))(c (a a))) REDUCED to normal form. ------ 190676/22424376. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b (a (^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b (a (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (a (^y.y)))) REDUCED to normal form. ------ 190677/22424403. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a ((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a ((^y.y) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 190678/22424457. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a a)(a (^z.z)))) REDUCED to normal form. ------ 190679/22424484. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(c a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(c a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(c a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(c a)) 5. ==[ beta ]==> ((b (^y.y))(c a)) 6. ==[ alpha ]==> ((b (^x.x))(c a)) REDUCED to normal form. ------ 190680/22424511. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(b b)) REDUCED to normal form. ------ 190681/22424565. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(b (a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(b (a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b (a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (a a))) 5. ==[ beta ]==> ((a (^y.y))(b (a a))) 6. ==[ alpha ]==> ((a (^x.x))(b (a a))) REDUCED to normal form. ------ 190682/22424583. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 190683/22424592. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a (a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a (a (^y.y)))) REDUCED to normal form. ------ 190684/22424619. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a a)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 190685/22424628. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1) b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190686/22424655. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 190687/22424735. ------ 1. ==[ start ]==> (^a.((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(x x)))) 3. ==[ beta ]==> (^x.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190688/22424736. ------ 1. ==[ start ]==> (a ((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (a (^y.y)) 4. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 190689/22436340. ------ 1. ==[ start ]==> ((^a.a)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190690/22436430. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190691/22436451. ------ 1. ==[ start ]==> (((a a)(a a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 190692/22436592. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (^x.(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^x.(b ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (^x.(b ((^y.y)(^z.z)))) 7. ==[ beta ]==> (^x.(b (^z.z))) 8. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 190693/22436835. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 190694/22436910. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 190695/22436934. ------ 1. ==[ start ]==> ((^a.(a (a a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((^y.(y (^z.z)))(a a))(((^y.(y (^z.z)))(a a))((^y.(y (^z.z)))(a a)))) 4. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(((^z.(z (^x1.x1)))(a a))((^y1.(y1 (^z1.z1)))(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.(z (^x1.x1)))(a a))((^y1.(y1 (^z1.z1)))(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.(y (^z.z)))(a a))((^x1.(x1 (^y1.y1)))(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(((a a)(^z.z))((^x1.(x1 (^y1.y1)))(a a)))) 8. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))((^z.(z (^x1.x1)))(a a)))) 9. ==[ beta ]==> (((a a)(^x.x))(((a a)(^y.y))((a a)(^x1.x1)))) 10. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 190696/22437285. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190697/22438050. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a) a)(b a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 190698/22438206. ------ 1. ==[ start ]==> ((((a a) a)(a a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 190699/22438824. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.(a a))(^x1.(a a)))((^z.(a a))(^x1.(a a))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(a a))(^z.(a a)))((^x1.(a a))(^y1.(a a))))) 5. ==[ beta ]==> (((^y.(a a))(^z.(a a)))((^x1.(a a))(^y1.(a a)))) 6. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a))(^x1.(a a)))) 7. ==[ beta ]==> ((a a)((^z.(a a))(^x1.(a a)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(a a)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 190700/22439499. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((((^z.z)((^x1.x1) a))((^z.z)((^x1.x1) a)))(^y.y)) 4. ==[ alpha ]==> ((((^x.x)((^y.y) a))((^z.z)((^x1.x1) a)))(^y1.y1)) 5. ==[ beta ]==> ((((^y.y) a)((^z.z)((^x1.x1) a)))(^y1.y1)) 6. ==[ alpha ]==> ((((^x.x) a)((^y.y)((^z.z) a)))(^x1.x1)) 7. ==[ beta ]==> ((a ((^y.y)((^z.z) a)))(^x1.x1)) 8. ==[ alpha ]==> ((a ((^x.x)((^y.y) a)))(^z.z)) 9. ==[ beta ]==> ((a ((^y.y) a))(^z.z)) 10. ==[ alpha ]==> ((a ((^x.x) a))(^y.y)) 11. ==[ beta ]==> ((a a)(^y.y)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 190701/22439790. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 190702/22440537. ------ 1. ==[ start ]==> (((^a.a)(b a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.((a a)(a a)))) 3. ==[ beta ]==> ((b a)(^y.((a a)(a a)))) 4. ==[ alpha ]==> ((b a)(^x.((a a)(a a)))) REDUCED to normal form. ------ 190703/22440906. ------ 1. ==[ start ]==> (((a (a a))(a b))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.((a a)(a a)))) REDUCED to normal form. ------ 190704/22441092. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.b)(^y1.b))) 3. ==[ beta ]==> (((^x1.b)(^y1.b))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.x1))) 5. ==[ beta ]==> (b (^z.(^x1.x1))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 190705/22441266. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> (b (^x1.((x1 x1)(x1 x1)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 190706/22441932. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((((a a)(^x.x))((^y.y) a))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(^z.z)) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 190707/22442877. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 190708/22443009. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.b)(^z.(^x1.x1)))((^y.b)(^z.(^x1.x1))))(((^y.b)(^z.(^x1.x1)))((^y.b)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.b)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1))))(((^x2.b)(^y2.(^z2.z2)))((^x3.b)(^y3.(^z3.z3))))) 5. ==[ beta ]==> ((b ((^x1.b)(^y1.(^z1.z1))))(((^x2.b)(^y2.(^z2.z2)))((^x3.b)(^y3.(^z3.z3))))) 6. ==[ alpha ]==> ((b ((^x.b)(^y.(^z.z))))(((^x1.b)(^y1.(^z1.z1)))((^x2.b)(^y2.(^z2.z2))))) 7. ==[ beta ]==> ((b b)(((^x1.b)(^y1.(^z1.z1)))((^x2.b)(^y2.(^z2.z2))))) 8. ==[ alpha ]==> ((b b)(((^x.b)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1))))) 9. ==[ beta ]==> ((b b)(b ((^x1.b)(^y1.(^z1.z1))))) 10. ==[ alpha ]==> ((b b)(b ((^x.b)(^y.(^z.z))))) 11. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 190709/22443183. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(z (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^z.(z (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 190710/22443453. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^c.(b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(b a))) 3. ==[ beta ]==> (((b a)(b a))(^y.(b a))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(b a))) REDUCED to normal form. ------ 190711/22443741. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^b.(b a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.(x a))) REDUCED to normal form. ------ 190712/22444263. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.((a a)(^y.y)))) REDUCED to normal form. ------ 190713/22445250. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(a a))(^y1.y1))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190714/22445424. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^d.(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(a b))) 3. ==[ beta ]==> (b (^x1.(a b))) 4. ==[ alpha ]==> (b (^x.(a b))) REDUCED to normal form. ------ 190715/22445838. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 190716/22446069. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((a a) a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((a a) a)(a a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 190717/22446225. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.b))) REDUCED to normal form. ------ 190718/22446387. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.((a a) a))) 3. ==[ beta ]==> ((b (a (a a)))(^y.((a a) a))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.((a a) a))) REDUCED to normal form. ------ 190719/22446492. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^z.a)(^x1.(x1 x1)))(((^z.a)(^x1.(x1 x1)))(^y.y))) 4. ==[ alpha ]==> (((^x.a)(^y.(y y)))(((^z.a)(^x1.(x1 x1)))(^y1.y1))) 5. ==[ beta ]==> (a (((^z.a)(^x1.(x1 x1)))(^y1.y1))) 6. ==[ alpha ]==> (a (((^x.a)(^y.(y y)))(^z.z))) 7. ==[ beta ]==> (a (a (^z.z))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 190720/22447098. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(a (a a)))) 3. ==[ beta ]==> (b (^y.(a (a a)))) 4. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 190721/22447341. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(z (z z)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z (z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y (y y)))) REDUCED to normal form. ------ 190722/22447365. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190723/22447440. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 190724/22447521. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^z.a)) REDUCED to normal form. ------ 190725/22447602. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.a))) REDUCED to normal form. ------ 190726/22447683. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.z))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 190727/22447782. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.b)) 3. ==[ beta ]==> ((b (^y.y))(^z.b)) 4. ==[ alpha ]==> ((b (^x.x))(^y.b)) REDUCED to normal form. ------ 190728/22447791. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 190729/22447815. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(b (^y1.y1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190730/22447827. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^c.(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190731/22447947. ------ 1. ==[ start ]==> ((a a)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a a)(^y.y)) 4. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 190732/22448037. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a (a (^z.z))))) REDUCED to normal form. ------ 190733/22448055. ------ 1. ==[ start ]==> (((a a)(a a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 190734/22448073. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190735/22448091. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a (^z.z)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190736/22448100. ------ 1. ==[ start ]==> (((a a) b)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a a) b)((^x.(x (^y.y))) b)) 3. ==[ beta ]==> (((a a) b)(b (^y.y))) 4. ==[ alpha ]==> (((a a) b)(b (^x.x))) REDUCED to normal form. ------ 190737/22448118. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 190738/22448145. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 190739/22448172. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 190740/22448199. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.a))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.a))(b (^y.y))) REDUCED to normal form. ------ 190741/22448280. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.a)(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 190742/22448307. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 190743/22448361. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (a (((a a) a)(a (^y.(^z.z))))) 6. ==[ alpha ]==> (a (((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 190744/22448388. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 190745/22448442. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a (^x.(x x)))(a (b (^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a (b (^y.y)))) REDUCED to normal form. ------ 190746/22448487. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 190747/22448514. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 190748/22448532. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a a)((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> ((a a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 190749/22448541. ------ 1. ==[ start ]==> ((a (a (a a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (a (a a)))((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> ((a (a (a a)))((a a)(^y.y))) 4. ==[ alpha ]==> ((a (a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 190750/22448613. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a b)(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a b)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 190751/22448640. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 190752/22448694. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((b a)(^z.b))) REDUCED to normal form. ------ 190753/22448721. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 190754/22448784. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.b)(b a))) 3. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 190755/22448838. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 190756/22448856. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (a a))(^y.(a a)))) 3. ==[ beta ]==> ((b b)((a (a a))(^y.(a a)))) 4. ==[ alpha ]==> ((b b)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 190757/22448865. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 190758/22448892. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 190759/22448991. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> (((a (a a)) b)((^y.y) b)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x) b)) 5. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 190760/22449018. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b (^z.z)) c)) 3. ==[ beta ]==> (((^y.y) a)((b (^z.z)) c)) 4. ==[ alpha ]==> (((^x.x) a)((b (^y.y)) c)) 5. ==[ beta ]==> (a ((b (^y.y)) c)) 6. ==[ alpha ]==> (a ((b (^x.x)) c)) REDUCED to normal form. ------ 190761/22449189. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 190762/22449270. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 190763/22449360. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b ((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)(b ((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190764/22449414. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> (a (((^z.(^x1.x1)) a)(a a))) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a)(a a))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 190765/22449495. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b)(a (a a)))) 5. ==[ beta ]==> (((a a) a)(b (a (a a)))) REDUCED to normal form. ------ 190766/22449522. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 190767/22449576. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(^z.z))(a b))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a)(^z.z))(a b))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(^y.y))(a b))) 7. ==[ beta ]==> ((a a)(((a a)(^y.y))(a b))) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 190768/22449657. ------ 1. ==[ start ]==> ((a (^a.b))(((a a) a)(b a))) 2. ==[ alpha ]==> ((a (^x.b))(((a a) a)(b a))) REDUCED to normal form. ------ 190769/22449810. ------ 1. ==[ start ]==> ((((a a) a)(a a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a a))(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 190770/22449828. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (b (((^y.(^z.z)) a)(^x1.x1))) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a)(^z.z))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190771/22449990. ------ 1. ==[ start ]==> ((((a a) a) b)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a) b)(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 190772/22450017. ------ 1. ==[ start ]==> (((a b) a)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b) a)(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a b) a)((a a)(^y.(a a)))) 4. ==[ alpha ]==> (((a b) a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 190773/22450044. ------ 1. ==[ start ]==> (((a a)(^a.b))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 190774/22450098. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 190775/22450125. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 190776/22450152. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.a)(((^z.z) a)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) a)(^z.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 190777/22450323. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(y y))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(x x))) REDUCED to normal form. ------ 190778/22450350. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 190779/22450404. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 190780/22450431. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 190781/22450602. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> (b (b (b (^x1.x1)))) 4. ==[ alpha ]==> (b (b (b (^x.x)))) REDUCED to normal form. ------ 190782/22450656. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b (^z.z))(a a))) 3. ==[ beta ]==> (((^y.y)(a a))((b (^z.z))(a a))) 4. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y))(a a))) 5. ==[ beta ]==> ((a a)((b (^y.y))(a a))) 6. ==[ alpha ]==> ((a a)((b (^x.x))(a a))) REDUCED to normal form. ------ 190783/22450683. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 190784/22450692. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 190785/22450737. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(a (a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((a (^y1.(^z1.z1)))(a (a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(a (a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.(^y1.y1)))(a (a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(a (a a)))) 9. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(a (a a)))) 10. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a (a a)))) 11. ==[ beta ]==> ((a (^y.(^z.z)))(a (a a))) 12. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 190786/22450818. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (b (((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a b))) 5. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 190787/22451043. ------ 1. ==[ start ]==> (((^a.b) c)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b) c)((b (^y.y))(^z.z))) 3. ==[ beta ]==> (b ((b (^y.y))(^z.z))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 190788/22451106. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z) a)) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y) a)) 5. ==[ beta ]==> ((a ((a a)(^x.x))) a) REDUCED to normal form. ------ 190789/22451286. ------ 1. ==[ start ]==> (((a b) c)(((^a.a)(^a.a))(^d.a))) 2. ==[ alpha ]==> (((a b) c)(((^x.x)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b) c)((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a b) c)((^x.x)(^y.a))) 5. ==[ beta ]==> (((a b) c)(^y.a)) 6. ==[ alpha ]==> (((a b) c)(^x.a)) REDUCED to normal form. ------ 190790/22451313. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (a a))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)((a (a a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 190791/22451340. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(a (^y.y))) REDUCED to normal form. ------ 190792/22451421. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((b (^z.z)) a)) 3. ==[ beta ]==> ((a (^y.b))((b (^z.z)) a)) 4. ==[ alpha ]==> ((a (^x.b))((b (^y.y)) a)) REDUCED to normal form. ------ 190793/22451475. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) b) c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b) c)) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b) c)) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190794/22451619. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) b) REDUCED to normal form. ------ 190795/22451700. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))((a a) a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (a a))((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 190796/22451727. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.x1))) 7. ==[ beta ]==> ((^y.y)((^z.a)(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 9. ==[ beta ]==> ((^y.a)(^z.z)) 10. ==[ alpha ]==> ((^x.a)(^y.y)) 11. ==[ beta ]==> a REDUCED to normal form. ------ 190797/22451952. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z)(a a))((a a) a))) 5. ==[ beta ]==> (b (((^z.z)(a a))((a a) a))) 6. ==[ alpha ]==> (b (((^x.x)(a a))((a a) a))) 7. ==[ beta ]==> (b ((a a)((a a) a))) REDUCED to normal form. ------ 190798/22452033. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b ((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (b ((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 190799/22452141. ------ 1. ==[ start ]==> (((^a.a)(b a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((a a)((a a)(a a)))) 3. ==[ beta ]==> ((b a)((a a)((a a)(a a)))) REDUCED to normal form. ------ 190800/22452204. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(a a)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 190801/22452231. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 190802/22452285. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 190803/22452312. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)(^y.a))) REDUCED to normal form. ------ 190804/22452339. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a b)(^z.b))) 3. ==[ beta ]==> (((a a)(^y.a))((a b)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.a))((a b)(^y.b))) REDUCED to normal form. ------ 190805/22452366. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(^x1.(a a)))) REDUCED to normal form. ------ 190806/22452429. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(x x))(b a))) 3. ==[ beta ]==> (((a a)(b a))((b a)(b a))) REDUCED to normal form. ------ 190807/22452456. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 190808/22452483. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((^z.z) b))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 190809/22452510. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(a b))((a a)(a a))) REDUCED to normal form. ------ 190810/22452564. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 190811/22452591. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 190812/22452699. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.b)(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 190813/22452870. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(a ((a a)(a a)))) 3. ==[ beta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 190814/22452978. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((a a)(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190815/22453005. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 190816/22453032. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a b)((a a) a))) 3. ==[ beta ]==> ((^y.y)((a b)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a b)((a a) a))) 5. ==[ beta ]==> ((a b)((a a) a)) REDUCED to normal form. ------ 190817/22453086. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))((^z.z)(a a)))) 9. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z)(a a)))) 10. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y)(a a)))) 11. ==[ beta ]==> (((a a)(a a))((^y.y)(a a))) 12. ==[ alpha ]==> (((a a)(a a))((^x.x)(a a))) 13. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 190818/22453167. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 190819/22453230. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(b (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(b (^z.z))) REDUCED to normal form. ------ 190820/22453284. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((b a)(^x1.a))) REDUCED to normal form. ------ 190821/22453347. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(a a)) REDUCED to normal form. ------ 190822/22453374. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.b)((a a) a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.b)((a a) a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.b)((a a) a))) 5. ==[ beta ]==> ((a ((a a)(^x.x))) b) REDUCED to normal form. ------ 190823/22453428. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 190824/22453455. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(x x))((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)(^y.y))((a a)(^y.y)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 190825/22453482. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.a)(b a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.a)(b a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.a)(b a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(b a))) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 190826/22453509. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 190827/22453536. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z) b)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y) b)) 7. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 190828/22453581. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190829/22453590. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 190830/22453788. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(d ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(d ((a a)(^z.z)))) 3. ==[ beta ]==> (b (d ((a a)(^z.z)))) 4. ==[ alpha ]==> (b (d ((a a)(^x.x)))) REDUCED to normal form. ------ 190831/22453896. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.(^x2.x2)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.(^x2.x2)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190832/22453905. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 190833/22453950. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (((a a)(^y.y))((^z.z) a))) 6. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y) a))) 7. ==[ beta ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 190834/22453959. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 190835/22453977. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(a (a a))) 6. ==[ alpha ]==> (((^x.x)(a a))(a (a a))) 7. ==[ beta ]==> ((a a)(a (a a))) REDUCED to normal form. ------ 190836/22454031. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 190837/22454112. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> (b (((^y.y) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (b (((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> (b (a ((a a)(^y.y)))) 6. ==[ alpha ]==> (b (a ((a a)(^x.x)))) REDUCED to normal form. ------ 190838/22454229. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((b a)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 190839/22454256. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 190840/22454292. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(a (a a)))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 190841/22454319. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z)))) b) REDUCED to normal form. ------ 190842/22454346. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.a)((a a) a))) 3. ==[ beta ]==> ((a (b a))((^y.a)((a a) a))) 4. ==[ alpha ]==> ((a (b a))((^x.a)((a a) a))) 5. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 190843/22454373. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 190844/22454400. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(x1 x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a a)((^y.(y y))((^z.z)(a a)))) 8. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y)(a a)))) 9. ==[ beta ]==> ((a a)(((^y.y)(a a))((^y.y)(a a)))) 10. ==[ alpha ]==> ((a a)(((^x.x)(a a))((^y.y)(a a)))) 11. ==[ beta ]==> ((a a)((a a)((^y.y)(a a)))) 12. ==[ alpha ]==> ((a a)((a a)((^x.x)(a a)))) 13. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 190845/22454427. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a b)) a) REDUCED to normal form. ------ 190846/22454454. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))(b a))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 190847/22454481. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.z)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 190848/22454508. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.z))) REDUCED to normal form. ------ 190849/22454589. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((b (a a))((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b (a a))((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> ((b (a a))(a a)) REDUCED to normal form. ------ 190850/22454616. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 190851/22454787. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(a (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 190852/22454895. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((a b)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190853/22454976. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a (a a))(a b))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(a b))) REDUCED to normal form. ------ 190854/22455003. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)(a a))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 190855/22455057. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a a)(b a))) 3. ==[ beta ]==> (((b a)(b a))((a a)(b a))) REDUCED to normal form. ------ 190856/22455120. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 190857/22455147. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.b))((a a)(^y.a))) REDUCED to normal form. ------ 190858/22455201. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 190859/22455255. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (a a))(^x1.b))) REDUCED to normal form. ------ 190860/22455282. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (^x1.(a a)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 190861/22455345. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.x)(b a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(b a)) REDUCED to normal form. ------ 190862/22455426. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a (a a))(b a))(a a)) REDUCED to normal form. ------ 190863/22455453. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.(z z)))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 190864/22455507. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 190865/22455534. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(y y))(^z.b))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(y y))(^z.b))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(x x))(^y.b))) 5. ==[ beta ]==> (((a a)((a a) a))((^y.b)(^y.b))) 6. ==[ alpha ]==> (((a a)((a a) a))((^x.b)(^y.b))) 7. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 190866/22455561. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 190867/22455786. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a (a a))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a (a a))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a (a a))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190868/22455867. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> (b ((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 190869/22456011. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b c)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b c)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((b c)(^y.(^z.z))) 8. ==[ alpha ]==> ((b c)(^x.(^y.y))) REDUCED to normal form. ------ 190870/22456038. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (a a))(^x.a))) REDUCED to normal form. ------ 190871/22456146. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(^z.z)) a)) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z)) a)) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 190872/22456173. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a a) b)) REDUCED to normal form. ------ 190873/22456353. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190874/22456389. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 190875/22456416. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 190876/22456587. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b (^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(b (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))(b (^y.(a a)))) 5. ==[ beta ]==> ((b a)(b (^y.(a a)))) 6. ==[ alpha ]==> ((b a)(b (^x.(a a)))) REDUCED to normal form. ------ 190877/22456641. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a b)(a a))((^y.(a a))(a a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(a a))(a a))) 5. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 190878/22456668. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a b))((^y.b)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 190879/22456749. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(((^x1.x1)(^y1.y1))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)(^y1.y1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(^x1.x1))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.x1)) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 190880/22456776. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)((a a) a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)((a a) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)((a a) a))) 5. ==[ beta ]==> ((b a)((^y.a)((a a) a))) 6. ==[ alpha ]==> ((b a)((^x.a)((a a) a))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 190881/22456803. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 190882/22456857. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(^z.z))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 190883/22457028. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(b (a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b (a b))) 3. ==[ beta ]==> (b (b (a b))) REDUCED to normal form. ------ 190884/22457136. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))((^y2.y2) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))((^y2.y2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190885/22457361. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 190886/22457388. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190887/22457442. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 190888/22457469. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a b) a)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a b) a)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a b) a)) REDUCED to normal form. ------ 190889/22457496. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((a a) a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((a a) a) b)) REDUCED to normal form. ------ 190890/22457658. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.b) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b) a)) 5. ==[ beta ]==> ((^y.y)((^z.b) a)) 6. ==[ alpha ]==> ((^x.x)((^y.b) a)) 7. ==[ beta ]==> ((^y.b) a) 8. ==[ alpha ]==> ((^x.b) a) 9. ==[ beta ]==> b REDUCED to normal form. ------ 190891/22457676. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((a a) a)(a a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((a a) a)(a a))) REDUCED to normal form. ------ 190892/22457775. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c (^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)(c (^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 190893/22457802. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b (^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b (^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b (^x1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.a))) REDUCED to normal form. ------ 190894/22457829. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (^a.b))) 2. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.b))) REDUCED to normal form. ------ 190895/22457856. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^c.a)(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(a a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 190896/22457883. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 190897/22457910. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(a ((^z.z) a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a ((^y.y) a))) 7. ==[ beta ]==> ((((a a)(^x.x))(a b))(a a)) REDUCED to normal form. ------ 190898/22457964. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 190899/22457991. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.y)((a a) a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.y)((a a) a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x)((a a) a))) 5. ==[ beta ]==> ((b (a (a a)))((a a) a)) REDUCED to normal form. ------ 190900/22458072. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((a a)((^y.(y y))(^z.a))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(^y.a))) 7. ==[ beta ]==> ((a a)((^y.a)(^y.a))) 8. ==[ alpha ]==> ((a a)((^x.a)(^y.a))) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 190901/22458099. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 190902/22458495. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (a a)) b)) 3. ==[ beta ]==> (((^y.y) b)((a (a a)) b)) 4. ==[ alpha ]==> (((^x.x) b)((a (a a)) b)) 5. ==[ beta ]==> (b ((a (a a)) b)) REDUCED to normal form. ------ 190903/22458567. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b (a (a a)))) 3. ==[ beta ]==> ((^y.y)(b (a (a a)))) 4. ==[ alpha ]==> ((^x.x)(b (a (a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 190904/22458621. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (a a))(a a))) REDUCED to normal form. ------ 190905/22458657. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a) c)) 5. ==[ beta ]==> ((^y.y)((^z.a) c)) 6. ==[ alpha ]==> ((^x.x)((^y.a) c)) 7. ==[ beta ]==> ((^y.a) c) 8. ==[ alpha ]==> ((^x.a) c) 9. ==[ beta ]==> a REDUCED to normal form. ------ 190906/22458702. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a a)(a (a a)))) 3. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 190907/22458765. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 190908/22458846. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a)) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a)) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 190909/22458873. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((^y.y) a) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a b)) REDUCED to normal form. ------ 190910/22458945. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(a (a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (a (a a)))) REDUCED to normal form. ------ 190911/22458954. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(z z)) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a a)) REDUCED to normal form. ------ 190912/22458972. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 190913/22459017. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b (^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b (^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.a))) REDUCED to normal form. ------ 190914/22459044. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a (^z.(z z)))) 3. ==[ beta ]==> ((a (b (^y.y)))(a (^z.(z z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 190915/22459071. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.a)(a a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 190916/22459098. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.x1)))) 8. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190917/22459125. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))((^x1.x1) a)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z) a)) 5. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 190918/22459152. ------ 1. ==[ start ]==> (((a b)(b a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.a)(^y.y))) 3. ==[ beta ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 190919/22459179. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 190920/22459206. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.a)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.a)) REDUCED to normal form. ------ 190921/22459260. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 190922/22459287. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a (^x1.a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a (^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a (^z.a))) 5. ==[ beta ]==> ((b (^y.y))(a (^z.a))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.a))) REDUCED to normal form. ------ 190923/22459314. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.(^y.y))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 190924/22459368. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 190925/22459386. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a) b)) 3. ==[ beta ]==> ((b (^y.y))((a a) b)) 4. ==[ alpha ]==> ((b (^x.x))((a a) b)) REDUCED to normal form. ------ 190926/22459395. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 190927/22459422. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(b (^x1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 190928/22459431. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190929/22459458. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(b a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(b a)) 3. ==[ beta ]==> ((^y.y)(b a)) 4. ==[ alpha ]==> ((^x.x)(b a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 190930/22461828. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.((^z.((^x1.(^y1.y1)) a))(^z.((^x1.(^y1.y1)) a)))) 4. ==[ alpha ]==> (^x.((^y.((^z.(^x1.x1)) a))(^y1.((^z1.(^x2.x2)) a)))) 5. ==[ beta ]==> (^x.((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> (^x.((^y.(^z.z)) a)) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190931/22471170. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190932/22471251. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190933/22471290. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190934/22471296. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((^z.(^x1.(^y1.y1))) a)(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190935/22471755. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a (a (^y.y)))(^z.z))(((a (a (^y.y)))(^z.z))((a (a (^y.y)))(^z.z)))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(((a (a (^z.z)))(^x1.x1))((a (a (^y1.y1)))(^z1.z1)))) REDUCED to normal form. ------ 190936/22471980. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190937/22473051. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> ((((^y.(^z.z)) a)(^x1.x1)) b) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z)) b) 5. ==[ beta ]==> (((^y.y)(^z.z)) b) 6. ==[ alpha ]==> (((^x.x)(^y.y)) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 190938/22473438. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (^y.(((^z.z)((^x1.(^y1.y1)) a))((^z.z)((^x1.(^y1.y1)) a)))) 4. ==[ alpha ]==> (^x.(((^y.y)((^z.(^x1.x1)) a))((^y1.y1)((^z1.(^x2.x2)) a)))) 5. ==[ beta ]==> (^x.(((^z.(^x1.x1)) a)((^y1.y1)((^z1.(^x2.x2)) a)))) 6. ==[ alpha ]==> (^x.(((^y.(^z.z)) a)((^x1.x1)((^y1.(^z1.z1)) a)))) 7. ==[ beta ]==> (^x.((^z.z)((^x1.x1)((^y1.(^z1.z1)) a)))) 8. ==[ alpha ]==> (^x.((^y.y)((^z.z)((^x1.(^y1.y1)) a)))) 9. ==[ beta ]==> (^x.((^z.z)((^x1.(^y1.y1)) a))) 10. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1)) a))) 11. ==[ beta ]==> (^x.((^z.(^x1.x1)) a)) 12. ==[ alpha ]==> (^x.((^y.(^z.z)) a)) 13. ==[ beta ]==> (^x.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190939/22473441. ------ 1. ==[ start ]==> ((a (^b.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.(a a)))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 190940/22473855. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((((^x.x)(a a)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x)(a a)) a)(^y.(^z.z))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 190941/22474320. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((((^z.z) b)(^x1.a))(((^z.z) b)(^x1.a)))(^y.y)) 4. ==[ alpha ]==> (((((^x.x) b)(^y.a))(((^z.z) b)(^x1.a)))(^y1.y1)) 5. ==[ beta ]==> (((b (^y.a))(((^z.z) b)(^x1.a)))(^y1.y1)) 6. ==[ alpha ]==> (((b (^x.a))(((^y.y) b)(^z.a)))(^x1.x1)) 7. ==[ beta ]==> (((b (^x.a))(b (^z.a)))(^x1.x1)) 8. ==[ alpha ]==> (((b (^x.a))(b (^y.a)))(^z.z)) REDUCED to normal form. ------ 190942/22475076. ------ 1. ==[ start ]==> ((^a.(b a))((^b.b) c)) 2. ==[ alpha ]==> ((^x.(b x))((^y.y) c)) 3. ==[ eta ]==> (b ((^y.y) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 190943/22475625. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190944/22475727. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.(a a)))) REDUCED to normal form. ------ 190945/22476087. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (b (^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 190946/22476831. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a) c)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a) c)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 190947/22478004. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 190948/22478910. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190949/22479606. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 190950/22480071. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(a a)) a)) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190951/22480488. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(z z)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(y y)))) 7. ==[ beta ]==> (^y.(^z.(y y))) 8. ==[ alpha ]==> (^x.(^y.(x x))) REDUCED to normal form. ------ 190952/22480875. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(^x1.(x1 b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z b))) 5. ==[ beta ]==> ((^y.y)(^z.(z b))) 6. ==[ alpha ]==> ((^x.x)(^y.(y b))) 7. ==[ beta ]==> (^y.(y b)) 8. ==[ alpha ]==> (^x.(x b)) REDUCED to normal form. ------ 190953/22481208. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.a))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.a))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.a))) REDUCED to normal form. ------ 190954/22482162. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 190955/22482171. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(z (z z)))) REDUCED to normal form. ------ 190956/22482504. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.c)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.c)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.c)) 5. ==[ beta ]==> ((b (^y.y))(^z.c)) 6. ==[ alpha ]==> ((b (^x.x))(^y.c)) REDUCED to normal form. ------ 190957/22482636. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190958/22482675. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 190959/22482786. ------ 1. ==[ start ]==> ((a (^a.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.x))(^z.z)) 4. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 190960/22482867. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 190961/22482876. ------ 1. ==[ start ]==> (((^a.a) b)(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)(b (a (a (^y.y))))) 3. ==[ beta ]==> (b (b (a (a (^y.y))))) 4. ==[ alpha ]==> (b (b (a (a (^x.x))))) REDUCED to normal form. ------ 190962/22482903. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 190963/22482912. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 190964/22482930. ------ 1. ==[ start ]==> (((a a) b)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a) b)((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 190965/22482957. ------ 1. ==[ start ]==> (((a (^a.a)) a)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.y))) REDUCED to normal form. ------ 190966/22482984. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 190967/22483011. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 190968/22483065. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 190969/22483146. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 190970/22483173. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a b)(b a))) 3. ==[ beta ]==> ((a a)((a b)(b a))) REDUCED to normal form. ------ 190971/22483200. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 190972/22483227. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)((^z1.z1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)((^y1.y1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1) b)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1) b)) 7. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 190973/22483254. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 190974/22483371. ------ 1. ==[ start ]==> ((a (a (a a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (a (a a)))((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 190975/22483380. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.(y y))((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.(x x))((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> (((^y.(y (^z.z)))(a a))((^y.(y (^z.z)))(a a))) 6. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(z (^x1.x1)))(a a))) 7. ==[ beta ]==> (((a a)(^y.y))((^z.(z (^x1.x1)))(a a))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z)))(a a))) 9. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.z))) 10. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 190976/22483488. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.y))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 190977/22483515. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 190978/22483596. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 190979/22483641. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 190980/22483668. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 190981/22483731. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(b (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190982/22483758. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190983/22483812. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 (^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 (^z1.z1)))(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 9. ==[ beta ]==> ((^z.z)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190984/22484280. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b ((b (^y.y))(a (^z.z)))) 6. ==[ alpha ]==> (b ((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 190985/22484307. ------ 1. ==[ start ]==> ((((a a) a) a)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a) a)(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> ((((a a) a) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 190986/22484361. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) REDUCED to normal form. ------ 190987/22484388. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b a)((a a) a))) 3. ==[ beta ]==> ((a (^y.(y y)))((b a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))((b a)((a a) a))) REDUCED to normal form. ------ 190988/22484415. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 190989/22484442. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(a a))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 190990/22484469. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 190991/22484667. ------ 1. ==[ start ]==> ((a (a b))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((a (a b))(((^x.(^y.y)) a)(^z.z))) 3. ==[ beta ]==> ((a (a b))((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 190992/22484757. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((^z.z)(a (a a)))) IRREDUCIBLE: cycle. ------ 190993/22484838. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190994/22484865. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a b)((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 190995/22484892. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.b)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.b)((a a)(^y.y))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 190996/22484946. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 190997/22485027. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 190998/22485054. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 190999/22485072. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a a)(a b))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> (((a a)(a b))((^y.y) a)) 4. ==[ alpha ]==> (((a a)(a b))((^x.x) a)) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 191000/22485099. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((b (^y.y)) b)) REDUCED to normal form. ------ 191001/22485270. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 191002/22485297. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 191003/22485351. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191004/22485441. ------ 1. ==[ start ]==> (((a b) b)(b (b (^a.a)))) 2. ==[ alpha ]==> (((a b) b)(b (b (^x.x)))) REDUCED to normal form. ------ 191005/22485468. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a) a)(a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a a) a)(a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a a) a)(a (^y.y))) 6. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 191006/22485495. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((b (^y.y))(a a))) REDUCED to normal form. ------ 191007/22485522. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 191008/22485576. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 191009/22485603. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))((b a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))((b a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((b a)((^y.y)(^z.z)))((b a)((^y.y)(^z.z)))) 8. ==[ alpha ]==> (((b a)((^x.x)(^y.y)))((b a)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> (((b a)(^y.y))((b a)((^z.z)(^x1.x1)))) 10. ==[ alpha ]==> (((b a)(^x.x))((b a)((^y.y)(^z.z)))) 11. ==[ beta ]==> (((b a)(^x.x))((b a)(^z.z))) 12. ==[ alpha ]==> (((b a)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 191010/22485630. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 191011/22485657. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 191012/22485684. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))((a b)(a a))) REDUCED to normal form. ------ 191013/22485882. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 191014/22485909. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 191015/22485936. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(b (^z.a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(b (^y.a))) REDUCED to normal form. ------ 191016/22485972. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191017/22486107. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191018/22486188. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 191019/22486215. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191020/22486350. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 191021/22486692. ------ 1. ==[ start ]==> ((a (b a))((^b.b) c)) 2. ==[ alpha ]==> ((a (b a))((^x.x) c)) 3. ==[ beta ]==> ((a (b a)) c) REDUCED to normal form. ------ 191022/22486926. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 191023/22486971. ------ 1. ==[ start ]==> (((^a.a)(b a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(b (^y.(a a)))) 3. ==[ beta ]==> ((b a)(b (^y.(a a)))) 4. ==[ alpha ]==> ((b a)(b (^x.(a a)))) REDUCED to normal form. ------ 191024/22487052. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (((a b)(a b))(a (^y.y))) 6. ==[ alpha ]==> (((a b)(a b))(a (^x.x))) REDUCED to normal form. ------ 191025/22487133. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191026/22487241. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 191027/22487286. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 191028/22487313. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))(^z.z))) 5. ==[ beta ]==> ((a (a a))((a (^y.y))(^z.z))) 6. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 191029/22487340. ------ 1. ==[ start ]==> (((a (a a))(a b))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((a a)(^x.(a a)))) REDUCED to normal form. ------ 191030/22487367. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((a a)(a a)) a)) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(a a)) a)) 5. ==[ beta ]==> (((a a) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 191031/22487394. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((^z.z) b) b)) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z) b) b)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) b) b)) 5. ==[ beta ]==> ((((a a) a)(^x.x))(b b)) REDUCED to normal form. ------ 191032/22487421. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 191033/22487538. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b)(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b)(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(^y1.b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191034/22487700. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 191035/22487817. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 191036/22487844. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 191037/22487925. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))((^z.z)(a a))) 6. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)(a a))) 7. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 191038/22487952. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.b)((a (a a))((a a)(^z.z)))) 6. ==[ alpha ]==> ((^x.b)((a (a a))((a a)(^y.y)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 191039/22487997. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(c (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (c (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 191040/22488006. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 191041/22488033. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a a)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a a) b)) REDUCED to normal form. ------ 191042/22488105. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191043/22488150. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 191044/22488177. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 191045/22488204. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a b)(^z.a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a b)(^z.a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)(^y.a))) REDUCED to normal form. ------ 191046/22488231. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((a a) a)(^y.b))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a) a)(^y.b))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a a) a)(^x.b))) REDUCED to normal form. ------ 191047/22488258. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a b)((^y.y)(^z.(a a)))) 8. ==[ alpha ]==> ((a b)((^x.x)(^y.(a a)))) 9. ==[ beta ]==> ((a b)(^y.(a a))) 10. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 191048/22488339. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (^y.y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191049/22488366. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)(^y.y))) REDUCED to normal form. ------ 191050/22488420. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 191051/22488447. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a) c)) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a) c)) 3. ==[ beta ]==> ((a b)((b a) c)) REDUCED to normal form. ------ 191052/22488618. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191053/22488735. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 191054/22488762. ------ 1. ==[ start ]==> ((((^a.a) b) a)((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((b a)(a (^y.y)))) 3. ==[ beta ]==> ((b a)((b a)(a (^y.y)))) 4. ==[ alpha ]==> ((b a)((b a)(a (^x.x)))) REDUCED to normal form. ------ 191055/22488789. ------ 1. ==[ start ]==> (((a a)(^b.b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 191056/22488816. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a a)(a (a a)))) REDUCED to normal form. ------ 191057/22488897. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))(a b))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))(a b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 191058/22488924. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a (a a))(a a))) REDUCED to normal form. ------ 191059/22488951. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.a))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 191060/22488978. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.x1))(b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.x1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.z))(b a))) REDUCED to normal form. ------ 191061/22489005. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 191062/22489050. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.(^x2.x2)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191063/22489122. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a) b)((a a)(^y.(y y)))) 6. ==[ alpha ]==> (((a a) b)((a a)(^x.(x x)))) REDUCED to normal form. ------ 191064/22489149. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 191065/22489176. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((a a) a)(^y.a))) 3. ==[ beta ]==> ((a (b a))(((a a) a)(^y.a))) 4. ==[ alpha ]==> ((a (b a))(((a a) a)(^x.a))) REDUCED to normal form. ------ 191066/22489203. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(^z.b)) 6. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 191067/22489230. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((a (a a))(^z.(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(^y.(a a)))) 7. ==[ beta ]==> ((a a)((a (a a))(^y.(a a)))) 8. ==[ alpha ]==> ((a a)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 191068/22489257. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x) a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a b))(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 191069/22489311. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191070/22489338. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 191071/22489482. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 191072/22489617. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 191073/22489761. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((b b)(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((b b)(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((b b)(((a a) a)(^y.y))) 6. ==[ alpha ]==> ((b b)(((a a) a)(^x.x))) REDUCED to normal form. ------ 191074/22489788. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(^y.y))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)((a a) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)((a a) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a a) a)) REDUCED to normal form. ------ 191075/22489842. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 191076/22489869. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a (^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 191077/22489968. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191078/22490076. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(^z1.z1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191079/22490202. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((b a) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((b a) a)) 3. ==[ beta ]==> (((a (^x.x)) b)((b a) a)) REDUCED to normal form. ------ 191080/22490229. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((a a)(^x1.x1)) b)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z)) b)) REDUCED to normal form. ------ 191081/22490256. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(a a)) c)) 3. ==[ beta ]==> (((a (a a))(b a))((a a) c)) REDUCED to normal form. ------ 191082/22490526. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(a a)) c)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(a a)) c)) 3. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 191083/22490697. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 191084/22490805. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.b)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191085/22490913. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(a b))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(a b))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 191086/22490940. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191087/22491075. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(y y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191088/22491183. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191089/22491192. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(b ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(b (a a))) REDUCED to normal form. ------ 191090/22491219. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(a ((a a)(^z.z)))) 3. ==[ beta ]==> ((b (^y.a))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (^x.a))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 191091/22491246. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 191092/22491309. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a) d)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a) d)) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 191093/22491471. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> (((a b)(a a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a b)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 191094/22491498. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 191095/22491525. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((a a) a)(^y.a))) REDUCED to normal form. ------ 191096/22491579. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 191097/22491606. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((b a)(((^y.y) a)(^z.a))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)(^y.a))) 7. ==[ beta ]==> ((b a)(a (^y.a))) 8. ==[ alpha ]==> ((b a)(a (^x.a))) REDUCED to normal form. ------ 191098/22491633. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 191099/22491687. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z)(a a)) a)) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a)) a)) 5. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 191100/22491777. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191101/22491858. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191102/22492083. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a a)(a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a a)(a b))) 3. ==[ beta ]==> (((^y.y) a)((a a)(a b))) 4. ==[ alpha ]==> (((^x.x) a)((a a)(a b))) 5. ==[ beta ]==> (a ((a a)(a b))) REDUCED to normal form. ------ 191103/22492101. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(a (^x1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.(a a)))) 5. ==[ beta ]==> ((^y.y)(a (^z.(a a)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(a a)))) 7. ==[ beta ]==> (a (^y.(a a))) 8. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 191104/22492128. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.b)(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 5. ==[ beta ]==> ((^y.b)(a a)) 6. ==[ alpha ]==> ((^x.b)(a a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 191105/22492182. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))((^x1.x1) a))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))((^z.z) a))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 191106/22492263. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191107/22492371. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))(^y2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191108/22492434. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(c (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(c (^y.y))) REDUCED to normal form. ------ 191109/22492488. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(a (a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(a (a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (a b))) 5. ==[ beta ]==> ((^y.y)(a (a b))) 6. ==[ alpha ]==> ((^x.x)(a (a b))) 7. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 191110/22492551. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 191111/22492686. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 191112/22492713. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 10. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 191113/22492740. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (a a))(^y.a))) REDUCED to normal form. ------ 191114/22492794. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 191115/22492821. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a a)(^y.a))) 3. ==[ beta ]==> ((b (a (a a)))((a a)(^y.a))) 4. ==[ alpha ]==> ((b (a (a a)))((a a)(^x.a))) REDUCED to normal form. ------ 191116/22492848. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((a a) a) a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((a a) a) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)(((a a) a) a)) REDUCED to normal form. ------ 191117/22492938. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^z.a)(^x1.(x1 x1)))(^y.y)) 6. ==[ alpha ]==> (((^x.a)(^y.(y y)))(^z.z)) 7. ==[ beta ]==> (a (^z.z)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 191118/22493343. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 9. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191119/22493370. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 191120/22493397. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191121/22493487. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (^z.z)))) 7. ==[ beta ]==> (((^y.y) a)(a (^z.z))) 8. ==[ alpha ]==> (((^x.x) a)(a (^y.y))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 191122/22493514. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1)) a)) REDUCED to normal form. ------ 191123/22493532. ------ 1. ==[ start ]==> (((^a.b)(b a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(b (^y.(y y)))) 3. ==[ beta ]==> (b (b (^y.(y y)))) 4. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 191124/22493640. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191125/22493757. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b ((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b ((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b ((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))(b ((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191126/22493775. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 191127/22493784. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (a (a a)))) REDUCED to normal form. ------ 191128/22493820. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^b.a) b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.a) b)) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 191129/22493901. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(((^x.x) a)(^y.y))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (^x.x))) REDUCED to normal form. ------ 191130/22493928. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b ((a (^y.y))(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 191131/22493955. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a)(^z.a))) REDUCED to normal form. ------ 191132/22493982. ------ 1. ==[ start ]==> (((a b)(b a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a b)(b a))(((^x.x) a) a)) 3. ==[ beta ]==> (((a b)(b a))(a a)) REDUCED to normal form. ------ 191133/22494009. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a (^z.z)) b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a (^z.z)) b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.y)) b)) REDUCED to normal form. ------ 191134/22494090. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 191135/22494117. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1) c)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z) c)) 5. ==[ beta ]==> ((b (^y.y))((^z.z) c)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) c)) 7. ==[ beta ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 191136/22494144. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 191137/22494198. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a (^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z)) a)) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z)) a)) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 191138/22494216. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(b (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(b (a a))) 3. ==[ beta ]==> ((b (^y.y))(b (a a))) 4. ==[ alpha ]==> ((b (^x.x))(b (a a))) REDUCED to normal form. ------ 191139/22494225. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a a) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a a) b)) REDUCED to normal form. ------ 191140/22494252. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 191141/22494261. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191142/22494288. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 191143/22494525. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^z.((^x1.x1)(^y1.(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191144/22505865. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191145/22506138. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 191146/22506144. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((^z.z)(^x1.(^y1.y1))))(^y.y)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.x1)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 191147/22506147. ------ 1. ==[ start ]==> ((a (a (^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a (^x.x)))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 191148/22506333. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b a)(a b))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b a)(a b))) 3. ==[ eta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 191149/22506597. ------ 1. ==[ start ]==> (((^a.(a a)) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191150/22506828. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191151/22507893. ------ 1. ==[ start ]==> (((^a.b) a)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.b) a)(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (b (^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (b (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 191152/22509486. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(y (^z.z)))) REDUCED to normal form. ------ 191153/22509873. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 191154/22509924. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) b)(a (^z.z)))) 3. ==[ eta ]==> (b (((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> (b (((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (b (b (a (^y.y)))) 6. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 191155/22511295. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 191156/22511364. ------ 1. ==[ start ]==> ((^a.(^b.b))((b a)(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191157/22513707. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(b z))) 3. ==[ eta ]==> ((((^x.x) b)(a (^y.y))) b) 4. ==[ beta ]==> ((b (a (^y.y))) b) 5. ==[ alpha ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 191158/22513758. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191159/22514211. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 191160/22514454. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 191161/22515534. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x)(a a))(^y.(a a))) a) 4. ==[ beta ]==> (((a a)(^y.(a a))) a) 5. ==[ alpha ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 191162/22515723. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.z))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 7. ==[ beta ]==> (^y.(^z.y)) 8. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 191163/22515738. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.b) a)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.b) a)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 191164/22515894. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.((a a) a))) REDUCED to normal form. ------ 191165/22516911. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a (a a)))) REDUCED to normal form. ------ 191166/22517019. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 191167/22517034. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(y1 y1)) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191168/22517109. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.((^z.z) a))) 5. ==[ beta ]==> ((a (b (^x.x)))(^y.a)) REDUCED to normal form. ------ 191169/22517352. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(a (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(a (^z.z)))) REDUCED to normal form. ------ 191170/22517484. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a (a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191171/22517487. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 191172/22517523. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> ((^y.y)(^y1.y1)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191173/22517652. ------ 1. ==[ start ]==> (((^a.a) a)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (a ((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 191174/22517733. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191175/22517742. ------ 1. ==[ start ]==> (((a a)(a a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))(b (a (a (^x.x))))) REDUCED to normal form. ------ 191176/22517760. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191177/22517769. ------ 1. ==[ start ]==> ((a (a (^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a (^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 191178/22517778. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191179/22517805. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 (^y1.y1))) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((^y.(y (^z.z))) b) 6. ==[ alpha ]==> ((^x.(x (^y.y))) b) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191180/22517904. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 191181/22517931. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 191182/22517958. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b a)(a b))) 2. ==[ alpha ]==> ((a ((^x.x) a))((b a)(a b))) 3. ==[ beta ]==> ((a a)((b a)(a b))) REDUCED to normal form. ------ 191183/22518147. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> (((a a) a)(a (b (^y.y)))) 6. ==[ alpha ]==> (((a a) a)(a (b (^x.x)))) REDUCED to normal form. ------ 191184/22518174. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 191185/22518201. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((a (a a))((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> ((a (a a))((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 191186/22518219. ------ 1. ==[ start ]==> (((^a.(a a)) a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 191187/22518237. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((^y.(y y))((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((^x.(x x))((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> (((a (a (^y.y)))(^z.z))((a (a (^y.y)))(^z.z))) 6. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 191188/22518264. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191189/22518318. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 7. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 191190/22518345. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 191191/22518354. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 191192/22518381. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 191193/22518426. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 191194/22518453. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 191195/22518543. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 191196/22518669. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a (^y1.y1))) a)) 5. ==[ beta ]==> ((^y.y)((a (a (^y1.y1))) a)) 6. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 7. ==[ beta ]==> ((a (a (^y.y))) a) 8. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 191197/22518678. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a (a a)) b)((^z.z)(^y.y))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 191198/22518723. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b (^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((b (^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z)) c)) 5. ==[ beta ]==> ((^y.y)((b (^z.z)) c)) 6. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 7. ==[ beta ]==> ((b (^y.y)) c) 8. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 191199/22518786. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 191200/22519101. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(z (^x1.x1))) a)) 5. ==[ beta ]==> (a ((^z.(z (^x1.x1))) a)) 6. ==[ alpha ]==> (a ((^x.(x (^y.y))) a)) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 191201/22519362. ------ 1. ==[ start ]==> (((a a)((a a) a))(((a a) a)(b a))) REDUCED to normal form. ------ 191202/22519389. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 191203/22519416. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((a (a (a a)))((a (a a))((^y.y) b))) 4. ==[ alpha ]==> ((a (a (a a)))((a (a a))((^x.x) b))) 5. ==[ beta ]==> ((a (a (a a)))((a (a a)) b)) REDUCED to normal form. ------ 191204/22519443. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x) a)((a a)(a a)))) 5. ==[ beta ]==> (((a (a a)) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 191205/22519470. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(b (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 191206/22519497. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a a)((^x.(^y.y)) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 191207/22519515. ------ 1. ==[ start ]==> (((^a.b) a)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.b) a)(a (^y.(y (^z.z))))) 3. ==[ beta ]==> (b (a (^y.(y (^z.z))))) 4. ==[ alpha ]==> (b (a (^x.(x (^y.y))))) REDUCED to normal form. ------ 191208/22519533. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.b)(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.b)(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 191209/22519614. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) b)(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 191210/22519695. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 191211/22519704. ------ 1. ==[ start ]==> (((a b) a)((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(a b))) 3. ==[ beta ]==> (((a b) a)(^y.y)) 4. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 191212/22519722. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> ((a b)((a a)(^y.(a a)))) 6. ==[ alpha ]==> ((a b)((a a)(^x.(a a)))) REDUCED to normal form. ------ 191213/22519731. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 191214/22519749. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 191215/22519785. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.a)(b a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(b a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(b a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 191216/22519803. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 191217/22519812. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 191218/22519839. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.a)((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.a)((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 191219/22519866. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) a) REDUCED to normal form. ------ 191220/22519893. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 191221/22520577. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 191222/22520604. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a b))((^z.z)(b a))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(b a))) 5. ==[ beta ]==> (((a (^x.x))(a b))(b a)) REDUCED to normal form. ------ 191223/22520631. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a ((a a) a))((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a ((a a) a))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 191224/22520658. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a ((^z.z) b))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(a ((^y.y) b))) 7. ==[ beta ]==> (((a (a a))(^x.x))(a b)) REDUCED to normal form. ------ 191225/22520685. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a (^y.y))((a a)(a a)))) 6. ==[ alpha ]==> ((a (a a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 191226/22520712. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a a)(b (^y.y)))) 3. ==[ beta ]==> ((((a a) a) a)((a a)(b (^y.y)))) 4. ==[ alpha ]==> ((((a a) a) a)((a a)(b (^x.x)))) REDUCED to normal form. ------ 191227/22520829. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 191228/22520964. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 191229/22520973. ------ 1. ==[ start ]==> (((a b) c)((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 191230/22521000. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))(b a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(b a))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 191231/22521027. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 191232/22521045. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 191233/22521081. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 191234/22521108. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> ((a (^x.b))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.b))(b (^y.y))) REDUCED to normal form. ------ 191235/22521126. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((b (^y.y)) a)) 3. ==[ beta ]==> ((((a a) a)((a a) a))((b (^y.y)) a)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((b (^x.x)) a)) REDUCED to normal form. ------ 191236/22521162. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191237/22521189. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.a)) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.a)) REDUCED to normal form. ------ 191238/22521216. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 191239/22521468. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(b ((a a)(a a)))) 3. ==[ beta ]==> (((a b) a)(b ((a a)(a a)))) REDUCED to normal form. ------ 191240/22521495. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(a (b (^z.z)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 191241/22521522. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 191242/22521549. ------ 1. ==[ start ]==> ((a (b a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (b a))(((^x.x) b)(a (^y.y)))) 3. ==[ beta ]==> ((a (b a))(b (a (^y.y)))) 4. ==[ alpha ]==> ((a (b a))(b (a (^x.x)))) REDUCED to normal form. ------ 191243/22521891. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))(a a))) 5. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 191244/22521909. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))(b (^y.(^z.z)))) 6. ==[ alpha ]==> (((a b)(a b))(b (^x.(^y.y)))) REDUCED to normal form. ------ 191245/22521918. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(a (^y.y))) REDUCED to normal form. ------ 191246/22521990. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 191247/22521999. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 191248/22522026. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 191249/22522053. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 191250/22522377. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191251/22522863. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 191252/22522890. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(b (^z.z))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 191253/22522917. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(a (^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(a (^z.(a a)))) REDUCED to normal form. ------ 191254/22522962. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191255/22522971. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 191256/22522989. ------ 1. ==[ start ]==> ((a (^b.b))((b a)(^b.a))) 2. ==[ alpha ]==> ((a (^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 191257/22523268. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191258/22523313. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a) c)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b a) c)) 3. ==[ beta ]==> ((^y.y)((b a) c)) 4. ==[ alpha ]==> ((^x.x)((b a) c)) 5. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 191259/22523583. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191260/22523808. ------ 1. ==[ start ]==> (((a b)(^c.a))(d (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(d (^y.(^z.z)))) REDUCED to normal form. ------ 191261/22523835. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(c (^d.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(c (^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(c (^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (^z.a))) REDUCED to normal form. ------ 191262/22523862. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(b (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 191263/22523907. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a (^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191264/22523916. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 191265/22524825. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 191266/22524834. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 191267/22524888. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z))) b) REDUCED to normal form. ------ 191268/22524942. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 191269/22524969. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))(a b))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a b)(a b))) REDUCED to normal form. ------ 191270/22524996. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) a) REDUCED to normal form. ------ 191271/22525302. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(b ((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b ((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b ((a a)(^z.z)))) REDUCED to normal form. ------ 191272/22525329. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(a (b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(a (b a))) 3. ==[ beta ]==> ((b (a (^y.y)))(a (b a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(a (b a))) REDUCED to normal form. ------ 191273/22525356. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 191274/22525383. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((a (b (^x.x)))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(a (^y.y)))) REDUCED to normal form. ------ 191275/22525662. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a b)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191276/22525698. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a)(a (a a)))) 3. ==[ beta ]==> ((b c)((^y.a)(a (a a)))) 4. ==[ alpha ]==> ((b c)((^x.a)(a (a a)))) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 191277/22525725. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 191278/22525770. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> ((b (^x.x))(a (^z.b))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.b))) REDUCED to normal form. ------ 191279/22525797. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(a a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 191280/22525833. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 191281/22525851. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((a a)(^x1.x1)) a)) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a)(^y1.y1)) a)) REDUCED to normal form. ------ 191282/22525941. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 191283/22525968. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 191284/22526049. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 191285/22526076. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 191286/22526166. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 191287/22526193. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 191288/22526220. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)((a (a a))((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a b)((a (a a))((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a b)((a (a a))(^y.y))) 8. ==[ alpha ]==> ((a b)((a (a a))(^x.x))) REDUCED to normal form. ------ 191289/22526247. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a ((a a) a))) REDUCED to normal form. ------ 191290/22526274. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (^z.z))(a b))) 3. ==[ beta ]==> (((^y.y)(b a))((a (^z.z))(a b))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))(a b))) 5. ==[ beta ]==> ((b a)((a (^y.y))(a b))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(a b))) REDUCED to normal form. ------ 191291/22526301. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((a a)(a a))) REDUCED to normal form. ------ 191292/22526823. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^c.a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191293/22526940. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b (^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(b (^z.b))) 3. ==[ beta ]==> (((^y.y) a)(b (^z.b))) 4. ==[ alpha ]==> (((^x.x) a)(b (^y.b))) 5. ==[ beta ]==> (a (b (^y.b))) 6. ==[ alpha ]==> (a (b (^x.b))) REDUCED to normal form. ------ 191294/22526985. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a b)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.y))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 191295/22527039. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(^x1.a))) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(^z.a))) 9. ==[ beta ]==> ((b b)((^y.y)(^z.a))) 10. ==[ alpha ]==> ((b b)((^x.x)(^y.a))) 11. ==[ beta ]==> ((b b)(^y.a)) 12. ==[ alpha ]==> ((b b)(^x.a)) REDUCED to normal form. ------ 191296/22527048. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 191297/22527075. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(a (a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191298/22527120. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 191299/22527129. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 191300/22527156. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.z)(a b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.z)(a b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(a b))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a b)) REDUCED to normal form. ------ 191301/22527183. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) b) REDUCED to normal form. ------ 191302/22527237. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 191303/22527264. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 191304/22527291. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 191305/22527345. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.b))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.b))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.b))) 7. ==[ beta ]==> ((^y.y)(^z.b)) 8. ==[ alpha ]==> ((^x.x)(^y.b)) 9. ==[ beta ]==> (^y.b) 10. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 191306/22527363. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.b) a)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.b) a)) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) b) REDUCED to normal form. ------ 191307/22527381. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((a a) a)(a a))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(a a))) REDUCED to normal form. ------ 191308/22527408. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 191309/22527435. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a (a a))((^y.y) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a (a a))((^y.y) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a (a a))((^x.x) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a (a a)) a)) REDUCED to normal form. ------ 191310/22527462. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y) a)(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x) a)(a (a a)))) 5. ==[ beta ]==> (((a (a a)) b)(a (a (a a)))) REDUCED to normal form. ------ 191311/22527489. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.z))(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 191312/22527516. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a a)((a a) a))) REDUCED to normal form. ------ 191313/22527777. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((a (^x.x))((^z.a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.a))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 191314/22528182. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191315/22528200. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (a a)) b)) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a)) b)) 5. ==[ beta ]==> ((^y.y)((a (a a)) b)) 6. ==[ alpha ]==> ((^x.x)((a (a a)) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 191316/22528209. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 6. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 191317/22528236. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 191318/22528308. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y)) a)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 191319/22528452. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(z z))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))((a a)(a a))) REDUCED to normal form. ------ 191320/22528497. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191321/22528533. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 191322/22528560. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))((^z.z)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 191323/22528614. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191324/22528641. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 191325/22528659. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 191326/22528677. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(((^y.y) a)(a a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a (a a))) REDUCED to normal form. ------ 191327/22528704. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 191328/22528731. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a)((^z.z) a))) 3. ==[ beta ]==> ((a (b (^y.y)))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)((^y.y) a))) 5. ==[ beta ]==> ((a (b (^x.x)))((a a) a)) REDUCED to normal form. ------ 191329/22528785. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(c b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(c b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(c b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(c b)) 5. ==[ beta ]==> (((^y.y) b)(c b)) 6. ==[ alpha ]==> (((^x.x) b)(c b)) 7. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 191330/22528812. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b c)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b c)) REDUCED to normal form. ------ 191331/22528893. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b (a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b (a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (a (^y.y)))) REDUCED to normal form. ------ 191332/22528947. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a (^z.z))(a a))) REDUCED to normal form. ------ 191333/22528974. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a)(a (^z.z)))) 5. ==[ beta ]==> ((b (^y.y))((a a)(a (^z.z)))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(a (^y.y)))) REDUCED to normal form. ------ 191334/22529073. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 191335/22529082. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(b (a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(b (a a))) REDUCED to normal form. ------ 191336/22529109. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a (a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 191337/22529118. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1)) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191338/22529145. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.y1) b)) 3. ==[ beta ]==> ((^y.y)((^y1.y1) b)) 4. ==[ alpha ]==> ((^x.x)((^y.y) b)) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 191339/22529391. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^z.(^x1.(^y1.(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191340/22529850. ------ 1. ==[ start ]==> ((^a.(a (a a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.(^y1.y1))))((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1)))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.(^y2.y2))))(^z2.(^x3.(^y3.(^z3.z3)))))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191341/22531146. ------ 1. ==[ start ]==> ((^a.(a b))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x b))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.(^z.(z (^x1.x1)))) b) 4. ==[ alpha ]==> ((^x.(^y.(y (^z.z)))) b) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 191342/22538166. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(^x1.((^y1.y1)(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))(^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191343/22538985. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^a.(a b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(x1 b))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 191344/22540281. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(y1 (y1 y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191345/22540731. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191346/22540911. ------ 1. ==[ start ]==> ((^a.(a a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^x1.(a a)))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191347/22541019. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^z.z)(^x1.(^y1.(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191348/22541022. ------ 1. ==[ start ]==> ((a (a (^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 191349/22541031. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.y1)(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1)(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191350/22541136. ------ 1. ==[ start ]==> ((^a.(^b.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (^y.(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> (^x.(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 191351/22541379. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 191352/22541478. ------ 1. ==[ start ]==> ((^a.(a (a a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (^y.(^z.(^x1.x1))))(a (^y.(^z.(^x1.x1)))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.(^y1.(^z1.z1))))(a (^x2.(^y2.(^z2.z2)))))) REDUCED to normal form. ------ 191353/22541481. ------ 1. ==[ start ]==> ((a (a (a a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191354/22541829. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191355/22542354. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.(z (z (^x1.x1))))) 5. ==[ beta ]==> (a (^z.(z (z (^x1.x1))))) 6. ==[ alpha ]==> (a (^x.(x (x (^y.y))))) REDUCED to normal form. ------ 191356/22542594. ------ 1. ==[ start ]==> ((^a.(^a.b))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 191357/22542774. ------ 1. ==[ start ]==> ((^a.(a b))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x b))(a (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a (^y.(y (^z.z)))) b) 4. ==[ alpha ]==> ((a (^x.(x (^y.y)))) b) REDUCED to normal form. ------ 191358/22542777. ------ 1. ==[ start ]==> ((a (a b))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a b))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 191359/22543182. ------ 1. ==[ start ]==> (((a a)(a b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a b))(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(a b))(^x.(^z.z))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 191360/22543596. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.x)((^y.y)(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 191361/22544361. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 191362/22545477. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(^y.((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.((a a)(a a)))) 6. ==[ alpha ]==> (((a a) a)(^x.((a a)(a a)))) REDUCED to normal form. ------ 191363/22545636. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((^x1.(a a))(^y1.a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(a a))(^y.a))(^z.(^x1.x1))) 5. ==[ beta ]==> ((a a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 191364/22546554. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 191365/22546836. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.((^x2.x2) b))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191366/22547448. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 191367/22547553. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((((^y.(a a))(^z.(z z)))((^y.(a a))(^z.(z z))))(((^y.(a a))(^z.(z z)))((^y.(a a))(^z.(z z))))) 4. ==[ alpha ]==> ((((^x.(a a))(^y.(y y)))((^z.(a a))(^x1.(x1 x1))))(((^y1.(a a))(^z1.(z1 z1)))((^x2.(a a))(^y2.(y2 y2))))) 5. ==[ beta ]==> (((a a)((^z.(a a))(^x1.(x1 x1))))(((^y1.(a a))(^z1.(z1 z1)))((^x2.(a a))(^y2.(y2 y2))))) 6. ==[ alpha ]==> (((a a)((^x.(a a))(^y.(y y))))(((^z.(a a))(^x1.(x1 x1)))((^y1.(a a))(^z1.(z1 z1))))) 7. ==[ beta ]==> (((a a)(a a))(((^z.(a a))(^x1.(x1 x1)))((^y1.(a a))(^z1.(z1 z1))))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.(a a))(^y.(y y)))((^z.(a a))(^x1.(x1 x1))))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^z.(a a))(^x1.(x1 x1))))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a))(^y.(y y))))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 191368/22548312. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.(z a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(z a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(y a))) REDUCED to normal form. ------ 191369/22549086. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 191370/22549581. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 191371/22549794. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191372/22549797. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^y.(a a))) REDUCED to normal form. ------ 191373/22550409. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.b))) REDUCED to normal form. ------ 191374/22550613. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(a (a b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(a (a b))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 191375/22550616. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^a.(a b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(z b))) REDUCED to normal form. ------ 191376/22550796. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.b))) REDUCED to normal form. ------ 191377/22550958. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.((a a) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.((a a) a))) REDUCED to normal form. ------ 191378/22551036. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^z.(z z))(^x1.a))(((^z.(z z))(^x1.a))(^y.y))) 4. ==[ alpha ]==> (((^x.(x x))(^y.a))(((^z.(z z))(^x1.a))(^y1.y1))) 5. ==[ beta ]==> (((^y.a)(^y.a))(((^z.(z z))(^x1.a))(^y1.y1))) 6. ==[ alpha ]==> (((^x.a)(^y.a))(((^z.(z z))(^x1.a))(^y1.y1))) 7. ==[ beta ]==> (a (((^z.(z z))(^x1.a))(^y1.y1))) 8. ==[ alpha ]==> (a (((^x.(x x))(^y.a))(^z.z))) 9. ==[ beta ]==> (a (((^y.a)(^y.a))(^z.z))) 10. ==[ alpha ]==> (a (((^x.a)(^y.a))(^z.z))) 11. ==[ beta ]==> (a (a (^z.z))) 12. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 191379/22551561. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^x.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 191380/22551786. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 191381/22551909. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (a (a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191382/22551912. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(x1 (x1 x1)))) REDUCED to normal form. ------ 191383/22552011. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 191384/22552092. ------ 1. ==[ start ]==> (((a b)(b a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.((^y.y) a))) 3. ==[ beta ]==> (((a b)(b a))(^x.a)) REDUCED to normal form. ------ 191385/22552254. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.x))) REDUCED to normal form. ------ 191386/22552308. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(a (^z.z)))) REDUCED to normal form. ------ 191387/22552359. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191388/22552362. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 191389/22552371. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191390/22552545. ------ 1. ==[ start ]==> ((a (a a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a (a a))(^y.y)) 4. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 191391/22552626. ------ 1. ==[ start ]==> (((a a)(a a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(^y.y)) 4. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 191392/22552653. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 191393/22552662. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a ((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191394/22552671. ------ 1. ==[ start ]==> (((a a) b)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 191395/22552689. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a (^y.y)))(a a)) 6. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 191396/22552698. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (((a (^x.x)) a)(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.y))) REDUCED to normal form. ------ 191397/22552716. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 191398/22552743. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 191399/22552770. ------ 1. ==[ start ]==> ((a (^b.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.a))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 191400/22552851. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b a)(a b))) 3. ==[ beta ]==> ((^y.a)((b a)(a b))) 4. ==[ alpha ]==> ((^x.a)((b a)(a b))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 191401/22552878. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 191402/22552932. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a b)(b a))) 3. ==[ beta ]==> (((^y.y) a)((a b)(b a))) 4. ==[ alpha ]==> (((^x.x) a)((a b)(b a))) 5. ==[ beta ]==> (a ((a b)(b a))) REDUCED to normal form. ------ 191403/22552959. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((a a) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 191404/22553013. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 191405/22553085. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a (a a))(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a (a a))(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 191406/22553112. ------ 1. ==[ start ]==> ((a (a (a a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 191407/22553184. ------ 1. ==[ start ]==> ((((^a.a) a) b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((a b)((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((a b)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 191408/22553211. ------ 1. ==[ start ]==> (((a (a a)) a)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 191409/22553238. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 191410/22553265. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 191411/22553292. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.b))) REDUCED to normal form. ------ 191412/22553319. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 191413/22553355. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 191414/22553382. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.b)(b a))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.b)(b a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.b)(b a))) 5. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 191415/22553427. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b b)(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((b b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b b)(^y.y)) 8. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 191416/22553436. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 191417/22553463. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 191418/22553562. ------ 1. ==[ start ]==> (((a (a a)) b)((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a)) b)((a (a (^x.x))) a)) REDUCED to normal form. ------ 191419/22553589. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((^y.y) a)(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (a (((^y.(^z.z)) a) b)) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 191420/22553616. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 191421/22553787. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 191422/22553868. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 191423/22553931. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(c (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(c (b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(c (b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(c (b (^y.y)))) 5. ==[ beta ]==> (c (b (^y.y))) 6. ==[ alpha ]==> (c (b (^x.x))) REDUCED to normal form. ------ 191424/22553985. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(a (a (a (^z.z))))) 3. ==[ beta ]==> (((^y.a)(^y.a))(a (a (a (^z.z))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(a (a (a (^z.z))))) 5. ==[ beta ]==> (a (a (a (a (^z.z))))) 6. ==[ alpha ]==> (a (a (a (a (^x.x))))) REDUCED to normal form. ------ 191425/22554066. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> (((a a) a)(((a a)(a a))((^y.y) a))) 4. ==[ alpha ]==> (((a a) a)(((a a)(a a))((^x.x) a))) 5. ==[ beta ]==> (((a a) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 191426/22554093. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> (((^y.y) b)(a (a a))) 6. ==[ alpha ]==> (((^x.x) b)(a (a a))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 191427/22554147. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((b a)((a a) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((b a)((a a) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b a)((a a) a))) 5. ==[ beta ]==> ((a ((^y.y) a))((b a)((a a) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))((b a)((a a) a))) 7. ==[ beta ]==> ((a a)((b a)((a a) a))) REDUCED to normal form. ------ 191428/22554228. ------ 1. ==[ start ]==> ((a (^a.b))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 191429/22554408. ------ 1. ==[ start ]==> ((a (a b))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a b))(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 191430/22554561. ------ 1. ==[ start ]==> ((((a a) a) b)((b a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a) b)((b a)(^x.a))) REDUCED to normal form. ------ 191431/22554588. ------ 1. ==[ start ]==> (((a b) a)(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b) a)(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 191432/22554615. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.(a a)))) REDUCED to normal form. ------ 191433/22554696. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 191434/22554723. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (a a))(^z.z))) 5. ==[ beta ]==> ((^y.a)((a (a a))(^z.z))) 6. ==[ alpha ]==> ((^x.a)((a (a a))(^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 191435/22554813. ------ 1. ==[ start ]==> (((a a)(a b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 191436/22554921. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(z z)))) 7. ==[ beta ]==> (a ((^y.y)(^z.(z z)))) 8. ==[ alpha ]==> (a ((^x.x)(^y.(y y)))) 9. ==[ beta ]==> (a (^y.(y y))) 10. ==[ alpha ]==> (a (^x.(x x))) REDUCED to normal form. ------ 191437/22554948. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 191438/22555173. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c ((a a)(a a)))) 3. ==[ beta ]==> (b (c ((a a)(a a)))) REDUCED to normal form. ------ 191439/22555227. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y)(a a))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)(a ((^y.(^z.z)) a))) 6. ==[ alpha ]==> ((a a)(a ((^x.(^y.y)) a))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 191440/22555254. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((b (^z.z))(a a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(a a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(a a))) 5. ==[ beta ]==> ((b (^y.y))(a a)) 6. ==[ alpha ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 191441/22555308. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b)((^z1.z1) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b)((^z1.z1) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b)((^y1.y1) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b)((^x1.x1) a))) 9. ==[ beta ]==> ((^y.y)(((^z.z) b)((^x1.x1) a))) 10. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z) a))) 11. ==[ beta ]==> (((^y.y) b)((^z.z) a)) 12. ==[ alpha ]==> (((^x.x) b)((^y.y) a)) 13. ==[ beta ]==> (b ((^y.y) a)) 14. ==[ alpha ]==> (b ((^x.x) a)) 15. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191442/22555389. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (b (((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 191443/22555857. ------ 1. ==[ start ]==> (((a b) c)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 191444/22555911. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191445/22555965. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 191446/22556046. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a)) b)) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191447/22556073. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) b) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(b c)) REDUCED to normal form. ------ 191448/22556190. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 191449/22556217. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 191450/22556244. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 191451/22556298. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.x1)))) 11. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))) 12. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 13. ==[ beta ]==> (^y.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191452/22556325. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.a)(^y.y))) 3. ==[ beta ]==> ((((a a) a)(a (a a))) a) REDUCED to normal form. ------ 191453/22556352. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 191454/22556523. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (b (((a a)(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y)(^z.z)))) 7. ==[ beta ]==> (b (((a a)(^x.x))(^z.z))) 8. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 191455/22556604. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (b (((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 191456/22556712. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> ((b a)((a (^y.y))((^z.z) b))) 4. ==[ alpha ]==> ((b a)((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> ((b a)((a (^x.x)) b)) REDUCED to normal form. ------ 191457/22556739. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a a)((a a)(a a)))) 5. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 191458/22556775. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 191459/22556802. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(b (^y.(^z.z)))) REDUCED to normal form. ------ 191460/22556856. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)(^z.(z z)))) REDUCED to normal form. ------ 191461/22556883. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 191462/22556910. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (((a a)(^x.a))((a a)(^z.a))) 6. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.a))) REDUCED to normal form. ------ 191463/22556937. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(^x1.b))) REDUCED to normal form. ------ 191464/22557000. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 191465/22557027. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((b a)(b a))) REDUCED to normal form. ------ 191466/22557054. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))((^y.a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (a a))((^x.a)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 191467/22557081. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 191468/22557108. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)((^y.y)((a a)(a a)))) 6. ==[ alpha ]==> (((a a) a)((^x.x)((a a)(a a)))) 7. ==[ beta ]==> (((a a) a)((a a)(a a))) REDUCED to normal form. ------ 191469/22557162. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 191470/22557189. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(^y1.a))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 191471/22557270. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 191472/22557441. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(b ((^x1.x1) b))) 3. ==[ beta ]==> (b (b ((^x1.x1) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 191473/22557549. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((b a)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191474/22557576. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 191475/22557603. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 191476/22557657. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((a a) a)(a b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a) a)(a b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a) a)(a b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a) a)(a b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a)(a b))) 7. ==[ beta ]==> (((a a)(a a))(((a a) a)(a b))) REDUCED to normal form. ------ 191477/22557738. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> (b (((^x1.x1) a)(b a))) 4. ==[ alpha ]==> (b (((^x.x) a)(b a))) 5. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 191478/22557855. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) REDUCED to normal form. ------ 191479/22557918. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.y)) REDUCED to normal form. ------ 191480/22557945. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 191481/22557972. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.b)((a a) a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.b)((a a) a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.b)((a a) a))) 5. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 191482/22557999. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.a)(a b))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.a)(a b))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.a)(a b))) 5. ==[ beta ]==> ((a b)((^y.a)(a b))) 6. ==[ alpha ]==> ((a b)((^x.a)(a b))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 191483/22558026. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 191484/22558053. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(^x.x))(((a a)(^z.z))((a a)(^z.z)))) 6. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 191485/22558080. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.a)(b a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.a)(b a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.a)(b a))) 5. ==[ beta ]==> (((a a)(a (a a))) a) REDUCED to normal form. ------ 191486/22558107. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 191487/22558152. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1) b) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191488/22558161. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 191489/22558188. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 191490/22558467. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(a ((^z1.z1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191491/22558476. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 191492/22558503. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 191493/22558521. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((b a)(a (^z.z)))) 3. ==[ beta ]==> (((^y.y) b)((b a)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)((b a)(a (^y.y)))) 5. ==[ beta ]==> (b ((b a)(a (^y.y)))) 6. ==[ alpha ]==> (b ((b a)(a (^x.x)))) REDUCED to normal form. ------ 191494/22558548. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(((a a)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 191495/22558602. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b)(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 191496/22558683. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> (b ((a (a a))((^y.y)(a a)))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 191497/22558800. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.x2))) REDUCED to normal form. ------ 191498/22558827. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 191499/22558863. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 191500/22558890. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a a)) REDUCED to normal form. ------ 191501/22558917. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (b a))((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (b a))((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 191502/22558971. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a b))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(a b))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(a b))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 191503/22558998. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(x x))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a b))(((^y.y)(a a))((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)(a b))((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> ((((a a) a)(a b))((a a)((^x.x)(a a)))) 7. ==[ beta ]==> ((((a a) a)(a b))((a a)(a a))) REDUCED to normal form. ------ 191504/22559025. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)((a a) a)) a) REDUCED to normal form. ------ 191505/22559052. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(b a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(b a))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 191506/22559079. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 191507/22559160. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 191508/22559187. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 191509/22559358. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(b (b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(b (b a))) 3. ==[ beta ]==> (b (b (b a))) REDUCED to normal form. ------ 191510/22559466. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((^y1.y1)(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191511/22559547. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)((a a) a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)((a a) a))) 7. ==[ beta ]==> (((a a)(a a))((a a) a)) REDUCED to normal form. ------ 191512/22559574. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a (a a))(a b))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a b))) 5. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 191513/22559628. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 191514/22559691. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((b a)(^y.y))) REDUCED to normal form. ------ 191515/22559718. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 191516/22559772. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(^x1.(x1 x1)))) REDUCED to normal form. ------ 191517/22559826. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.a)) REDUCED to normal form. ------ 191518/22559853. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a))(^x1.b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a))(^x1.b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a))(^z.b))) REDUCED to normal form. ------ 191519/22559880. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a (^z.(a a)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 191520/22559916. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 191521/22559943. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.z)(b a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(b a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(b a))) 5. ==[ beta ]==> (((a (^x.x)) b)(b a)) REDUCED to normal form. ------ 191522/22559997. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 191523/22560024. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 191524/22560051. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)(^y.(y y)))) 5. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 191525/22560078. ------ 1. ==[ start ]==> (((a b)(a b))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 191526/22560105. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 191527/22560132. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(^x1.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((^x1.b)(^x1.b))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(^x1.b))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 191528/22560357. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))((^z2.z2)(^x3.x3)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(^y2.y2))((^z2.z2)(^x3.x3)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191529/22560438. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 191530/22560582. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a) a)(^y.(y y)))) 3. ==[ beta ]==> ((b c)(((a a) a)(^y.(y y)))) 4. ==[ alpha ]==> ((b c)(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 191531/22560609. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) b)(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) b)(^x.(^y.y))) REDUCED to normal form. ------ 191532/22560717. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 191533/22560744. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 191534/22561158. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(c (^z.b))) 3. ==[ beta ]==> (((^y.y)(b a))(c (^z.b))) 4. ==[ alpha ]==> (((^x.x)(b a))(c (^y.b))) 5. ==[ beta ]==> ((b a)(c (^y.b))) 6. ==[ alpha ]==> ((b a)(c (^x.b))) REDUCED to normal form. ------ 191535/22561185. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 191536/22561212. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a (^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 191537/22561239. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a a)(a b))((^y.(a a))(a a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(a a))(a a))) 5. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 191538/22561266. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 191539/22561320. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.z)) REDUCED to normal form. ------ 191540/22561347. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.(y y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.(x x))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((^y.y)(^z.z)))) 8. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((b a)((^y.y)((^z.z)(^x1.x1)))) 10. ==[ alpha ]==> ((b a)((^x.x)((^y.y)(^z.z)))) 11. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 12. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 13. ==[ beta ]==> ((b a)(^y.y)) 14. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 191541/22561374. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) a) REDUCED to normal form. ------ 191542/22561428. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 191543/22561599. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c ((a a) a))) 3. ==[ beta ]==> (b (c ((a a) a))) REDUCED to normal form. ------ 191544/22561707. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a) a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191545/22561842. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a a)(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a a)(a b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a a)(a b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a a)(a b))) 5. ==[ beta ]==> ((^y.y)((a a)(a b))) 6. ==[ alpha ]==> ((^x.x)((a a)(a b))) 7. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 191546/22561932. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.a)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.a)) REDUCED to normal form. ------ 191547/22561959. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a (a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (a a))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (a a))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191548/22562013. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 191549/22562040. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a a)(^z.b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(^y.b))) REDUCED to normal form. ------ 191550/22562067. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a b) a)) REDUCED to normal form. ------ 191551/22562121. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1) c)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1) c)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) c) REDUCED to normal form. ------ 191552/22562247. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(a (a b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (a b))) REDUCED to normal form. ------ 191553/22562400. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b (^c.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))(b (^x.a))) REDUCED to normal form. ------ 191554/22562427. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.b))) REDUCED to normal form. ------ 191555/22562481. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 191556/22562535. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 191557/22562562. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 191558/22562589. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.y)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)((a a) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)((a a) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a a) a)) REDUCED to normal form. ------ 191559/22562643. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 191560/22562670. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y))(^z.a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.a)(^z.a))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a)(^z.a))) 5. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 191561/22563066. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> (b (((^y.y)(^z.z)) a)) 6. ==[ alpha ]==> (b (((^x.x)(^y.y)) a)) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191562/22563093. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (a a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (a a)) b)) REDUCED to normal form. ------ 191563/22563192. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (^y.y))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.x))) REDUCED to normal form. ------ 191564/22563228. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z)) b)) 5. ==[ beta ]==> ((^y.y)((^z.(z z)) b)) 6. ==[ alpha ]==> ((^x.x)((^y.(y y)) b)) 7. ==[ beta ]==> ((^y.(y y)) b) 8. ==[ alpha ]==> ((^x.(x x)) b) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 191565/22563255. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 191566/22563273. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> (b ((a (^y.y))((^z.z) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) a))) 5. ==[ beta ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 191567/22563336. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (a a))(^z.z))) REDUCED to normal form. ------ 191568/22563417. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.(z z)))) REDUCED to normal form. ------ 191569/22563444. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (a a)) a)) REDUCED to normal form. ------ 191570/22563516. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b ((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.y))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 191571/22563543. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (a (a a)))) REDUCED to normal form. ------ 191572/22563615. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b (^z.a))) 3. ==[ beta ]==> ((a (b (^y.y)))(b (^z.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(b (^y.a))) REDUCED to normal form. ------ 191573/22563642. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (^x.(x x)))) REDUCED to normal form. ------ 191574/22563669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.a)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.a)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)(a a))) 5. ==[ beta ]==> (((^y.y) b)((^z.a)(a a))) 6. ==[ alpha ]==> (((^x.x) b)((^y.a)(a a))) 7. ==[ beta ]==> (b ((^y.a)(a a))) 8. ==[ alpha ]==> (b ((^x.a)(a a))) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191575/22563696. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 191576/22563723. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.x)((^y.y) a))) 3. ==[ beta ]==> (((a b)(b a))((^y.y) a)) 4. ==[ alpha ]==> (((a b)(b a))((^x.x) a)) 5. ==[ beta ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 191577/22563750. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 191578/22563777. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 191579/22563858. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 191580/22563885. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(a (^x.a))) REDUCED to normal form. ------ 191581/22563939. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 191582/22563957. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a (^z.z)) a)) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z)) a)) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 191583/22563966. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 191584/22563993. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 191585/22564002. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a (^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191586/22564029. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a a)(a a))) 3. ==[ beta ]==> ((^y.y)((a a)(a a))) 4. ==[ alpha ]==> ((^x.x)((a a)(a a))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 191587/22573878. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(^y1.x1))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 191588/22575174. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191589/22575933. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191590/22575942. ------ 1. ==[ start ]==> (((a a) b)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 191591/22576392. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(y y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(x x))(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.(^x1.(^y1.y1))))(^y.(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191592/22576605. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191593/22576824. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(a (a (^z1.z1))))) 5. ==[ beta ]==> ((^y.y)(^y1.(a (a (^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 7. ==[ beta ]==> (^y.(a (a (^z.z)))) 8. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 191594/22577256. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (a (^z.(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> (a (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 191595/22577670. ------ 1. ==[ start ]==> (((^a.b) a)(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) a)(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b (^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b (^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 191596/22577688. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.b)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.b)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 191597/22578063. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(b (^y1.y1)))((^z.(^x1.x1))(b (^y1.y1))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(b (^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2))))) 5. ==[ beta ]==> (^x.((^z.z)((^y1.(^z1.z1))(b (^x2.x2))))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(b (^y1.y1))))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(b (^y1.y1)))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(b (^x1.x1)))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191598/22578507. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 191599/22578885. ------ 1. ==[ start ]==> (((^a.b) c)(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(b (^z.z)))) 3. ==[ beta ]==> (b (^y.(b (^z.z)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 191600/22578945. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((((a a)(a a))(^z.(^x1.x1)))(((a a)(a a))(^z.(^x1.x1))))(^y.y)) 4. ==[ alpha ]==> (((((a a)(a a))(^x.(^y.y)))(((a a)(a a))(^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 191601/22579281. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(^y.(y (^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 191602/22579701. ------ 1. ==[ start ]==> ((^a.(b a))((^c.(a a)) b)) 2. ==[ alpha ]==> ((^x.(b x))((^y.(a a)) b)) 3. ==[ eta ]==> (b ((^y.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 191603/22581072. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^z.b)) REDUCED to normal form. ------ 191604/22581141. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191605/22581456. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 191606/22581738. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191607/22581747. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^z.b)) REDUCED to normal form. ------ 191608/22582062. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191609/22583214. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^c.(^d.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.a))) REDUCED to normal form. ------ 191610/22583535. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191611/22584006. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.((a a)(^z1.z1)))) REDUCED to normal form. ------ 191612/22584258. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.((z z)(^x1.x1)))) REDUCED to normal form. ------ 191613/22584696. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a a)(^x1.(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191614/22585140. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(y y)))) 5. ==[ beta ]==> (^y.(^z.(y y))) 6. ==[ alpha ]==> (^x.(^y.(x x))) REDUCED to normal form. ------ 191615/22585515. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.x1)(^y1.b))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 191616/22585518. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.(^a.b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(^x1.z))) REDUCED to normal form. ------ 191617/22586463. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 191618/22586811. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(z1 z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191619/22586814. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(y1 y1)))) REDUCED to normal form. ------ 191620/22586994. ------ 1. ==[ start ]==> (((a b)(b a))(^c.(^b.a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.a))) REDUCED to normal form. ------ 191621/22587156. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.c)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.c)) REDUCED to normal form. ------ 191622/22587228. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.c)) 3. ==[ beta ]==> ((b (^y.y))(^z.c)) 4. ==[ alpha ]==> ((b (^x.x))(^y.c)) REDUCED to normal form. ------ 191623/22587261. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a a) b)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191624/22587273. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191625/22587465. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191626/22587528. ------ 1. ==[ start ]==> (((^a.a) b)(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x) b)(c ((^y.(^z.z)) a))) 3. ==[ beta ]==> (b (c ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (b (c ((^x.(^y.y)) a))) 5. ==[ beta ]==> (b (c (^y.y))) 6. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 191627/22587555. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)(b (a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)(b (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 191628/22587573. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191629/22587582. ------ 1. ==[ start ]==> (((a a) b)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)(a ((^x.x)(^y.(^z.z))))) 3. ==[ beta ]==> (((a a) b)(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 191630/22587609. ------ 1. ==[ start ]==> (((a (^a.a)) a)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 191631/22587636. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 191632/22587663. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((b (^z.z)) a)) REDUCED to normal form. ------ 191633/22587717. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191634/22587798. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 191635/22587825. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a a)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 191636/22587852. ------ 1. ==[ start ]==> (((a a)(^b.a))((a b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.a))((a b)(b a))) REDUCED to normal form. ------ 191637/22587879. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a) a)(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 191638/22587906. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x))((^z.z) b)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 9. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 191639/22588014. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((a a)((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> ((a a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 191640/22588032. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.(y y))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 191641/22588059. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 191642/22588167. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191643/22588248. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 191644/22588320. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191645/22588347. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 191646/22588383. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191647/22588410. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 191648/22588464. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(a (a (^z1.z1))))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(a (a (^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 7. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 8. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 191649/22588599. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 191650/22588896. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.z)(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (a ((^z.z)(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(y (^z.z))))) 7. ==[ beta ]==> (a (^y.(y (^z.z)))) 8. ==[ alpha ]==> (a (^x.(x (^y.y)))) REDUCED to normal form. ------ 191651/22588932. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (b (((^y.(^z.z)) a)(a a))) 6. ==[ alpha ]==> (b (((^x.(^y.y)) a)(a a))) 7. ==[ beta ]==> (b ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 191652/22588959. ------ 1. ==[ start ]==> ((((a a) a) a)((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 191653/22589013. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (a (a a)))) REDUCED to normal form. ------ 191654/22589040. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 191655/22589067. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((b a)((a a) a))) REDUCED to normal form. ------ 191656/22589094. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191657/22589121. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 191658/22589310. ------ 1. ==[ start ]==> (((^a.b) a)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) a)((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (b ((a a)((^y.(^z.z)) a))) 4. ==[ alpha ]==> (b ((a a)((^x.(^y.y)) a))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 191659/22589328. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.b)(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.b)(a (^y.(y (^z.z))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 191660/22589517. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 191661/22589544. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 191662/22589679. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (b ((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191663/22589706. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 191664/22589751. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z) a)) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y) a)) 5. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 191665/22589778. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((b (^x1.x1)) b)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((b (^x1.x1)) b)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b (^z.z)) b)) 5. ==[ beta ]==> ((a (^y.y))((b (^z.z)) b)) 6. ==[ alpha ]==> ((a (^x.x))((b (^y.y)) b)) REDUCED to normal form. ------ 191666/22589922. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 191667/22589949. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(a a))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 191668/22590003. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.a))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 7. ==[ beta ]==> ((^y.a)(^z.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 191669/22590084. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191670/22590093. ------ 1. ==[ start ]==> (((a b) b)(c ((a a)(a a)))) REDUCED to normal form. ------ 191671/22590120. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)(b (b (^y.y)))) 3. ==[ beta ]==> (((a a) a)(b (b (^y.y)))) 4. ==[ alpha ]==> (((a a) a)(b (b (^x.x)))) REDUCED to normal form. ------ 191672/22590147. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 191673/22590174. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((b (^z.z))(a a))) REDUCED to normal form. ------ 191674/22590228. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b ((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 191675/22590255. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((a (^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((a (^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(y y))((a (^z.(^x1.x1)))(a (a a)))) 6. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z)))(a (a a)))) 7. ==[ beta ]==> (((a (^y.(^z.z)))(a (a a)))((a (^y.(^z.z)))(a (a a)))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 191676/22590282. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((b a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((b a)(^y.y))) REDUCED to normal form. ------ 191677/22590309. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))((a a) a))) REDUCED to normal form. ------ 191678/22590336. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(a b))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(a b))) REDUCED to normal form. ------ 191679/22590525. ------ 1. ==[ start ]==> (((^a.b) c)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((a a)(b (^y.y)))) 3. ==[ beta ]==> (b ((a a)(b (^y.y)))) 4. ==[ alpha ]==> (b ((a a)(b (^x.x)))) REDUCED to normal form. ------ 191680/22590561. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((b (^y.y))(^z.z))) 3. ==[ beta ]==> (((a a)(a a))((b (^y.y))(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((b (^x.x))(^y.y))) REDUCED to normal form. ------ 191681/22590588. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 191682/22590624. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 191683/22590759. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 191684/22590840. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 191685/22590867. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) b))) 5. ==[ beta ]==> ((^y.a)((^z.z) b)) 6. ==[ alpha ]==> ((^x.a)((^y.y) b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 191686/22590921. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(b (^y.y)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(b (^y.y))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(b (^x.x))) REDUCED to normal form. ------ 191687/22591002. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.z)(^x1.a))) 3. ==[ beta ]==> (b ((^z.z)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 191688/22591344. ------ 1. ==[ start ]==> ((a (b a))((^c.(a a)) b)) 2. ==[ alpha ]==> ((a (b a))((^x.(a a)) b)) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 191689/22591578. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (a a))(b a))) REDUCED to normal form. ------ 191690/22591623. ------ 1. ==[ start ]==> (((^a.a)(b a))(c (^b.b))) 2. ==[ alpha ]==> (((^x.x)(b a))(c (^y.y))) 3. ==[ beta ]==> ((b a)(c (^y.y))) 4. ==[ alpha ]==> ((b a)(c (^x.x))) REDUCED to normal form. ------ 191691/22591650. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(b (^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(b (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 191692/22591704. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a b)(a b))((^y.(a a))(a a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.(a a))(a a))) 5. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 191693/22591911. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(b a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 191694/22591965. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (a a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (a a))(a (^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a (a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 191695/22591992. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 191696/22592046. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((a a)(a a)) a)) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((a a)(a a)) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(a a)) a)) REDUCED to normal form. ------ 191697/22592073. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x) b) b)) 3. ==[ beta ]==> (((a b)(a (a a)))(b b)) REDUCED to normal form. ------ 191698/22592190. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(^y1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191699/22592271. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 191700/22592352. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191701/22592469. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((b a)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((b a) a)) REDUCED to normal form. ------ 191702/22592496. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((a a)(^x1.x1))(a (a a)))) REDUCED to normal form. ------ 191703/22592577. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a) a)(a b))) REDUCED to normal form. ------ 191704/22592604. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 191705/22592658. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (b a))) REDUCED to normal form. ------ 191706/22592685. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 191707/22592712. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a) b)) REDUCED to normal form. ------ 191708/22592757. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.x1)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191709/22592784. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 191710/22592802. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((b a)(^z.a))) REDUCED to normal form. ------ 191711/22592829. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 191712/22592856. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 191713/22592883. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a b)(^y.a))) 3. ==[ beta ]==> (((a (a a))(a a))((a b)(^y.a))) 4. ==[ alpha ]==> (((a (a a))(a a))((a b)(^x.a))) REDUCED to normal form. ------ 191714/22592910. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a) a)(^z.b))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a) a)(^y.b))) 5. ==[ beta ]==> ((a b)(((a a) a)(^y.b))) 6. ==[ alpha ]==> ((a b)(((a a) a)(^x.b))) REDUCED to normal form. ------ 191715/22592937. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(^y.(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(a a))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(a a))) REDUCED to normal form. ------ 191716/22592964. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^y.y))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 191717/22593018. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 191718/22593072. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z) b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(b a)) REDUCED to normal form. ------ 191719/22593099. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.(^z.z))) b)) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z))) b)) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 191720/22593108. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191721/22593270. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191722/22593378. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191723/22593387. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(a ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a b)) REDUCED to normal form. ------ 191724/22593414. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 191725/22593441. ------ 1. ==[ start ]==> (((a a)(^b.b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((b a)(a (^y.y)))) REDUCED to normal form. ------ 191726/22593468. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1)) a)) REDUCED to normal form. ------ 191727/22593549. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a) a)((a a) a))) 5. ==[ beta ]==> ((^y.(a a))(((a a) a)((a a) a))) 6. ==[ alpha ]==> ((^x.(a a))(((a a) a)((a a) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 191728/22593576. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.z)(a b))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)(a b))) 5. ==[ beta ]==> ((((a a) a)(^x.b))(a b)) REDUCED to normal form. ------ 191729/22593603. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))((a (a a))(a a))) REDUCED to normal form. ------ 191730/22593630. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a ((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 191731/22593657. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a (^z.z))(b a))) REDUCED to normal form. ------ 191732/22593702. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(a (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191733/22593774. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 191734/22593801. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 191735/22593828. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (b a))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a (b a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 191736/22593882. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(^x1.b))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.b))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.b))) 9. ==[ beta ]==> ((a a)((^y.y)(^z.b))) 10. ==[ alpha ]==> ((a a)((^x.x)(^y.b))) 11. ==[ beta ]==> ((a a)(^y.b)) 12. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 191737/22593909. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 191738/22593936. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)((a a) a))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a b)((a a) a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 191739/22593990. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191740/22594044. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((b a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((b a) b)) REDUCED to normal form. ------ 191741/22594071. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a)(^y.y)) c)) 3. ==[ beta ]==> ((b (a a))(((a a)(^y.y)) c)) 4. ==[ alpha ]==> ((b (a a))(((a a)(^x.x)) c)) REDUCED to normal form. ------ 191742/22594134. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 191743/22594413. ------ 1. ==[ start ]==> ((((^a.a) b) b)((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((a b)(a (a a)))) 3. ==[ beta ]==> ((b b)((a b)(a (a a)))) REDUCED to normal form. ------ 191744/22594440. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((a a) a)((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((a a) a)(^x.x))) REDUCED to normal form. ------ 191745/22594494. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(a b))) REDUCED to normal form. ------ 191746/22594521. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)((^y1.y1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a ((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((^x1.x1)(a a)))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 191747/22594539. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(c (^y.(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(c (^y.(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 191748/22594881. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((b a) a)) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((b a) a)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((b a) a)) REDUCED to normal form. ------ 191749/22594908. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))(b a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 191750/22595178. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z)) b)) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 191751/22595349. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(c (^z.(a a)))) 3. ==[ beta ]==> (b (c (^z.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 191752/22595457. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(a a))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191753/22595565. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(y y))((a a) a))) 5. ==[ beta ]==> ((b (^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 191754/22595592. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.a)(a b))) 3. ==[ beta ]==> ((^y.y)((^z.a)(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a b))) 5. ==[ beta ]==> ((^y.a)(a b)) 6. ==[ alpha ]==> ((^x.a)(a b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 191755/22595646. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)((a a)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^y1.y1))) REDUCED to normal form. ------ 191756/22595727. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b)(^x1.a))) 3. ==[ beta ]==> (b ((^z.b)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.b)(^y.a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 191757/22595835. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191758/22595871. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(b ((^z.z)(a a)))) 3. ==[ beta ]==> ((b (^y.a))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (^x.a))(b ((^y.y)(a a)))) 5. ==[ beta ]==> ((b (^x.a))(b (a a))) REDUCED to normal form. ------ 191759/22595898. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 191760/22595961. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b) c)) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 191761/22596150. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y)(a a))(^z.z))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a))(^y.y))) 5. ==[ beta ]==> (((a a)(a b))((a a)(^y.y))) 6. ==[ alpha ]==> (((a a)(a b))((a a)(^x.x))) REDUCED to normal form. ------ 191762/22596177. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 191763/22596231. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(z z))) REDUCED to normal form. ------ 191764/22596258. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)((a (a a))(^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 191765/22596339. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a a)(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 191766/22596429. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 7. ==[ beta ]==> ((^y.a)(^z.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 191767/22596510. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191768/22596735. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.z))((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.y))((a a) a))) 5. ==[ beta ]==> (a ((a (^y.y))((a a) a))) 6. ==[ alpha ]==> (a ((a (^x.x))((a a) a))) REDUCED to normal form. ------ 191769/22596753. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b (^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(b (^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(b (^x1.b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(b (^z.b))) 5. ==[ beta ]==> ((^y.y)(b (^z.b))) 6. ==[ alpha ]==> ((^x.x)(b (^y.b))) 7. ==[ beta ]==> (b (^y.b)) 8. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 191770/22596780. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(a (^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(a a)))) 5. ==[ beta ]==> (a (^y.(a a))) 6. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 191771/22596834. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(a (^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(a (^z.z)))) 7. ==[ beta ]==> ((b b)((^y.a)(a (^z.z)))) 8. ==[ alpha ]==> ((b b)((^x.a)(a (^y.y)))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 191772/22596915. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191773/22597140. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(b ((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b ((a a) a))) 5. ==[ beta ]==> ((^y.y)(b ((a a) a))) 6. ==[ alpha ]==> ((^x.x)(b ((a a) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 191774/22597158. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(^x1.b))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.b)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.b)) REDUCED to normal form. ------ 191775/22597176. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.b) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.b) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b) a)) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 191776/22597203. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a) b)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 191777/22597230. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y)) c)) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 191778/22597365. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a) a)(^z.z))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a)(^y.y))) 5. ==[ beta ]==> (((a a)(a a))(((a a) a)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 191779/22597392. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 191780/22597446. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1) a)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (^y1.(y1 y1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.(x1 x1)))) REDUCED to normal form. ------ 191781/22597473. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 191782/22597554. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z)) b)) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y)) b)) 7. ==[ beta ]==> ((a a)((^y.y) b)) 8. ==[ alpha ]==> ((a a)((^x.x) b)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 191783/22597590. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(x1 x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(x1 x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z))(^x1.a))) 5. ==[ beta ]==> (((^z.(z z))(^x1.a))(^y.y)) 6. ==[ alpha ]==> (((^x.(x x))(^y.a))(^z.z)) 7. ==[ beta ]==> (((^y.a)(^y.a))(^z.z)) 8. ==[ alpha ]==> (((^x.a)(^y.a))(^z.z)) 9. ==[ beta ]==> (a (^z.z)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 191784/22597995. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191785/22598022. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 191786/22598049. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a)(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 191787/22598103. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 191788/22598139. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a a))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(a a))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a a))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a a))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 191789/22598166. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (a (^x1.x1)))) REDUCED to normal form. ------ 191790/22598184. ------ 1. ==[ start ]==> (((^a.b)(b a))(c (^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(c (^y.a))) 3. ==[ beta ]==> (b (c (^y.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 191791/22598292. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191792/22598427. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 191793/22598436. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b ((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(b a)) REDUCED to normal form. ------ 191794/22598454. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(y1 y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(x1 x1))) REDUCED to normal form. ------ 191795/22598472. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(y y)) a)) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a a)) REDUCED to normal form. ------ 191796/22598499. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^b.a) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.a) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 191797/22598526. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 191798/22598580. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.z))) 7. ==[ beta ]==> (b (((^y.y) a)(^z.z))) 8. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 9. ==[ beta ]==> (b (a (^y.y))) 10. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 191799/22598607. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 191800/22598634. ------ 1. ==[ start ]==> (((a b)(b a))((a a)(^b.a))) 2. ==[ alpha ]==> (((a b)(b a))((a a)(^x.a))) REDUCED to normal form. ------ 191801/22598661. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(((^z.z) a) a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(((^z.z) a) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) a) a)) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 191802/22598688. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a (^z.z)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^z.z)) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y)) b)) REDUCED to normal form. ------ 191803/22598742. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^b.a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a)) a) REDUCED to normal form. ------ 191804/22598769. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) b)) 6. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) b)) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 191805/22598850. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 191806/22598868. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a c)) 3. ==[ beta ]==> ((b (^y.y))(a c)) 4. ==[ alpha ]==> ((b (^x.x))(a c)) REDUCED to normal form. ------ 191807/22598877. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a (^a.a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a (^y.y)) a)) REDUCED to normal form. ------ 191808/22598904. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a a) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 191809/22598913. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191810/22598940. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(b (^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(b (^y1.y1))) 3. ==[ beta ]==> ((^y.y)(b (^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(b (^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191811/22600959. ------ 1. ==[ start ]==> ((^a.(a b))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.((^z.(^x1.x1)) a)) b) 4. ==[ alpha ]==> ((^x.((^y.(^z.z)) a)) b) 5. ==[ beta ]==> ((^y.(^z.z)) a) 6. ==[ alpha ]==> ((^x.(^y.y)) a) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191812/22610094. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.d)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.d)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191813/22610850. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))(b (a (a (^z.z))))) 3. ==[ beta ]==> ((b (a (a (^z.z))))(^y.y)) 4. ==[ alpha ]==> ((b (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 191814/22610871. ------ 1. ==[ start ]==> (((a a) b)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191815/22611039. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ eta ]==> ((^y.y)((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 191816/22611309. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> (((a a)(a (a (^y.y))))(((a a)(a (a (^y.y))))((a a)(a (a (^y.y)))))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(((a a)(a (a (^y.y))))((a a)(a (a (^z.z)))))) REDUCED to normal form. ------ 191817/22611534. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191818/22611762. ------ 1. ==[ start ]==> (((a (a a)) b)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 191819/22612605. ------ 1. ==[ start ]==> ((^a.(a b))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x b))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)((^y.(^z.z)) a)) b) 4. ==[ alpha ]==> (((a a)((^x.(^y.y)) a)) b) 5. ==[ beta ]==> (((a a)(^y.y)) b) 6. ==[ alpha ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 191820/22612608. ------ 1. ==[ start ]==> ((a (a b))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a b))(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a b))(^x.(^z.z))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 191821/22613814. ------ 1. ==[ start ]==> (((^a.b) c)(^d.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 191822/22613823. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(^y.(b (^z.z)))) REDUCED to normal form. ------ 191823/22614606. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(b (^z.z)))) REDUCED to normal form. ------ 191824/22614630. ------ 1. ==[ start ]==> ((^a.(b a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((^x.(b x))(((a a)(a a))(a a))) 3. ==[ eta ]==> (b (((a a)(a a))(a a))) REDUCED to normal form. ------ 191825/22615179. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a) a)(^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 191826/22616070. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191827/22616352. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z))) b)(^y1.y1)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191828/22616676. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 191829/22617000. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 191830/22617891. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 191831/22618440. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^a.(b a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(b x))) 3. ==[ eta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 191832/22618464. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a)(^z.z))(a a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191833/22618944. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 191834/22619187. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 191835/22619412. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(a a))(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(a a))(^x.(a a))) REDUCED to normal form. ------ 191836/22620267. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^b.(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(a z))) 3. ==[ eta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 191837/22620465. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^a.(a b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.(z b))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(z b))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(y b))) REDUCED to normal form. ------ 191838/22620627. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^c.((a a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.((a a) a))) REDUCED to normal form. ------ 191839/22621266. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> (b (^x.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 191840/22621536. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 191841/22621644. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(a (a a)))) REDUCED to normal form. ------ 191842/22621743. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.d)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.d)) REDUCED to normal form. ------ 191843/22621761. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(y (y y)))) REDUCED to normal form. ------ 191844/22622031. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 191845/22622157. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(a (^z.z)))) REDUCED to normal form. ------ 191846/22622190. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(b (a a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191847/22622202. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^c.b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191848/22622412. ------ 1. ==[ start ]==> (((a a) a)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)(^y.y)) 4. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 191849/22622493. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191850/22622502. ------ 1. ==[ start ]==> ((a (a (^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))(b (a (a (^y.y))))) REDUCED to normal form. ------ 191851/22622520. ------ 1. ==[ start ]==> (((a a) b)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 191852/22622538. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191853/22622565. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 191854/22622637. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 191855/22622664. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.y))) REDUCED to normal form. ------ 191856/22622691. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 191857/22622880. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (((a a) a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 191858/22622907. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 191859/22622934. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a a))((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 191860/22622952. ------ 1. ==[ start ]==> (((^a.(a a)) a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a a)(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 191861/22622961. ------ 1. ==[ start ]==> ((a (a (a a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 191862/22622997. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 191863/22623051. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 7. ==[ beta ]==> ((b (^y.y))(^z.a)) 8. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 191864/22623078. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a (a a))(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 191865/22623105. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 191866/22623114. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.z)) REDUCED to normal form. ------ 191867/22623141. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 191868/22623159. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((b a)(^y.b))) 3. ==[ beta ]==> (((a a)(a a))((b a)(^y.b))) 4. ==[ alpha ]==> (((a a)(a a))((b a)(^x.b))) REDUCED to normal form. ------ 191869/22623186. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 191870/22623276. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b b)((^y.a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b b)((^x.a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 191871/22623321. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191872/22623402. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a a)(^y1.(y1 (^z1.z1))))) 5. ==[ beta ]==> ((^y.y)((a a)(^y1.(y1 (^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 7. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 8. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 191873/22623411. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> (((a (a a)) b)(a (a (^y.y)))) 4. ==[ alpha ]==> (((a (a a)) b)(a (a (^x.x)))) REDUCED to normal form. ------ 191874/22623438. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> (a ((^y.(y (^z.z)))(^x1.x1))) 6. ==[ alpha ]==> (a ((^x.(x (^y.y)))(^z.z))) 7. ==[ beta ]==> (a ((^z.z)(^y.y))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 191875/22623456. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a) b)) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a) b)) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 7. ==[ beta ]==> (((^y.(^z.z)) a) b) 8. ==[ alpha ]==> (((^x.(^y.y)) a) b) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 191876/22623483. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((b (^z.z)) c)) 3. ==[ beta ]==> ((^y.y)((b (^z.z)) c)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 5. ==[ beta ]==> ((b (^y.y)) c) 6. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 191877/22623519. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 191878/22623546. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 191879/22624095. ------ 1. ==[ start ]==> (((a a)((a a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 191880/22624122. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a) a)(b a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(b a))) REDUCED to normal form. ------ 191881/22624149. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a (a a)))((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (a (a a)))((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a (a (a a)))(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a (a (a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 191882/22624176. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a (a a)) a)((a (a a))((^y.y) b))) 4. ==[ alpha ]==> (((a (a a)) a)((a (a a))((^x.x) b))) 5. ==[ beta ]==> (((a (a a)) a)((a (a a)) b)) REDUCED to normal form. ------ 191883/22624203. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((a a)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((a a)(a a)))) 7. ==[ beta ]==> ((a (^x.x))(a ((a a)(a a)))) REDUCED to normal form. ------ 191884/22624230. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 191885/22624257. ------ 1. ==[ start ]==> ((a (a b))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a b))((a a)((^x.(^y.y)) a))) 3. ==[ beta ]==> ((a (a b))((a a)(^y.y))) 4. ==[ alpha ]==> ((a (a b))((a a)(^x.x))) REDUCED to normal form. ------ 191886/22624347. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(a a))(^z.a))) IRREDUCIBLE: cycle. ------ 191887/22624410. ------ 1. ==[ start ]==> ((((a a) a) b)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a) b)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 191888/22624428. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((b a)(^z.a))) 3. ==[ beta ]==> (b ((b a)(^z.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 191889/22624455. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a b))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 191890/22624464. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 191891/22624482. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(a a))) 7. ==[ beta ]==> ((a a)(^y.(a a))) 8. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 191892/22624518. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 191893/22624572. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 191894/22624599. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(((^x1.x1) b)((^x1.x1) b))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b)((^x1.x1) b))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b ((^x1.x1) b))) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b ((^z.z) b))) 7. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 191895/22624617. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (b (a (^y.(a a)))) 6. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 191896/22624626. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 191897/22624815. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 191898/22625031. ------ 1. ==[ start ]==> (((a b) b)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.a)(^y.(a a)))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 191899/22625310. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)(a a))((a b)(a a))) REDUCED to normal form. ------ 191900/22625337. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 191901/22625364. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> ((a ((a a) a))((^y.y)(b a))) 6. ==[ alpha ]==> ((a ((a a) a))((^x.x)(b a))) 7. ==[ beta ]==> ((a ((a a) a))(b a)) REDUCED to normal form. ------ 191902/22625391. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 191903/22625418. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> ((a (a a))(((^y.y) a)((^z.z) b))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) a)((^y.y) b))) 7. ==[ beta ]==> ((a (a a))(a ((^y.y) b))) 8. ==[ alpha ]==> ((a (a a))(a ((^x.x) b))) 9. ==[ beta ]==> ((a (a a))(a b)) REDUCED to normal form. ------ 191904/22625445. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 191905/22625463. ------ 1. ==[ start ]==> (((^a.b) c)(b (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(b (^y.(^z.z)))) 3. ==[ beta ]==> (b (b (^y.(^z.z)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 191906/22625472. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 191907/22625562. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (((^y.y) b)(^z.a)) 6. ==[ alpha ]==> (((^x.x) b)(^y.a)) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 191908/22625697. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a b)(^z.(a a)))) 3. ==[ beta ]==> (b ((a b)(^z.(a a)))) 4. ==[ alpha ]==> (b ((a b)(^x.(a a)))) REDUCED to normal form. ------ 191909/22625706. ------ 1. ==[ start ]==> (((a b) c)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b) c) b) REDUCED to normal form. ------ 191910/22625733. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) b)((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 191911/22625760. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 191912/22625778. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191913/22625805. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((^y.y) a)(^z.z)) 6. ==[ alpha ]==> (((^x.x) a)(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 191914/22625814. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 191915/22625841. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 191916/22625940. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) b) c)) 3. ==[ beta ]==> (b (((^z.z) b) c)) 4. ==[ alpha ]==> (b (((^x.x) b) c)) 5. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 191917/22625949. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.a)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.a)) REDUCED to normal form. ------ 191918/22625976. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 191919/22626201. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(c ((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(c ((^y.y) b))) 3. ==[ beta ]==> (((a b) a)(c ((^y.y) b))) 4. ==[ alpha ]==> (((a b) a)(c ((^x.x) b))) 5. ==[ beta ]==> (((a b) a)(c b)) REDUCED to normal form. ------ 191920/22626228. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(b ((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(b ((a a)(a a)))) REDUCED to normal form. ------ 191921/22626255. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(a (b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (b (^y.y)))) REDUCED to normal form. ------ 191922/22626282. ------ 1. ==[ start ]==> ((a (b a))(((a a)(a a))(a a))) REDUCED to normal form. ------ 191923/22626642. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a)(a a))(^y.y))) 3. ==[ beta ]==> (((a b)(a b))(((a a)(a a))(^y.y))) 4. ==[ alpha ]==> (((a b)(a b))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 191924/22626651. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a a)) REDUCED to normal form. ------ 191925/22626705. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 191926/22626723. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((b a)(^y.(y y)))) 3. ==[ beta ]==> (b ((b a)(^y.(y y)))) 4. ==[ alpha ]==> (b ((b a)(^x.(x x)))) REDUCED to normal form. ------ 191927/22626759. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 191928/22626786. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 191929/22626831. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^x1.(a a)))) REDUCED to normal form. ------ 191930/22627650. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(b (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(b (^z.z))) REDUCED to normal form. ------ 191931/22627695. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191932/22627704. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 191933/22627722. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 191934/22628001. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.x1)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191935/22628046. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z))) b)) 5. ==[ beta ]==> ((a (^y.(^z.z))) b) 6. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 191936/22628073. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((b a) c)) 3. ==[ beta ]==> ((^y.y)((b a) c)) 4. ==[ alpha ]==> ((^x.x)((b a) c)) 5. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 191937/22628325. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 191938/22628370. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1))) b)) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) b)) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 191939/22628649. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.y1))) REDUCED to normal form. ------ 191940/22628676. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 191941/22629315. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191942/22629540. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 191943/22629558. ------ 1. ==[ start ]==> (((^a.b)(a b))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a b))((b a)(^y.y))) 3. ==[ beta ]==> (b ((b a)(^y.y))) 4. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 191944/22629621. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 191945/22629666. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((a a) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191946/22629675. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) a) REDUCED to normal form. ------ 191947/22629702. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 191948/22629729. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(y y))(a b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a b)(a b))) REDUCED to normal form. ------ 191949/22630062. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(b ((a a)(^z.z)))) 3. ==[ beta ]==> ((b (a (^y.y)))(b ((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(b ((a a)(^y.y)))) REDUCED to normal form. ------ 191950/22630089. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(a (b a))) REDUCED to normal form. ------ 191951/22630116. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 191952/22630395. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191953/22630431. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b)((^z.z) a))) 3. ==[ beta ]==> ((b c)((^y.b)((^z.z) a))) 4. ==[ alpha ]==> ((b c)((^x.b)((^y.y) a))) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 191954/22630458. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b) a) REDUCED to normal form. ------ 191955/22630503. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (a a))(^z.a))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))(^y.a))) REDUCED to normal form. ------ 191956/22630530. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.b))) 5. ==[ beta ]==> (((^y.y) a)(^z.b)) 6. ==[ alpha ]==> (((^x.x) a)(^y.b)) 7. ==[ beta ]==> (a (^y.b)) 8. ==[ alpha ]==> (a (^x.b)) REDUCED to normal form. ------ 191957/22630566. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 191958/22630593. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 191959/22630665. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a b) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a b) c)) 3. ==[ beta ]==> (b ((a b) c)) REDUCED to normal form. ------ 191960/22630674. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 191961/22630701. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 191962/22630782. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 191963/22630809. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 191964/22630899. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 191965/22630926. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(((a a) a) a)) REDUCED to normal form. ------ 191966/22630953. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(a (a a)))) 7. ==[ beta ]==> ((a b)((^y.y)(a (a a)))) 8. ==[ alpha ]==> ((a b)((^x.x)(a (a a)))) 9. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 191967/22630980. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a (a a))(^z.z))) REDUCED to normal form. ------ 191968/22631007. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((b a)(((^y.y) a)((a a) a))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)((a a) a))) 7. ==[ beta ]==> ((b a)(a ((a a) a))) REDUCED to normal form. ------ 191969/22631034. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (^y.y))(a b))) REDUCED to normal form. ------ 191970/22631061. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a a))((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b)(a a))((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (((a b)(a a))((a a)(a a))) REDUCED to normal form. ------ 191971/22631367. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a) c)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a) c)) 5. ==[ beta ]==> ((^y.y)(((a a) a) c)) 6. ==[ alpha ]==> ((^x.x)(((a a) a) c)) 7. ==[ beta ]==> (((a a) a) c) REDUCED to normal form. ------ 191972/22631556. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191973/22631772. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((a a) a)(^y.(^z.z)))) 7. ==[ beta ]==> ((b b)(((a a) a)(^y.(^z.z)))) 8. ==[ alpha ]==> ((b b)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 191974/22631781. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 191975/22631808. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((^y2.y2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((^y2.y2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 191976/22631853. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 191977/22631862. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 191978/22631889. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 191979/22631916. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a b)) REDUCED to normal form. ------ 191980/22631961. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((a a) a) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 191981/22631970. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 191982/22631997. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 191983/22632024. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 191984/22632114. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(a (a b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(a (a b))) 3. ==[ beta ]==> (((a a)(^y.y))(a (a b))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (a b))) REDUCED to normal form. ------ 191985/22632141. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 191986/22632168. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((a ((a a)(a a)))(a (^y.y))) 8. ==[ alpha ]==> ((a ((a a)(a a)))(a (^x.x))) REDUCED to normal form. ------ 191987/22632195. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (a a))((^y.y) a))) 3. ==[ beta ]==> (((a (a a)) b)((a (a a))((^y.y) a))) 4. ==[ alpha ]==> (((a (a a)) b)((a (a a))((^x.x) a))) 5. ==[ beta ]==> (((a (a a)) b)((a (a a)) a)) REDUCED to normal form. ------ 191988/22632222. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1) a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) a)(a (a a)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(a (a a)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (a (a a)))) REDUCED to normal form. ------ 191989/22632249. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))((a (^x.x))(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(b a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 191990/22632276. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a a)((a a) a))) REDUCED to normal form. ------ 191991/22632510. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 191992/22632915. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 191993/22632933. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1)(^y1.y1)) a)) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1)(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) a)) 7. ==[ beta ]==> (((^y.y)(^z.z)) a) 8. ==[ alpha ]==> (((^x.x)(^y.y)) a) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 191994/22632942. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 191995/22632960. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (a a)) b)) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a a)) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a a)) b)) REDUCED to normal form. ------ 191996/22632969. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 191997/22633122. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a) c)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a) c)) 3. ==[ beta ]==> (b ((^y.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 191998/22633185. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 191999/22633230. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192000/22633266. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 192001/22633293. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a (a a))) REDUCED to normal form. ------ 192002/22633347. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192003/22633374. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 192004/22633410. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a (a (a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (a (a a)))) REDUCED to normal form. ------ 192005/22633437. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 192006/22633464. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 192007/22633491. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a a)((^x.x) a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))((a a) a)) REDUCED to normal form. ------ 192008/22633572. ------ 1. ==[ start ]==> (((a b)(b a))(b c)) REDUCED to normal form. ------ 192009/22633680. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a ((^z.z) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(a a)) REDUCED to normal form. ------ 192010/22633707. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a (^x1.x1))(a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a (^z.z))(a a))) 5. ==[ beta ]==> ((b (^y.y))((a (^z.z))(a a))) 6. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 192011/22633734. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a a)(a (^x.x)))) REDUCED to normal form. ------ 192012/22633788. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(b b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(b b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b b)) 5. ==[ beta ]==> ((a (^y.y))(b b)) 6. ==[ alpha ]==> ((a (^x.x))(b b)) REDUCED to normal form. ------ 192013/22633806. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 192014/22633842. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(b (a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 192015/22633851. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a) b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192016/22633878. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 5. ==[ beta ]==> ((^y.(^z.z)) a) 6. ==[ alpha ]==> ((^x.(^y.y)) a) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192017/22634012. ------ 1. ==[ start ]==> (^a.((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 192018/22634013. ------ 1. ==[ start ]==> (a ((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (a ((^x.b)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (a b) REDUCED to normal form. ------ 192019/22645665. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a)))) a) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1)))) a) 3. ==[ beta ]==> (b a) REDUCED to normal form. ------ 192020/22645671. ------ 1. ==[ start ]==> ((^a.a)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192021/22645725. ------ 1. ==[ start ]==> ((^a.b)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 192022/22645806. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((^y.y)(^y1.y1)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192023/22645845. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.((^y1.y1)(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.y1)(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192024/22645923. ------ 1. ==[ start ]==> ((^a.(^b.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.x))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (^y.((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (^x.((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> (^x.((b (^y.y)) a)) REDUCED to normal form. ------ 192025/22646166. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 192026/22646265. ------ 1. ==[ start ]==> ((^a.(a (a a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((b (^y.(y (^z.z))))((b (^y.(y (^z.z))))(b (^y.(y (^z.z)))))) 4. ==[ alpha ]==> ((b (^x.(x (^y.y))))((b (^z.(z (^x1.x1))))(b (^y1.(y1 (^z1.z1)))))) REDUCED to normal form. ------ 192027/22646616. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192028/22646718. ------ 1. ==[ start ]==> (((a (a a)) b)(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 192029/22647048. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((^y.(^z.z))(^x1.x1))((^y.(^z.z))(^x1.x1)))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1)))((^x2.(^y2.y2))(^z2.z2))) 5. ==[ beta ]==> (((^y.y)((^x1.(^y1.y1))(^z1.z1)))((^x2.(^y2.y2))(^z2.z2))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.x1))((^y1.(^z1.z1))(^x2.x2))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 9. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.z1))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192030/22647381. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 192031/22647573. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.b)(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.b)(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192032/22647996. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(^z.z))) REDUCED to normal form. ------ 192033/22648410. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.(^y.y))(a b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(a b))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192034/22650291. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(^z.((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(^z.((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.((a a)(a a)))) REDUCED to normal form. ------ 192035/22651308. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192036/22651317. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 192037/22651341. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192038/22653126. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(^x1.(x1 a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(^x1.(x1 a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(z a))) REDUCED to normal form. ------ 192039/22654395. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 192040/22654581. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(a b))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192041/22655025. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^c.(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(a b))) 3. ==[ beta ]==> ((^y.y)(^x1.(a b))) 4. ==[ alpha ]==> ((^x.x)(^y.(a b))) 5. ==[ beta ]==> (^y.(a b)) 6. ==[ alpha ]==> (^x.(a b)) REDUCED to normal form. ------ 192042/22655223. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.b))) REDUCED to normal form. ------ 192043/22655400. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(b ((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(b ((a a) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 192044/22655421. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.(^x1.z))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.z))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 192045/22655610. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(^x1.b))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.b))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.b))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.b))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.b))) REDUCED to normal form. ------ 192046/22655823. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y1.(^z1.z1)))(((^z.(^x1.x1))(^y1.(^z1.z1)))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1))(^x2.(^y2.y2)))(^z2.z2))) 5. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1))(^x2.(^y2.y2)))(^z2.z2))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(^x1.(^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.y1)))(^z1.z1)) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 9. ==[ beta ]==> ((^y.y)(^y1.y1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192047/22656222. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 192048/22656696. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b ((^y1.y1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192049/22656717. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.(z z)))) REDUCED to normal form. ------ 192050/22656825. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z)))) 7. ==[ beta ]==> (b (^y.(^z.(z z)))) 8. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 192051/22656906. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.((^z.z) a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 192052/22656987. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.a))) REDUCED to normal form. ------ 192053/22657113. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 192054/22657122. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(a (^z.z)))) REDUCED to normal form. ------ 192055/22657146. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192056/22657185. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 5. ==[ beta ]==> (^y.(y (^z.z))) 6. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 192057/22657320. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> (b (^y1.y1)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192058/22657332. ------ 1. ==[ start ]==> ((a a)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)((^x.b)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 192059/22657386. ------ 1. ==[ start ]==> ((a b)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 192060/22657467. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 192061/22657476. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (a (^z.z))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192062/22657503. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a ((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a ((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 192063/22657512. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 192064/22657530. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> ((a (^y.y))((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 192065/22657539. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 192066/22657557. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 192067/22657584. ------ 1. ==[ start ]==> ((a (^b.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.a))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.a))((b (^y.y)) a)) REDUCED to normal form. ------ 192068/22657665. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 192069/22657692. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((b a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(a b))) 3. ==[ beta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 192070/22657746. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (a (((^y.y)(a a))((a a)(^z.z)))) 6. ==[ alpha ]==> (a (((^x.x)(a a))((a a)(^y.y)))) 7. ==[ beta ]==> (a ((a a)((a a)(^y.y)))) 8. ==[ alpha ]==> (a ((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 192071/22657773. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 192072/22657827. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.(x x))) b) REDUCED to normal form. ------ 192073/22657926. ------ 1. ==[ start ]==> ((a (a (a a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 192074/22657935. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((^y.(y y))((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.(x x))((a a)(a (a (^y.y))))) 5. ==[ beta ]==> (((a a)(a (a (^y.y))))((a a)(a (a (^y.y))))) 6. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 192075/22657998. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a b)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 192076/22658025. ------ 1. ==[ start ]==> (((a (a a)) a)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a)) a)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 192077/22658052. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 192078/22658079. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 192079/22658133. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((b a)(^y.b))) REDUCED to normal form. ------ 192080/22658196. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a a)) REDUCED to normal form. ------ 192081/22658223. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.b)(b a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.b)(b a))) 5. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 192082/22658241. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b b)(((a a) a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b b)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 192083/22658277. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 192084/22658376. ------ 1. ==[ start ]==> (((a (a a)) b)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 192085/22658403. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a (a (^z.z))) a)) 3. ==[ beta ]==> (((^y.y) a)((a (a (^z.z))) a)) 4. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y))) a)) 5. ==[ beta ]==> (a ((a (a (^y.y))) a)) 6. ==[ alpha ]==> (a ((a (a (^x.x))) a)) REDUCED to normal form. ------ 192086/22658430. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 192087/22658457. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b (^z.z)) c)) REDUCED to normal form. ------ 192088/22658628. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 192089/22658709. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((a ((a a) a))(^y.y)) 4. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 192090/22658799. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.a)(^y.a))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (a (b ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> (a (b ((^x.(^y.y)) a))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 192091/22658835. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y) b)((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> (b ((^y.(y (^z.z))) a)) 6. ==[ alpha ]==> (b ((^x.(x (^y.y))) a)) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 192092/22658880. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a a) a)((b (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((a a) a)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 192093/22658907. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((a a)(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.x) a)) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 192094/22658916. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(a a)) d)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a)) d)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 192095/22658961. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((a a)((a (^x.(^y.y)))(^x1.x1))) 10. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 192096/22659042. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.b))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.b))((a a)(a a))) REDUCED to normal form. ------ 192097/22659231. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.b)((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.b)((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192098/22659375. ------ 1. ==[ start ]==> ((((a a) a) b)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 192099/22659402. ------ 1. ==[ start ]==> (((a b) a)((b a)(^c.a))) 2. ==[ alpha ]==> (((a b) a)((b a)(^x.a))) REDUCED to normal form. ------ 192100/22659429. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 192101/22659483. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 192102/22659537. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.a)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 192103/22659564. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 192104/22659591. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.x))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 192105/22659627. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 192106/22659654. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 192107/22659762. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.(z z))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 192108/22659789. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 192109/22660041. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b (b (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a a))(b (b (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (b (^y.y)))) 6. ==[ alpha ]==> ((a a)(b (b (^x.x)))) REDUCED to normal form. ------ 192110/22660068. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.y)(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> (a ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (a ((^x.(^y.y)) a)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 192111/22660122. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(a a))(a (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(a a))(a (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a))(a (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a))(a (^x1.x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a))(a (^z.z)))) 9. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (^z.z)))) 10. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (^y.y)))) 11. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 12. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 192112/22660131. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 192113/22660203. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((b a)(^y.y))) 6. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 192114/22660671. ------ 1. ==[ start ]==> (((a b) c)((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b) c)((a b)(^x.(a a)))) REDUCED to normal form. ------ 192115/22660698. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 192116/22660779. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(a (^z.z))) REDUCED to normal form. ------ 192117/22660806. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 192118/22660860. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b (^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b (^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1)) a)) 5. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192119/22660887. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((a a)(a a)) b)) REDUCED to normal form. ------ 192120/22660914. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) b) c)) 3. ==[ beta ]==> (((a b)(^x.a))(b c)) REDUCED to normal form. ------ 192121/22661031. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(a a))(^z.b))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a a)) REDUCED to normal form. ------ 192122/22661058. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((a (a b))((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> ((a (a b))((^x.b)(^y.(a a)))) 5. ==[ beta ]==> ((a (a b)) b) REDUCED to normal form. ------ 192123/22661139. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 192124/22661166. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a b) a)((^y.a)(^z.z))) 4. ==[ alpha ]==> (((a b) a)((^x.a)(^y.y))) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 192125/22661337. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((b a)(a (a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((b a)(a (a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((b a)(a (a a)))) 5. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 192126/22661418. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a b)(a b))) 3. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 192127/22661526. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b a)(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b a)(((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((b a)(a (a (^y.(^z.z))))) 6. ==[ alpha ]==> ((b a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 192128/22661553. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (^y.y))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 192129/22661616. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 192130/22661670. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 192131/22661697. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((b a)(^y.(y y)))) REDUCED to normal form. ------ 192132/22661724. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 192133/22661814. ------ 1. ==[ start ]==> (((a a)(b a))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(b a)) a) REDUCED to normal form. ------ 192134/22661841. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 192135/22661868. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(z z))(b a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(z z))(b a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(y y))(b a))) 5. ==[ beta ]==> ((a (a a))((^y.(y y))(b a))) 6. ==[ alpha ]==> ((a (a a))((^x.(x x))(b a))) 7. ==[ beta ]==> ((a (a a))((b a)(b a))) REDUCED to normal form. ------ 192136/22661895. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a (a a))(a b)) a) REDUCED to normal form. ------ 192137/22661922. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.z) b))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 192138/22661949. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)((a a)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 192139/22661976. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(a a))(^y.y))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 192140/22662003. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 192141/22662030. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 192142/22662255. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(c (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (c (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 192143/22662363. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((a (^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192144/22662390. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((b a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((b a) a)) REDUCED to normal form. ------ 192145/22662417. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(a (a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 192146/22662471. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a b)((a a) a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a b)((a a) a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a b)((a a) a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a b)((a a) a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a b)((a a) a))) 7. ==[ beta ]==> (((a a)(a a))((a b)((a a) a))) REDUCED to normal form. ------ 192147/22662552. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((a (a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 192148/22662669. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(b (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (^x1.x1))) REDUCED to normal form. ------ 192149/22662705. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 192150/22662786. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 192151/22662813. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.b)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.b)((a a) a))) 5. ==[ beta ]==> ((a b)((^y.b)((a a) a))) 6. ==[ alpha ]==> ((a b)((^x.b)((a a) a))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 192152/22662867. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 192153/22662894. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(y y))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (((a a)(a (a a)))(((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 192154/22662921. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.a)(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.a)(b a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 192155/22662966. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192156/22662975. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z) b)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) b) REDUCED to normal form. ------ 192157/22663002. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.b)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)(^z.z))) 3. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 192158/22663281. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(b (a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192159/22663317. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.y) a)) 3. ==[ beta ]==> ((b a)((^y.y) a)) 4. ==[ alpha ]==> ((b a)((^x.x) a)) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 192160/22663335. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z)))(a a))) 5. ==[ beta ]==> (b ((a (^y.(^z.z)))(a a))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 192161/22663344. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 192162/22663362. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((b a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((b a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(a (^y.y)))) 5. ==[ beta ]==> ((b a)(a (^y.y))) 6. ==[ alpha ]==> ((b a)(a (^x.x))) REDUCED to normal form. ------ 192163/22663416. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))((a a)(a (a a)))) REDUCED to normal form. ------ 192164/22663497. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(a b))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a b))) 5. ==[ beta ]==> (b ((^y.y)(a b))) 6. ==[ alpha ]==> (b ((^x.x)(a b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 192165/22663605. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192166/22663641. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 192167/22663731. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((a (b a))((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> ((a (b a))((^x.(a a))(a (a a)))) 5. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 192168/22663758. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x))) b) REDUCED to normal form. ------ 192169/22663812. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y))(a b))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.x)) REDUCED to normal form. ------ 192170/22663839. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(x x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)((a a) a))(((^y.y)(a a))((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)((a a) a))((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> (((a b)((a a) a))((a a)((^x.x)(a a)))) 7. ==[ beta ]==> (((a b)((a a) a))((a a)(a a))) REDUCED to normal form. ------ 192171/22663866. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((a a)(^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 192172/22663893. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 192173/22663947. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 192174/22664172. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(c ((a a)(^z.z)))) 3. ==[ beta ]==> (b (c ((a a)(^z.z)))) 4. ==[ alpha ]==> (b (c ((a a)(^x.x)))) REDUCED to normal form. ------ 192175/22664280. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((a a)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192176/22664361. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(((a a) a)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 192177/22664388. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((a a) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a a) a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a a) a)) 7. ==[ beta ]==> ((^y.y)((a a) a)) 8. ==[ alpha ]==> ((^x.x)((a a) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 192178/22664442. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((b a)(b a))(a ((^y.y)(a a)))) 6. ==[ alpha ]==> (((b a)(b a))(a ((^x.x)(a a)))) 7. ==[ beta ]==> (((b a)(b a))(a (a a))) REDUCED to normal form. ------ 192179/22664532. ------ 1. ==[ start ]==> (((a b)(^a.b))((b a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.b))((b a)(^y.y))) REDUCED to normal form. ------ 192180/22664586. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.a))) REDUCED to normal form. ------ 192181/22664640. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 192182/22664667. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.a))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.a)) 8. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 192183/22664694. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (a a))(^y.b))) REDUCED to normal form. ------ 192184/22664730. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)((a a)(a a))) a) REDUCED to normal form. ------ 192185/22664757. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 192186/22664784. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.x1)(b a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.x1)(b a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(b a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(b a)) REDUCED to normal form. ------ 192187/22664865. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 192188/22664892. ------ 1. ==[ start ]==> (((a b)(a b))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.b)(^y.(y y)))) 3. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 192189/22664946. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 192190/22665000. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 192191/22665027. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 192192/22665171. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a) a)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192193/22665252. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z) a)(a b))) 3. ==[ beta ]==> (b (((^z.z) a)(a b))) 4. ==[ alpha ]==> (b (((^x.x) a)(a b))) 5. ==[ beta ]==> (b (a (a b))) REDUCED to normal form. ------ 192194/22665396. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b)(^y.a))) 3. ==[ beta ]==> ((b c)((a b)(^y.a))) 4. ==[ alpha ]==> ((b c)((a b)(^x.a))) REDUCED to normal form. ------ 192195/22665423. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 192196/22665531. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 192197/22665639. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b) c)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b) c)) REDUCED to normal form. ------ 192198/22666026. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(b (^y.(a a)))) 3. ==[ beta ]==> (((a b)(a a))(b (^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(b (^x.(a a)))) REDUCED to normal form. ------ 192199/22666053. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(a (^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a b))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 192200/22666080. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 192201/22666161. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 192202/22666188. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(y y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(^z.z))) 9. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 10. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 192203/22666242. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 192204/22666413. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(d ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(d ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (d ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (d ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (d (^y.y))) 6. ==[ alpha ]==> (b (d (^x.x))) REDUCED to normal form. ------ 192205/22666521. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a b)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192206/22666656. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a (^x1.x1))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a (^z.z))((a a) a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a) a))) 7. ==[ beta ]==> ((a (^y.y))((a a) a)) 8. ==[ alpha ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 192207/22666683. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a a)(a b))) 3. ==[ beta ]==> ((^y.y)((a a)(a b))) 4. ==[ alpha ]==> ((^x.x)((a a)(a b))) 5. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 192208/22666746. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 192209/22666773. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192210/22666827. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 192211/22666854. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 192212/22666881. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)(^z.b))) REDUCED to normal form. ------ 192213/22666935. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a) a) b)) REDUCED to normal form. ------ 192214/22666962. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z)) c)) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z) c)) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y) c)) 7. ==[ beta ]==> ((b (^x.(x x))) c) REDUCED to normal form. ------ 192215/22667061. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(b ((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(b ((a a) a))) REDUCED to normal form. ------ 192216/22667079. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 192217/22667214. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 192218/22667241. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b (^y.a))) REDUCED to normal form. ------ 192219/22667268. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(a (^z.b))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(a (^z.b))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a (^y.b))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.b))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.b))) REDUCED to normal form. ------ 192220/22667295. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^c.a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 192221/22667349. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(y1 y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(y1 y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(x1 x1))((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(((^y1.y1) a)((^y1.y1) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)((^y1.y1) a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a ((^y1.y1) a))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a ((^x1.x1) a))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 192222/22667376. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)(a (a a)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)(a (a a)))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 192223/22667403. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 192224/22667475. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1)) b)) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z)) b)) 5. ==[ beta ]==> ((a (^x.x))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 192225/22667484. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 192226/22667880. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a a)(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 192227/22667907. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> (((a (a (^x.x))) a)((^z.z) a)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y) a)) 5. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 192228/22667934. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (a a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (a a)) b)) REDUCED to normal form. ------ 192229/22668006. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (a (a a)))) REDUCED to normal form. ------ 192230/22668042. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 7. ==[ beta ]==> ((^y.(^z.z)) a) 8. ==[ alpha ]==> ((^x.(^y.y)) a) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192231/22668069. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 192232/22668087. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> (b (((^y.y) a)(a (^z.z)))) 4. ==[ alpha ]==> (b (((^x.x) a)(a (^y.y)))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 192233/22668231. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 192234/22668258. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 192235/22668312. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.y1) a) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a) b)) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a) b)) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192236/22668357. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b ((^x1.x1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b a)) REDUCED to normal form. ------ 192237/22668375. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.(z z))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(y y))) REDUCED to normal form. ------ 192238/22668429. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 192239/22668456. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b (^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(b (^x.a))) REDUCED to normal form. ------ 192240/22668483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (^z.(z z)))) 5. ==[ beta ]==> (((^y.y) b)(a (^z.(z z)))) 6. ==[ alpha ]==> (((^x.x) b)(a (^y.(y y)))) 7. ==[ beta ]==> (b (a (^y.(y y)))) 8. ==[ alpha ]==> (b (a (^x.(x x)))) REDUCED to normal form. ------ 192241/22668510. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.a)(a a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 192242/22668537. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 192243/22668564. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))((^z.z) a)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y) a)) 7. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 192244/22668591. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 192245/22668645. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.a)) REDUCED to normal form. ------ 192246/22668672. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(c (^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(c (^x1.x1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(c (^x1.x1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(c (^z.z))) 5. ==[ beta ]==> ((b (^y.y))(c (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(c (^y.y))) REDUCED to normal form. ------ 192247/22668699. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 192248/22668753. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a a))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 192249/22668771. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 192250/22668780. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(a (^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a (^y.y))) REDUCED to normal form. ------ 192251/22668807. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 192252/22668816. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192253/22668843. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(a (a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(a (a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 5. ==[ beta ]==> (a (a (^y.y))) 6. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 192254/22668978. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a a)) 3. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 192255/22680639. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a)))) b) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1)))) b) 3. ==[ beta ]==> (b b) REDUCED to normal form. ------ 192256/22680663. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192257/22680828. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 192258/22680837. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 192259/22681287. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 192260/22681599. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192261/22682160. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) b)(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(y (y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (y (^z.z))))) 6. ==[ alpha ]==> (b (^x.(x (x (^y.y))))) REDUCED to normal form. ------ 192262/22682931. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> (^y.(((^z.a)((a a)(a a)))((^z.a)((a a)(a a))))) 4. ==[ alpha ]==> (^x.(((^y.a)((a a)(a a)))((^z.a)((a a)(a a))))) 5. ==[ beta ]==> (^x.(a ((^z.a)((a a)(a a))))) 6. ==[ alpha ]==> (^x.(a ((^y.a)((a a)(a a))))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 192263/22683402. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((a (^x.x))(^y.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 192264/22683813. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((b (^z.z))(^x1.x1))((b (^z.z))(^x1.x1)))(^y.y)) 4. ==[ alpha ]==> ((((b (^x.x))(^y.y))((b (^z.z))(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 192265/22684914. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(^z.((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(^z.((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 192266/22685118. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.b)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.b)(a b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192267/22686009. ------ 1. ==[ start ]==> ((^a.(^b.b))((^b.b)(a a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192268/22686324. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a) b) a)) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z) b) a)) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192269/22686642. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.((^z.z) b))) 3. ==[ beta ]==> ((b a)(^y.((^z.z) b))) 4. ==[ alpha ]==> ((b a)(^x.((^y.y) b))) 5. ==[ beta ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 192270/22687830. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^c.(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(b a))) REDUCED to normal form. ------ 192271/22687848. ------ 1. ==[ start ]==> (((^a.b)(a b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 192272/22689564. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (^x1.x1))(^y1.b))) 3. ==[ eta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192273/22690806. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z)(^x1.x1)) b)) 3. ==[ beta ]==> ((((^z.z)(^x1.x1)) b)((((^z.z)(^x1.x1)) b)(^y.y))) 4. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((((^z.z)(^x1.x1)) b)(^y1.y1))) 5. ==[ beta ]==> (((^y.y) b)((((^z.z)(^x1.x1)) b)(^y1.y1))) 6. ==[ alpha ]==> (((^x.x) b)((((^y.y)(^z.z)) b)(^x1.x1))) 7. ==[ beta ]==> (b ((((^y.y)(^z.z)) b)(^x1.x1))) 8. ==[ alpha ]==> (b ((((^x.x)(^y.y)) b)(^z.z))) 9. ==[ beta ]==> (b (((^y.y) b)(^z.z))) 10. ==[ alpha ]==> (b (((^x.x) b)(^y.y))) 11. ==[ beta ]==> (b (b (^y.y))) 12. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 192274/22691223. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192275/22691367. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192276/22691475. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(a (a a)))) REDUCED to normal form. ------ 192277/22691679. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192278/22692129. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a (^y1.y1)) a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192279/22692168. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192280/22692303. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (b (^y1.(^z1.z1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 192281/22692333. ------ 1. ==[ start ]==> ((a (^a.a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 192282/22692387. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 192283/22692468. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192284/22692477. ------ 1. ==[ start ]==> (((a a) b)(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)(b (a (a (^x.x))))) REDUCED to normal form. ------ 192285/22692495. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192286/22692504. ------ 1. ==[ start ]==> (((a (^a.a)) a)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(^z.z)))) REDUCED to normal form. ------ 192287/22692531. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a (^z.z)))(a a))) REDUCED to normal form. ------ 192288/22692558. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 192289/22692612. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 192290/22692693. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b a)(a b))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b a)(a b))) REDUCED to normal form. ------ 192291/22692720. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 192292/22692747. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.a))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 192293/22692774. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a b)(b a))) REDUCED to normal form. ------ 192294/22692801. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 192295/22692909. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a a)((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a a)((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 192296/22692927. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.(y y))(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.(x x))(b (^y.(y (^z.z))))) 5. ==[ beta ]==> ((b (^y.(y (^z.z))))(b (^y.(y (^z.z))))) 6. ==[ alpha ]==> ((b (^x.(x (^y.y))))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 192297/22692954. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 192298/22693116. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 192299/22693161. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 192300/22693242. ------ 1. ==[ start ]==> (((a (a a))(a a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 192301/22693269. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 192302/22693278. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192303/22693305. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 192304/22693359. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.(^y2.y2)) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192305/22693413. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 9. ==[ beta ]==> ((^z.z)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192306/22693737. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(a a))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(a a))) 7. ==[ beta ]==> ((^y.(a a))(^y.(a a))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 192307/22693827. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(a (a (a (^z.z))))) 3. ==[ beta ]==> (((^y.y) b)(a (a (a (^z.z))))) 4. ==[ alpha ]==> (((^x.x) b)(a (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (a (^y.y))))) 6. ==[ alpha ]==> (b (a (a (a (^x.x))))) REDUCED to normal form. ------ 192308/22693854. ------ 1. ==[ start ]==> ((((a a) a) a)(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((a a) a) a)(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> ((((a a) a) a)((^y.y)(a a))) 4. ==[ alpha ]==> ((((a a) a) a)((^x.x)(a a))) 5. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 192309/22693908. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(a a)) a)) REDUCED to normal form. ------ 192310/22693935. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> ((a (^x.(x x)))(b (a (a a)))) REDUCED to normal form. ------ 192311/22693962. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.a))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 192312/22693989. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((b a)((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((b a)((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192313/22694016. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 192314/22694205. ------ 1. ==[ start ]==> (((^a.b) a)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> (b ((a (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> (b ((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 192315/22694385. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 192316/22694493. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> (((a (a a))(a (a a))) b) REDUCED to normal form. ------ 192317/22694574. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (b ((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> (b (((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> (b (((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> (b (b ((^y.y) b))) 8. ==[ alpha ]==> (b (b ((^x.x) b))) 9. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 192318/22694601. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 192319/22694673. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a) a)) 6. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a) a)) 7. ==[ beta ]==> ((a (^x.x))((^z.z) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 192320/22694700. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((b (^x.x)) b)) REDUCED to normal form. ------ 192321/22694844. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192322/22694898. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 192323/22694979. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 5. ==[ beta ]==> (b ((^y.y)(^y.y))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192324/22695042. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(b (b (^y.y)))) REDUCED to normal form. ------ 192325/22695069. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(a (^z.z))) REDUCED to normal form. ------ 192326/22695123. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 192327/22695150. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((^x1.x1) b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((^x1.x1) b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(y y))(((^z.z) b)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)((^z.z) a))) 7. ==[ beta ]==> ((((^y.y) b)((^z.z) a))(((^y.y) b)((^z.z) a))) 8. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z) b)((^x1.x1) a))) 9. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) b)((^x1.x1) a))) 10. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) b)((^z.z) a))) 11. ==[ beta ]==> ((b a)(((^y.y) b)((^z.z) a))) 12. ==[ alpha ]==> ((b a)(((^x.x) b)((^y.y) a))) 13. ==[ beta ]==> ((b a)(b ((^y.y) a))) 14. ==[ alpha ]==> ((b a)(b ((^x.x) a))) 15. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 192328/22695177. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 192329/22695204. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 192330/22695231. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 192331/22695420. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> (b ((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 192332/22695483. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 192333/22695519. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 192334/22695654. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a))(a b))) 3. ==[ beta ]==> (b ((^z.(a a))(a b))) 4. ==[ alpha ]==> (b ((^x.(a a))(a b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 192335/22695735. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(b a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 192336/22695762. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.(y y))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(x x))(a (^y.(^z.z)))) 7. ==[ beta ]==> ((a (^y.(^z.z)))(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 192337/22695816. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 192338/22695897. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 192339/22696473. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x)) b)((a a)(^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x)) b)((a a)(^y.y))) REDUCED to normal form. ------ 192340/22696581. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 192341/22696680. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 192342/22696788. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.b)(a b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.b)(a b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 192343/22696806. ------ 1. ==[ start ]==> (((a a)(b a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 192344/22696887. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(a b))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))(a b))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 192345/22696914. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.y))(^z.z))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(^z.z))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 192346/22696968. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((a a)(a a)) a)) REDUCED to normal form. ------ 192347/22696995. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z) b) b)) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z) b) b)) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) b) b)) 5. ==[ beta ]==> (((a a) a)(((^y.y) b) b)) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b) b)) 7. ==[ beta ]==> (((a a) a)(b b)) REDUCED to normal form. ------ 192348/22697166. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((a a)((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.(a a)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 192349/22697247. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 192350/22697364. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 192351/22697391. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((b a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))((b a) a)) REDUCED to normal form. ------ 192352/22697472. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a b)((a a) a))) REDUCED to normal form. ------ 192353/22697499. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a) a)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a) a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)(a b))) 5. ==[ beta ]==> ((^y.b)(((a a) a)(a b))) 6. ==[ alpha ]==> ((^x.b)(((a a) a)(a b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 192354/22697553. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))((a a)(^z.z)))) REDUCED to normal form. ------ 192355/22697580. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) a)(b a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(a (b a))) REDUCED to normal form. ------ 192356/22697607. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (^z.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 192357/22697679. ------ 1. ==[ start ]==> ((a (^b.b))((^b.b)(a a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 3. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 192358/22697697. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 192359/22697724. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((b a)(^y.a))) REDUCED to normal form. ------ 192360/22697751. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 192361/22697778. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a a))((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (((a (a a))(a a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 192362/22697805. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a b)(^z.a))) 3. ==[ beta ]==> (((^y.y)(a b))((a b)(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a b))((a b)(^y.a))) 5. ==[ beta ]==> ((a b)((a b)(^y.a))) 6. ==[ alpha ]==> ((a b)((a b)(^x.a))) REDUCED to normal form. ------ 192363/22697832. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a) a)(^x.b))) REDUCED to normal form. ------ 192364/22697859. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((a b)(^x.x))((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.(a a)))) 7. ==[ beta ]==> (((a b)(^x.x))(^z.(a a))) 8. ==[ alpha ]==> (((a b)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 192365/22697967. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a a)(^z.z))) REDUCED to normal form. ------ 192366/22697994. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a) b) a)) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y) b) a)) 3. ==[ beta ]==> ((a b)(((^y.y) b) a)) 4. ==[ alpha ]==> ((a b)(((^x.x) b) a)) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 192367/22698003. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192368/22698030. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3)))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192369/22698165. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(^x1.b))) 3. ==[ beta ]==> (b ((^z.a)(^x1.b))) 4. ==[ alpha ]==> (b ((^x.a)(^y.b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 192370/22698273. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3))))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192371/22698282. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 192372/22698309. ------ 1. ==[ start ]==> ((((^a.a) b) a)(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) b) a)(a ((^y.y) b))) 3. ==[ beta ]==> ((b a)(a ((^y.y) b))) 4. ==[ alpha ]==> ((b a)(a ((^x.x) b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 192373/22698336. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 192374/22698363. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((b a)(a (^y1.y1)))) REDUCED to normal form. ------ 192375/22698444. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((a b)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.(a a))((a b)((^y.y)(^z.z)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 192376/22698471. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a) a)((a a) a))) REDUCED to normal form. ------ 192377/22698498. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.z)(a b))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(a b))) 5. ==[ beta ]==> (((a b)(^x.a))(a b)) REDUCED to normal form. ------ 192378/22698525. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (a a))(a a))) REDUCED to normal form. ------ 192379/22698552. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 192380/22698597. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(b (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192381/22698606. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 192382/22698669. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 192383/22698696. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.a))) REDUCED to normal form. ------ 192384/22698723. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> ((a (b a))((a a)(^y.(y y)))) 6. ==[ alpha ]==> ((a (b a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 192385/22698750. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 192386/22698804. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(a b))((^y.y)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(a b))((^x.x)(^y.b))) 5. ==[ beta ]==> ((((a a) a)(a b))(^y.b)) 6. ==[ alpha ]==> ((((a a) a)(a b))(^x.b)) REDUCED to normal form. ------ 192387/22698831. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 192388/22698939. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a (^x1.(^y1.y1))) a)) REDUCED to normal form. ------ 192389/22698966. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((b a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((b a) b)) 3. ==[ beta ]==> ((b (a a))((b a) b)) REDUCED to normal form. ------ 192390/22699029. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(z z))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(y y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 192391/22699164. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 192392/22699308. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> ((b b)(((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> ((b b)((a a)((^y.y) a))) 6. ==[ alpha ]==> ((b b)((a a)((^x.x) a))) 7. ==[ beta ]==> ((b b)((a a) a)) REDUCED to normal form. ------ 192393/22699335. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((a b)(a (a a)))) REDUCED to normal form. ------ 192394/22699389. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)((a a) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a) a)) REDUCED to normal form. ------ 192395/22699416. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a (a a))(a b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a (a a))(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))(a b))) REDUCED to normal form. ------ 192396/22699497. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a a)(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)(b a))) REDUCED to normal form. ------ 192397/22699515. ------ 1. ==[ start ]==> (((^a.b)(a b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a b))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (b (a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 192398/22699623. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.b)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192399/22699722. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(a (^x.(a a)))) REDUCED to normal form. ------ 192400/22699749. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 192401/22699803. ------ 1. ==[ start ]==> (((a (a a))(b a))((b a) a)) REDUCED to normal form. ------ 192402/22699830. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a)(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(^z.z)) b)) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z)) b)) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 192403/22700460. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 192404/22700487. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a) a))) 5. ==[ beta ]==> ((^y.(y y))((a a) a)) 6. ==[ alpha ]==> ((^x.(x x))((a a) a)) 7. ==[ beta ]==> (((a a) a)((a a) a)) REDUCED to normal form. ------ 192405/22700541. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 192406/22700622. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 192407/22700766. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(c (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(c (a b))) 3. ==[ beta ]==> ((b (^y.a))(c (a b))) 4. ==[ alpha ]==> ((b (^x.a))(c (a b))) REDUCED to normal form. ------ 192408/22700793. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(b ((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 192409/22700856. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(a a)) b)) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 192410/22700883. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b) c)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 192411/22700910. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a) d)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a) d)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a) d)) 5. ==[ beta ]==> ((a b)((^y.a) d)) 6. ==[ alpha ]==> ((a b)((^x.a) d)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 192412/22701072. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a a)(^y.y))) REDUCED to normal form. ------ 192413/22701126. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((a a) a)(^z.a))) REDUCED to normal form. ------ 192414/22701153. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((b a)((^y.y)(^z.(z z)))) 8. ==[ alpha ]==> ((b a)((^x.x)(^y.(y y)))) 9. ==[ beta ]==> ((b a)(^y.(y y))) 10. ==[ alpha ]==> ((b a)(^x.(x x))) REDUCED to normal form. ------ 192415/22701180. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 192416/22701234. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.b))) REDUCED to normal form. ------ 192417/22701324. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 192418/22701405. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192419/22701630. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a (((^y.y) a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.x) a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (a (a ((^y.y)(^z.z)))) 8. ==[ alpha ]==> (a (a ((^x.x)(^y.y)))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 192420/22701675. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(b (^x1.b))) 3. ==[ beta ]==> ((^y.y)(b (^x1.b))) 4. ==[ alpha ]==> ((^x.x)(b (^y.b))) 5. ==[ beta ]==> (b (^y.b)) 6. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 192421/22701729. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.b)(a a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.b)(a a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.b)(a a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.b)(a a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.b)(a a))) 7. ==[ beta ]==> ((b b)((^y.b)(a a))) 8. ==[ alpha ]==> ((b b)((^x.b)(a a))) 9. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 192422/22701810. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (b ((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (a a)))) 5. ==[ beta ]==> (b ((a (a a))(a (a a)))) REDUCED to normal form. ------ 192423/22701819. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d e)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d e)) REDUCED to normal form. ------ 192424/22701918. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.b)(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b)(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192425/22702098. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.b) a)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) b) REDUCED to normal form. ------ 192426/22702152. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z)) c)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y)) c)) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 192427/22702287. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((a a) a)(^y.y))) REDUCED to normal form. ------ 192428/22702341. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (a a))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a))(^x1.a))) REDUCED to normal form. ------ 192429/22702368. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> ((b (a (a a)))(a (^y.(y y)))) 6. ==[ alpha ]==> ((b (a (a a)))(a (^x.(x x)))) REDUCED to normal form. ------ 192430/22702395. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 192431/22702449. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((a a) a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((a a) a) a)) 3. ==[ beta ]==> (((^y.y)(a a))(((a a) a) a)) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a) a) a)) 5. ==[ beta ]==> ((a a)(((a a) a) a)) REDUCED to normal form. ------ 192432/22702476. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y)(^z.z)) b)) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.z) b)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y) b)) 5. ==[ beta ]==> ((a (a (a (^x.x)))) b) REDUCED to normal form. ------ 192433/22702485. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((^z.(^x1.x1))(^y1.(^z1.z1)))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.y1)) 7. ==[ beta ]==> ((^y.y)(^y1.y1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192434/22702890. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192435/22702917. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 192436/22702944. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(y1 y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 7. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192437/22702998. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 192438/22703034. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> (a ((^y.y)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 192439/22703061. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (a a))(a a))) REDUCED to normal form. ------ 192440/22703142. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a)(a (a a)))) REDUCED to normal form. ------ 192441/22703187. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192442/22703223. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c c)) REDUCED to normal form. ------ 192443/22703322. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 192444/22703349. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 192445/22703394. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z)) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 192446/22703421. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.a) b)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.a) b)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.a) b)) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 192447/22703502. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (^z.z))) REDUCED to normal form. ------ 192448/22703529. ------ 1. ==[ start ]==> (((a b)(b a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 192449/22703556. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a)(^z.a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a)(^z.a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)(^y.a))) REDUCED to normal form. ------ 192450/22703583. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(((^z.z) a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(((^z.z) a) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) a) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 192451/22703664. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.a) a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.a) a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.a) a)) 5. ==[ beta ]==> ((b (^y.y))((^z.a) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.a) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 192452/22703691. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.(^y.y)) b)) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 192453/22703745. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 192454/22703763. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(b b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(b b)) 3. ==[ beta ]==> ((b (^y.y))(b b)) 4. ==[ alpha ]==> ((b (^x.x))(b b)) REDUCED to normal form. ------ 192455/22703772. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 192456/22703799. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a (^x1.x1)) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 192457/22703808. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192458/22703835. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192459/22703970. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> (b (a (^y1.y1))) 4. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 192460/22707906. ------ 1. ==[ start ]==> ((^a.(b a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(^y.(b (^z.z)))) 3. ==[ eta ]==> (b (^y.(b (^z.z)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 192461/22711740. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(b z))) 3. ==[ eta ]==> ((^x.(b (^y.y))) b) 4. ==[ beta ]==> (b (^y.y)) 5. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192462/22715640. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a)))) c) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1)))) c) 3. ==[ beta ]==> (b c) REDUCED to normal form. ------ 192463/22715847. ------ 1. ==[ start ]==> (((a (^a.a)) a)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 192464/22715988. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ eta ]==> ((^y.y)(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192465/22716258. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (^y.y))((^z.(^x1.x1)) a))(((a (^y.y))((^z.(^x1.x1)) a))((a (^y.y))((^z.(^x1.x1)) a)))) 4. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(((a (^x1.x1))((^y1.(^z1.z1)) a))((a (^x2.x2))((^y2.(^z2.z2)) a)))) 5. ==[ beta ]==> (((a (^x.x))(^z.z))(((a (^x1.x1))((^y1.(^z1.z1)) a))((a (^x2.x2))((^y2.(^z2.z2)) a)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a (^z.z))((^x1.(^y1.y1)) a))((a (^z1.z1))((^x2.(^y2.y2)) a)))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(((a (^z.z))(^y1.y1))((a (^z1.z1))((^x2.(^y2.y2)) a)))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a (^z.z))(^x1.x1))((a (^y1.y1))((^z1.(^x2.x2)) a)))) 9. ==[ beta ]==> (((a (^x.x))(^y.y))(((a (^z.z))(^x1.x1))((a (^y1.y1))(^x2.x2)))) 10. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a (^z.z))(^x1.x1))((a (^y1.y1))(^z1.z1)))) REDUCED to normal form. ------ 192466/22716483. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192467/22716738. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (a (^y.(a (a (^z.z))))) 6. ==[ alpha ]==> (a (^x.(a (a (^y.y))))) REDUCED to normal form. ------ 192468/22717170. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> (b (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 192469/22717554. ------ 1. ==[ start ]==> ((^a.(a b))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a (^y.y))(b (^z.z))) b) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y))) b) REDUCED to normal form. ------ 192470/22717941. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (^y.((((^z.z) a)(^x1.(a a)))(((^z.z) a)(^x1.(a a))))) 4. ==[ alpha ]==> (^x.((((^y.y) a)(^z.(a a)))(((^x1.x1) a)(^y1.(a a))))) 5. ==[ beta ]==> (^x.((a (^z.(a a)))(((^x1.x1) a)(^y1.(a a))))) 6. ==[ alpha ]==> (^x.((a (^y.(a a)))(((^z.z) a)(^x1.(a a))))) 7. ==[ beta ]==> (^x.((a (^y.(a a)))(a (^x1.(a a))))) 8. ==[ alpha ]==> (^x.((a (^y.(a a)))(a (^z.(a a))))) REDUCED to normal form. ------ 192471/22719195. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192472/22719579. ------ 1. ==[ start ]==> ((^a.(b a))(a (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))(a (b (^y.y)))) 3. ==[ eta ]==> (b (a (b (^y.y)))) 4. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 192473/22719582. ------ 1. ==[ start ]==> ((a (b a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((a (b a))(^x.(b (^y.y)))) REDUCED to normal form. ------ 192474/22720128. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a b)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a b)(^y1.b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192475/22721019. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192476/22721652. ------ 1. ==[ start ]==> ((((^a.a) b) a)(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)(^y.(^z.z))) 3. ==[ beta ]==> ((b a)(^y.(^z.z))) 4. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 192477/22721976. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^a.(^b.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 192478/22722867. ------ 1. ==[ start ]==> (((a b)(^a.b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 192479/22723413. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(a (b a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(a (b a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192480/22723416. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^a.(b a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(b y))) 3. ==[ eta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 192481/22724388. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(a b))(^y.((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(a b))(^x.(a a))) REDUCED to normal form. ------ 192482/22725441. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(z b))) REDUCED to normal form. ------ 192483/22726242. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.z))) REDUCED to normal form. ------ 192484/22726377. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192485/22726689. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a)) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1)) c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192486/22726737. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z (z z)))) REDUCED to normal form. ------ 192487/22726818. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1) a))) 6. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) a))) 7. ==[ beta ]==> (b (^y.((^z.z) a))) 8. ==[ alpha ]==> (b (^x.((^y.y) a))) 9. ==[ beta ]==> (b (^x.a)) REDUCED to normal form. ------ 192488/22727007. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((^x.x) b)((^y.y)(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.z)) 7. ==[ beta ]==> ((b (^y.y))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 192489/22727313. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> (b (^y1.a)) 4. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 192490/22727361. ------ 1. ==[ start ]==> (((^a.a) a)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a ((^y.b)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a ((^x.b)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a b) REDUCED to normal form. ------ 192491/22727415. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 192492/22727496. ------ 1. ==[ start ]==> (((a a) b)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 192493/22727523. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 192494/22727541. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 192495/22727568. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((^y.(y (^z.z))) b) 6. ==[ alpha ]==> ((^x.(x (^y.y))) b) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192496/22727613. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((b (^y.y)) a)) REDUCED to normal form. ------ 192497/22727640. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 192498/22727667. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 192499/22727856. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a a) a)((^y.y)((^z.z) b))) 6. ==[ alpha ]==> (((a a) a)((^x.x)((^y.y) b))) 7. ==[ beta ]==> (((a a) a)((^y.y) b)) 8. ==[ alpha ]==> (((a a) a)((^x.x) b)) 9. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 192500/22727883. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 192501/22727910. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> ((a (a a))(a (b (^y.y)))) 6. ==[ alpha ]==> ((a (a a))(a (b (^x.x)))) REDUCED to normal form. ------ 192502/22727937. ------ 1. ==[ start ]==> ((a (a (a a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (a (a a)))((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a (a a)))((a (^x.x))(^z.z))) 4. ==[ alpha ]==> ((a (a (a a)))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 192503/22728009. ------ 1. ==[ start ]==> ((((^a.a) a) b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a b)((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((a b)((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((a b)((a a)(^y.y))) 6. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 192504/22728027. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 8. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192505/22728054. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((a (a a))((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((a (a a))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 192506/22728081. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 192507/22728090. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 192508/22728117. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 192509/22728144. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 192510/22728162. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.b))) REDUCED to normal form. ------ 192511/22728252. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.b)(b a))) 3. ==[ beta ]==> ((b b)((^y.b)(b a))) 4. ==[ alpha ]==> ((b b)((^x.b)(b a))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 192512/22728297. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192513/22728387. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 192514/22728414. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> (a ((^y.y)(a (a (^z.z))))) 6. ==[ alpha ]==> (a ((^x.x)(a (a (^y.y))))) 7. ==[ beta ]==> (a (a (a (^y.y)))) 8. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 192515/22728432. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a (^z.z))) a)) 5. ==[ beta ]==> ((^y.y)((a (a (^z.z))) a)) 6. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 7. ==[ beta ]==> ((a (a (^y.y))) a) 8. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 192516/22728441. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^y1.y1)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 192517/22728459. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((^y.(^z.z)) a) b) 6. ==[ alpha ]==> (((^x.(^y.y)) a) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 192518/22728549. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192519/22728846. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (b ((^y.y)(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(y (^z.z))))) 7. ==[ beta ]==> (b (^y.(y (^z.z)))) 8. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 192520/22729071. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)((a a) a))((a a)(a a))) REDUCED to normal form. ------ 192521/22729098. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)((a a)(^z.z)))) REDUCED to normal form. ------ 192522/22729125. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((a a) a)(b a))) 3. ==[ beta ]==> ((a (a (a a)))(((a a) a)(b a))) REDUCED to normal form. ------ 192523/22729152. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (a a)) a)((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a (a a)) a)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> (((a (a a)) a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> (((a (a a)) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 192524/22729179. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a (a a))((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (a a))((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (a a))((^z.z) b))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))((^y.y) b))) 7. ==[ beta ]==> ((a (^x.x))((a (a a)) b)) REDUCED to normal form. ------ 192525/22729206. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(a ((a a)(a a)))) REDUCED to normal form. ------ 192526/22729224. ------ 1. ==[ start ]==> (((^a.b) a)(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)(c (^y.(^z.z)))) 3. ==[ beta ]==> (b (c (^y.(^z.z)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 192527/22729233. ------ 1. ==[ start ]==> ((a (a b))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 192528/22729323. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b (^z.z))(^x1.(^y1.y1)))) IRREDUCIBLE: cycle. ------ 192529/22729386. ------ 1. ==[ start ]==> ((((a a) a) b)((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.x)(a (a a)))) 3. ==[ beta ]==> ((((a a) a) b)(a (a a))) REDUCED to normal form. ------ 192530/22729404. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 192531/22729413. ------ 1. ==[ start ]==> (((a b) a)((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 192532/22729431. ------ 1. ==[ start ]==> (((^a.a)(a b))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a b))((b a)(^y.a))) 3. ==[ beta ]==> ((a b)((b a)(^y.a))) 4. ==[ alpha ]==> ((a b)((b a)(^x.a))) REDUCED to normal form. ------ 192533/22729458. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.b)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 192534/22729494. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 192535/22729512. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 192536/22729521. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x))) b) REDUCED to normal form. ------ 192537/22729548. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.a)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.a)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(b a))) 5. ==[ beta ]==> ((^y.a)((^z.a)(b a))) 6. ==[ alpha ]==> ((^x.a)((^y.a)(b a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 192538/22729575. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 192539/22729593. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a a))((a (a a))(^y.y))) 3. ==[ beta ]==> (b ((a (a a))(^y.y))) 4. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 192540/22729602. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.x))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> (((a b)(^x.x))(b ((^z.z) b))) 6. ==[ alpha ]==> (((a b)(^x.x))(b ((^y.y) b))) 7. ==[ beta ]==> (((a b)(^x.x))(b b)) REDUCED to normal form. ------ 192541/22729620. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 192542/22729791. ------ 1. ==[ start ]==> (((^a.b) b)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 192543/22730007. ------ 1. ==[ start ]==> (((a b) b)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a b) b)((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a b) b)((^y.y)(^y.y))) 4. ==[ alpha ]==> (((a b) b)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a b) b)(^y.y)) 6. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 192544/22730034. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 192545/22730286. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(a b))) 5. ==[ beta ]==> (((a a)(a a))((a a)(a b))) REDUCED to normal form. ------ 192546/22730313. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a b)(a a))) REDUCED to normal form. ------ 192547/22730340. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> ((a ((a a) a))(((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((a ((a a) a))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 192548/22730367. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(b a))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(b a))) 7. ==[ beta ]==> (((a (a a))(^x.x))(b a)) REDUCED to normal form. ------ 192549/22730394. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (a a))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a a))((a (a a))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a (a a))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 192550/22730421. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> ((((a a) a) a)(a ((^y.y) b))) 6. ==[ alpha ]==> ((((a a) a) a)(a ((^x.x) b))) 7. ==[ beta ]==> ((((a a) a) a)(a b)) REDUCED to normal form. ------ 192551/22730439. ------ 1. ==[ start ]==> (((^a.b) c)(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) c)(c (^y.(a a)))) 3. ==[ beta ]==> (b (c (^y.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 192552/22730448. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 192553/22730475. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a a)(b (^y.y)))) 3. ==[ beta ]==> (((a a)(a a))((a a)(b (^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))((a a)(b (^x.x)))) REDUCED to normal form. ------ 192554/22730538. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 192555/22730673. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (b ((a a)(^y.b))) 6. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 192556/22730682. ------ 1. ==[ start ]==> (((a b) c)((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b) c)((^x.(a a))(a b))) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 192557/22730709. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) b)((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 192558/22730781. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 192559/22730790. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 192560/22730817. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.b))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.b))((^y.a)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 192561/22730871. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(b (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(b (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(b (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192562/22730916. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((a a)(a a)) b)) 3. ==[ beta ]==> (b (((a a)(a a)) b)) REDUCED to normal form. ------ 192563/22730925. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 192564/22730952. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.a)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 192565/22730979. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 192566/22731231. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b ((a a)(a a)))) REDUCED to normal form. ------ 192567/22731258. ------ 1. ==[ start ]==> ((a (b a))(a (b (^a.a)))) 2. ==[ alpha ]==> ((a (b a))(a (b (^x.x)))) REDUCED to normal form. ------ 192568/22731600. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(b (^z.(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(b (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b (^y.(a a)))) REDUCED to normal form. ------ 192569/22731681. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 192570/22731699. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 192571/22731708. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 192572/22731807. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a b)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)(^x1.b))) REDUCED to normal form. ------ 192573/22732374. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.y1) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192574/22732626. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(c (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 192575/22732698. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 192576/22732977. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192577/22733022. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b) a)) 3. ==[ beta ]==> ((^y.y)(((^z.z) b) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) a)) 5. ==[ beta ]==> (((^y.y) b) a) 6. ==[ alpha ]==> (((^x.x) b) a) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 192578/22733049. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.(^x2.x2))) b)) 3. ==[ beta ]==> ((^y.y)((a (^z1.(^x2.x2))) b)) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z))) b)) 5. ==[ beta ]==> ((a (^y.(^z.z))) b) 6. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 192579/22733301. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 192580/22733328. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.y)(^z.z))) 3. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 192581/22733346. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.b) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z) a)) 3. ==[ beta ]==> (((^y.y) b)((^z.z) a)) 4. ==[ alpha ]==> (((^x.x) b)((^y.y) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 192582/22733373. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.(^x2.x2))) b)) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) b) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) b) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192583/22733625. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 192584/22733652. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(a (^z.z))) 3. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 4. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 192585/22734543. ------ 1. ==[ start ]==> (((a b)(^a.b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.b))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 192586/22734597. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 192587/22734642. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192588/22734651. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a)) b) REDUCED to normal form. ------ 192589/22734678. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 192590/22734705. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 192591/22735038. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(c ((^z.z)(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(c ((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(c ((^y.y)(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))(c (a a))) REDUCED to normal form. ------ 192592/22735065. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(b ((a a)(^x.x)))) REDUCED to normal form. ------ 192593/22735092. ------ 1. ==[ start ]==> ((a (b (^a.a)))(a (b a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(a (b a))) REDUCED to normal form. ------ 192594/22735371. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((a a)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192595/22735407. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> ((b c)((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((b c)((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 192596/22735434. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.b)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a)) b) b) REDUCED to normal form. ------ 192597/22735479. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 192598/22735542. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(a b))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(a b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(a b))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 192599/22735560. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(^z1.(a a)))) REDUCED to normal form. ------ 192600/22735569. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 192601/22735641. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> (b (((^z.z)(a a)) b)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) b)) 5. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 192602/22735650. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 192603/22735677. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 192604/22735785. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(^x1.b))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.b))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 192605/22735812. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 192606/22735875. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 192607/22735902. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 192608/22735929. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((a b)(((a a) a)((^y.y) a))) 6. ==[ alpha ]==> ((a b)(((a a) a)((^x.x) a))) 7. ==[ beta ]==> ((a b)(((a a) a) a)) REDUCED to normal form. ------ 192609/22735956. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 192610/22735983. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)((a (a a))((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((b a)((a (a a))((^x.x)(^y.y)))) 7. ==[ beta ]==> ((b a)((a (a a))(^y.y))) 8. ==[ alpha ]==> ((b a)((a (a a))(^x.x))) REDUCED to normal form. ------ 192611/22736010. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 192612/22736037. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a (^y.y))(a b))) 3. ==[ beta ]==> (((a b)(a a))((a (^y.y))(a b))) 4. ==[ alpha ]==> (((a b)(a a))((a (^x.x))(a b))) REDUCED to normal form. ------ 192613/22736064. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a b))((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)(a b))((a a)((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)(a b))((a a)(a a))) REDUCED to normal form. ------ 192614/22736343. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a b) b)) 3. ==[ beta ]==> (((^y.y)(^y.y))((a b) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b) b)) 5. ==[ beta ]==> ((^y.y)((a b) b)) 6. ==[ alpha ]==> ((^x.x)((a b) b)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 192615/22736532. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192616/22736748. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a b)(^z.z))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a b)(^z.z))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a b)(^z.z))) 5. ==[ beta ]==> ((b ((^y.y) b))((a b)(^z.z))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a b)(^y.y))) 7. ==[ beta ]==> ((b b)((a b)(^y.y))) 8. ==[ alpha ]==> ((b b)((a b)(^x.x))) REDUCED to normal form. ------ 192617/22736757. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 192618/22736829. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> (b ((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(x x)))) REDUCED to normal form. ------ 192619/22736838. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 192620/22736865. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 192621/22736892. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 192622/22736937. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a b) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192623/22736946. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 192624/22736973. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 192625/22737000. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 192626/22737054. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 192627/22737090. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(b ((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(b ((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))(b ((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(b ((a a) a))) REDUCED to normal form. ------ 192628/22737117. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (a b))) REDUCED to normal form. ------ 192629/22737144. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((a a) a)(a a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 192630/22737171. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a (a a)) b)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (((a (a a)) b)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (((a (a a)) b)(a (^y.y))) 8. ==[ alpha ]==> (((a (a a)) b)(a (^x.x))) REDUCED to normal form. ------ 192631/22737198. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a (a a))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a (a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (a a))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))((^z.z) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((a (a a)) a)) REDUCED to normal form. ------ 192632/22737225. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x) a)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(b a))(a (a (a a)))) REDUCED to normal form. ------ 192633/22737252. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 192634/22737279. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a a)((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a a)((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a a)((a a) a))) 5. ==[ beta ]==> (((a a)(a a))((a a)((a a) a))) REDUCED to normal form. ------ 192635/22737504. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a)(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1)(^y1.y1)) b)) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1)(^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(^x1.x1)) b)) 5. ==[ beta ]==> ((((^z.z)(^x1.x1)) b)(^y.y)) 6. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(^z.z)) 7. ==[ beta ]==> (((^y.y) b)(^z.z)) 8. ==[ alpha ]==> (((^x.x) b)(^y.y)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192636/22737891. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a (a a)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192637/22737909. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 192638/22737918. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 6. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 192639/22737936. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z) a)) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y) a)) 7. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 192640/22737945. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 192641/22737963. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (a a)) b)) 3. ==[ beta ]==> ((^y.y)((a (a a)) b)) 4. ==[ alpha ]==> ((^x.x)((a (a a)) b)) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 192642/22738053. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192643/22738098. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(y y)) b)) 3. ==[ beta ]==> (b ((^y.(y y)) b)) 4. ==[ alpha ]==> (b ((^x.(x x)) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 192644/22738161. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (^z.(z z)))) REDUCED to normal form. ------ 192645/22738206. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192646/22738242. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 192647/22738269. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 192648/22738323. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192649/22738341. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(((^z.z) a) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a) b)) 5. ==[ beta ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 192650/22738350. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 192651/22738368. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a)) c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1)) c)) REDUCED to normal form. ------ 192652/22738386. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b ((^y.y) a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(b a)) REDUCED to normal form. ------ 192653/22738413. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a (a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a (a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a (a a)))) REDUCED to normal form. ------ 192654/22738440. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))(((^z.z) a)(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(a a))) 5. ==[ beta ]==> ((a (b (^x.x)))(a (a a))) REDUCED to normal form. ------ 192655/22738467. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 192656/22738494. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)((^z.z) a))) 5. ==[ beta ]==> (((^y.y) b)((a a)((^z.z) a))) 6. ==[ alpha ]==> (((^x.x) b)((a a)((^y.y) a))) 7. ==[ beta ]==> (b ((a a)((^y.y) a))) 8. ==[ alpha ]==> (b ((a a)((^x.x) a))) 9. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 192657/22738548. ------ 1. ==[ start ]==> (((a b)(b a))(c b)) REDUCED to normal form. ------ 192658/22738575. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b c)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b c)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b c)) REDUCED to normal form. ------ 192659/22738656. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b (a (^z.z)))) REDUCED to normal form. ------ 192660/22738683. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a ((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))(a ((^z.z) a))) 6. ==[ alpha ]==> ((b (^x.x))(a ((^y.y) a))) 7. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 192661/22738710. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a (^x.x))(a a))) REDUCED to normal form. ------ 192662/22738782. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 192663/22738791. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(b b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(b b)) REDUCED to normal form. ------ 192664/22738827. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1)) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192665/22738854. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a a) b)) 3. ==[ beta ]==> ((^y.y)((a a) b)) 4. ==[ alpha ]==> ((^x.x)((a a) b)) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 192666/22738989. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> (b ((^y1.y1) a)) 4. ==[ alpha ]==> (b ((^x.x) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 192667/22744689. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.((^x1.x1) z))) 3. ==[ eta ]==> ((^x.((^y.y) b))(^x1.x1)) 4. ==[ alpha ]==> ((^x.((^y.y) b))(^z.z)) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 192668/22750494. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192669/22750728. ------ 1. ==[ start ]==> ((^a.(a a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.b)(^z.(^x1.(^y1.y1))))((^y.b)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(^x2.(^y2.y2))))) 5. ==[ beta ]==> (b ((^y1.b)(^z1.(^x2.(^y2.y2))))) 6. ==[ alpha ]==> (b ((^x.b)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 192670/22750755. ------ 1. ==[ start ]==> ((^a.b)((^c.a)(^b.b))) 2. ==[ alpha ]==> ((^x.b)((^y.a)(^z.z))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 192671/22750902. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.x))(^y.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 192672/22750953. ------ 1. ==[ start ]==> ((^a.(^b.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (^x.((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> (^x.((^y.y)(a (^z.z)))) 7. ==[ beta ]==> (^x.(a (^z.z))) 8. ==[ alpha ]==> (^x.(a (^y.y))) REDUCED to normal form. ------ 192673/22751196. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 192674/22751334. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 192675/22752411. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 192676/22752591. ------ 1. ==[ start ]==> ((^a.(a b))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))(c (^y.(^z.z)))) 3. ==[ beta ]==> ((c (^y.(^z.z))) b) 4. ==[ alpha ]==> ((c (^x.(^y.y))) b) REDUCED to normal form. ------ 192677/22753053. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^y.y))(^z.((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a (^x.x))(^y.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 192678/22753185. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))((^x2.(^y2.(^z2.z2)))(^x3.(^y3.y3))))) 5. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))((^x2.(^y2.(^z2.z2)))(^x3.(^y3.y3)))) 6. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3)))) 7. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3)))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192679/22754232. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192680/22754979. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(^y.((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(^y.((a a)(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(^x.((a a)(a a)))) REDUCED to normal form. ------ 192681/22755348. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.((a a)(a a)))) REDUCED to normal form. ------ 192682/22756371. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192683/22756374. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^b.((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.((^z.z) y))) 3. ==[ eta ]==> ((a ((^x.x) b))(^z.z)) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.y)) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 192684/22756707. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z) b))) 5. ==[ beta ]==> (b (^y.((^z.z) b))) 6. ==[ alpha ]==> (b (^x.((^y.y) b))) 7. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 192685/22757319. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 192686/22757895. ------ 1. ==[ start ]==> (((^a.b)(a b))(^c.(b a))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(b a))) 3. ==[ beta ]==> (b (^y.(b a))) 4. ==[ alpha ]==> (b (^x.(b a))) REDUCED to normal form. ------ 192687/22758183. ------ 1. ==[ start ]==> (((a (a a))(b a))(^b.(b a))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(x a))) REDUCED to normal form. ------ 192688/22759611. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.a)((a a) a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192689/22759893. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.((^x2.x2)(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2)(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192690/22760478. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 192691/22760667. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.b))) REDUCED to normal form. ------ 192692/22760829. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^b.((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.((a a) a))) 5. ==[ beta ]==> ((a a)(^y.((a a) a))) 6. ==[ alpha ]==> ((a a)(^x.((a a) a))) REDUCED to normal form. ------ 192693/22761726. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(c (a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(c (a (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192694/22761774. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 192695/22761882. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 192696/22761963. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^y.a)) REDUCED to normal form. ------ 192697/22762044. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.a))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 192698/22762125. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.z))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.z))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 192699/22762176. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192700/22762179. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (^x1.x1)))) REDUCED to normal form. ------ 192701/22762188. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.c)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.c)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192702/22762350. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(y1 y1))) 3. ==[ beta ]==> (b (^y1.(y1 y1))) 4. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 192703/22762416. ------ 1. ==[ start ]==> ((a (a a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))((^x.b)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 192704/22762443. ------ 1. ==[ start ]==> ((a b)((^c.a)(^b.b))) 2. ==[ alpha ]==> ((a b)((^x.a)(^y.y))) 3. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 192705/22762560. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b (a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(b (a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 192706/22762587. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 192707/22762596. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 192708/22762614. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a (^y.y)))(a a)) 6. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 192709/22762623. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.z))) REDUCED to normal form. ------ 192710/22762641. ------ 1. ==[ start ]==> ((a (^b.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.a))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.a))(a (^y.y))) REDUCED to normal form. ------ 192711/22762722. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.a)(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 192712/22762749. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 192713/22762803. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (a (((a a)(^y.y))((^z.z)(a a)))) 6. ==[ alpha ]==> (a (((a a)(^x.x))((^y.y)(a a)))) 7. ==[ beta ]==> (a (((a a)(^x.x))(a a))) REDUCED to normal form. ------ 192714/22762830. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1)(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 192715/22762884. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 192716/22762992. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(y y))((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(x x))((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a (^y.y))((^z.(^x1.x1)) a))((a (^y.y))((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1))((^y1.(^z1.z1)) a))) 7. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))((^y1.(^z1.z1)) a))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 9. ==[ beta ]==> (((a (^x.x))(^y.y))((a (^z.z))(^y1.y1))) 10. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 192717/22763019. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a a)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 192718/22763055. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a b)((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> ((a b)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 192719/22763082. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a)) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 192720/22763109. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 192721/22763136. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a)(a a))(^z.(z z)))) REDUCED to normal form. ------ 192722/22763163. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 192723/22763280. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 192724/22763307. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.b)(b a))) 3. ==[ beta ]==> (((a (a a))(a a)) b) REDUCED to normal form. ------ 192725/22763460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y) a)((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) a)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> (a ((a a)(^y.(y (^z.z))))) 6. ==[ alpha ]==> (a ((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 192726/22763487. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 192727/22763514. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 192728/22763541. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((b (^z.z)) c)) 3. ==[ beta ]==> ((a (^y.a))((b (^z.z)) c)) 4. ==[ alpha ]==> ((a (^x.a))((b (^y.y)) c)) REDUCED to normal form. ------ 192729/22763712. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 192730/22763856. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))(c (b (^z.z)))) 3. ==[ beta ]==> (((^y.a)(^y.a))(c (b (^z.z)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))(c (b (^z.z)))) 5. ==[ beta ]==> (a (c (b (^z.z)))) 6. ==[ alpha ]==> (a (c (b (^x.x)))) REDUCED to normal form. ------ 192731/22763919. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(x (^y.y))) a)) 3. ==[ beta ]==> ((((a a) a) a)(a (^y.y))) 4. ==[ alpha ]==> ((((a a) a) a)(a (^x.x))) REDUCED to normal form. ------ 192732/22763937. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a a) a)(((^y.(^z.z)) a)(a a))) 4. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a)(a a))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 192733/22763964. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((b (^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b (^y.y))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 192734/22764018. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.z) b)(a (a a)))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.y) b)(a (a a)))) 7. ==[ beta ]==> ((a a)(((^y.y) b)(a (a a)))) 8. ==[ alpha ]==> ((a a)(((^x.x) b)(a (a a)))) 9. ==[ beta ]==> ((a a)(b (a (a a)))) REDUCED to normal form. ------ 192735/22764099. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 192736/22764279. ------ 1. ==[ start ]==> ((a (a b))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((a (a b))(c (^x.(^y.y)))) REDUCED to normal form. ------ 192737/22764288. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.b)((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192738/22764432. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a) b)(b (^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a) b)(b (^x.(x x)))) REDUCED to normal form. ------ 192739/22764459. ------ 1. ==[ start ]==> (((a b) a)((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 192740/22764486. ------ 1. ==[ start ]==> (((a a)(^a.b))((b a)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.b))((b a)(^y.a))) REDUCED to normal form. ------ 192741/22764540. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 192742/22764567. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 192743/22764621. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 192744/22764648. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 192745/22764684. ------ 1. ==[ start ]==> (((a a)(a b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 192746/22764711. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 192747/22764738. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a (^x.x))((^z.(^x1.x1)) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 192748/22764846. ------ 1. ==[ start ]==> (((a b)(a a))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(y y))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(x x))) REDUCED to normal form. ------ 192749/22764873. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 192750/22765125. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(b (b (^z.z)))) 3. ==[ beta ]==> ((^y.y)(b (b (^z.z)))) 4. ==[ alpha ]==> ((^x.x)(b (b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 192751/22765179. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((b (^x1.x1))(a a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b (^y1.y1))(a a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b (^y1.y1))(a a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b (^x1.x1))(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((b (^x1.x1))(a a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z))(a a))) 9. ==[ beta ]==> ((^y.y)((b (^z.z))(a a))) 10. ==[ alpha ]==> ((^x.x)((b (^y.y))(a a))) 11. ==[ beta ]==> ((b (^y.y))(a a)) 12. ==[ alpha ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 192752/22765260. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 192753/22765494. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(c (^y.(a a)))) REDUCED to normal form. ------ 192754/22765728. ------ 1. ==[ start ]==> (((a b) c)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b) c)(((^x.x)(a a))(^y.b))) 3. ==[ beta ]==> (((a b) c)((a a)(^y.b))) 4. ==[ alpha ]==> (((a b) c)((a a)(^x.b))) REDUCED to normal form. ------ 192755/22765755. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a b)(^y.(a a)))) 3. ==[ beta ]==> (((a a) b)((a b)(^y.(a a)))) 4. ==[ alpha ]==> (((a a) b)((a b)(^x.(a a)))) REDUCED to normal form. ------ 192756/22765836. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 192757/22765863. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((a (^x.b))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.b))(a (^y.y))) REDUCED to normal form. ------ 192758/22765944. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((b (^y.y)) a)) REDUCED to normal form. ------ 192759/22765971. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(a a)) b)) REDUCED to normal form. ------ 192760/22765998. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) b) c)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) b) c)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) b) c)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b c)) REDUCED to normal form. ------ 192761/22766115. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))(^z.b))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.b))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 192762/22766142. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.b)(^y.(a a)))) 3. ==[ beta ]==> (((a (a a))((a a) a)) b) REDUCED to normal form. ------ 192763/22766223. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b) a)((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b) a)((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b) a)((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 192764/22766250. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.a)(^z.z))) 5. ==[ beta ]==> (((a a)(a (^x.x))) a) REDUCED to normal form. ------ 192765/22766394. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.b)(^y.b))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (b ((a (^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z) a))) 7. ==[ beta ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 192766/22766475. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> (b (((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> (b ((a a)((a a) a))) REDUCED to normal form. ------ 192767/22766583. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (a a))(b a))) 3. ==[ beta ]==> ((b a)((a (a a))(b a))) REDUCED to normal form. ------ 192768/22766610. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((^y.y) a)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)(a (^y.(^z.z)))) 7. ==[ beta ]==> (a (a (^y.(^z.z)))) 8. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 192769/22766664. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a b))((a a)((a a)(a a)))) REDUCED to normal form. ------ 192770/22766727. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 192771/22766754. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 192772/22766781. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.a))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.a))((b a)(^y.(y y)))) REDUCED to normal form. ------ 192773/22766808. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 192774/22766871. ------ 1. ==[ start ]==> (((a a)(b a))((^a.b)(a b))) 2. ==[ alpha ]==> (((a a)(b a))((^x.b)(a b))) 3. ==[ beta ]==> (((a a)(b a)) b) REDUCED to normal form. ------ 192775/22766925. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 192776/22766952. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(x x))(b a))) 3. ==[ beta ]==> (((a (a a))(a b))((b a)(b a))) REDUCED to normal form. ------ 192777/22766979. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)((^y.a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) a)((^x.a)(a (^y.(^z.z))))) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 192778/22767006. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 192779/22767033. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 192780/22767087. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 192781/22767420. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(((^y1.y1) b)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192782/22767429. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 192783/22767447. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 192784/22767474. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((b a)((^z.z) a))) 3. ==[ beta ]==> ((^y.y)((b a)((^z.z) a))) 4. ==[ alpha ]==> ((^x.x)((b a)((^y.y) a))) 5. ==[ beta ]==> ((b a)((^y.y) a)) 6. ==[ alpha ]==> ((b a)((^x.x) a)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 192785/22767528. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))((^y.y)(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^y.y)(^z.z)))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x)(^y.y)))) 11. ==[ beta ]==> (((a a)(a a))((a a)(^y.y))) 12. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 192786/22767609. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> (b ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 192787/22767717. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a a)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192788/22767762. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((^b.b)(a a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)(a a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 192789/22767789. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.z))) REDUCED to normal form. ------ 192790/22767870. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.(a a))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.(a a))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 192791/22767897. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.b)((a a) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a)) b) REDUCED to normal form. ------ 192792/22767924. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.a)(a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.a)(a b))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(a b))) 5. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 192793/22767951. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 192794/22767978. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a)(^z.z))((a a)(^z.z)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 192795/22768023. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192796/22768032. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 192797/22768059. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)((^z.z) b))) 3. ==[ beta ]==> ((a b)((^y.y)((^z.z) b))) 4. ==[ alpha ]==> ((a b)((^x.x)((^y.y) b))) 5. ==[ beta ]==> ((a b)((^y.y) b)) 6. ==[ alpha ]==> ((a b)((^x.x) b)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 192798/22768392. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(a ((^z.z) b))) 3. ==[ beta ]==> (((^y.y) b)(a ((^z.z) b))) 4. ==[ alpha ]==> (((^x.x) b)(a ((^y.y) b))) 5. ==[ beta ]==> (b (a ((^y.y) b))) 6. ==[ alpha ]==> (b (a ((^x.x) b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 192799/22768401. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.b) a)) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 192800/22768419. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 192801/22768428. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2))) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) REDUCED to normal form. ------ 192802/22768473. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 192803/22768554. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((a a) a)((a a) a))) 3. ==[ beta ]==> (b (((a a) a)((a a) a))) REDUCED to normal form. ------ 192804/22768662. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a (^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192805/22768734. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 192806/22768788. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (b a))(^y.y)) 6. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 192807/22768815. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 192808/22768842. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.b)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.b)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.b)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.b)((^y.y)(^z.z)))) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 192809/22768869. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.a)((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a b)) a) REDUCED to normal form. ------ 192810/22768896. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))(a b))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 192811/22768923. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(((^z.z)(a a))((^z.z)(a a)))) 8. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))((^z.z)(a a)))) 9. ==[ beta ]==> (((a a)(^x.x))((a a)((^z.z)(a a)))) 10. ==[ alpha ]==> (((a a)(^x.x))((a a)((^y.y)(a a)))) 11. ==[ beta ]==> (((a a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 192812/22768950. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) a) REDUCED to normal form. ------ 192813/22769004. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 192814/22769031. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((b (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((b (a a))(^x.(^y.y))) REDUCED to normal form. ------ 192815/22769337. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((b a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192816/22769373. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z)) c)) 3. ==[ beta ]==> ((b b)((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((b b)((^x.(^y.y)) c)) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 192817/22769418. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((a b)(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))((a b)(a (a a)))) REDUCED to normal form. ------ 192818/22769445. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 192819/22769499. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a (a a))(a b))) 3. ==[ beta ]==> (((b a)(b a))((a (a a))(a b))) REDUCED to normal form. ------ 192820/22769580. ------ 1. ==[ start ]==> (((^a.b)(a b))((a a)(b a))) 2. ==[ alpha ]==> (((^x.b)(a b))((a a)(b a))) 3. ==[ beta ]==> (b ((a a)(b a))) REDUCED to normal form. ------ 192821/22769643. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 192822/22769697. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a b)(^x1.(x1 x1)))) REDUCED to normal form. ------ 192823/22769724. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 192824/22769787. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(x x))(a b))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a b)(a b))) REDUCED to normal form. ------ 192825/22769814. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 192826/22769841. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 192827/22769868. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(b a))) 3. ==[ beta ]==> (((a (a a))(b a))(b a)) REDUCED to normal form. ------ 192828/22769949. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 192829/22769976. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.b)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.b)(^y.(y y)))) 5. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 192830/22770057. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(x1 x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(x1 x1))(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(z z))(^x1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b)(^x1.b))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(^x1.b))) 7. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 192831/22770084. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 192832/22770228. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((a b)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((a b)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((a b)((^x2.x2) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)((^x2.x2) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192833/22770309. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a (a a))((a a) a))) 3. ==[ beta ]==> (b ((a (a a))((a a) a))) REDUCED to normal form. ------ 192834/22770453. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((b c)((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((b c)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 192835/22770480. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a b)(^x.a))) REDUCED to normal form. ------ 192836/22770588. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.b))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.b))) REDUCED to normal form. ------ 192837/22770615. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(a a)))) REDUCED to normal form. ------ 192838/22770696. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a a) b)) REDUCED to normal form. ------ 192839/22770723. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b) c)) 3. ==[ beta ]==> (((a a)(^y.b))((a b) c)) 4. ==[ alpha ]==> (((a a)(^x.b))((a b) c)) REDUCED to normal form. ------ 192840/22771083. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c (^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c (^y.b))) 3. ==[ beta ]==> (((a b)(a a))(c (^y.b))) 4. ==[ alpha ]==> (((a b)(a a))(c (^x.b))) REDUCED to normal form. ------ 192841/22771110. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(b (^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b))(b (^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(b (^x.(a a)))) REDUCED to normal form. ------ 192842/22771191. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 192843/22771218. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((b a)((^y.a)((^z.z) a))) 6. ==[ alpha ]==> ((b a)((^x.a)((^y.y) a))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 192844/22771245. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 192845/22771299. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.a)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a) a))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 192846/22771578. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(a ((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192847/22771713. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.z))) 9. ==[ beta ]==> (a ((^y.y)(^z.z))) 10. ==[ alpha ]==> (a ((^x.x)(^y.y))) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 192848/22771740. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (^x1.x1))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a) a))) 5. ==[ beta ]==> ((a (^y.y))((a a) a)) 6. ==[ alpha ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 192849/22771803. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 192850/22771830. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((a a) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192851/22771884. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 192852/22771911. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 192853/22771938. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 192854/22771992. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b) a)) REDUCED to normal form. ------ 192855/22772019. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((a a) a) b)) 3. ==[ beta ]==> ((b (^y.(y y)))(((a a) a) b)) 4. ==[ alpha ]==> ((b (^x.(x x)))(((a a) a) b)) REDUCED to normal form. ------ 192856/22772046. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z) c)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y) c)) 5. ==[ beta ]==> ((((a a)(a a))(^x.a)) c) REDUCED to normal form. ------ 192857/22772163. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.b)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.b)) REDUCED to normal form. ------ 192858/22772298. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 192859/22772325. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b (^z.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b (^z.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (^y.a))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.a))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.a))) REDUCED to normal form. ------ 192860/22772352. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a (^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.b))) REDUCED to normal form. ------ 192861/22772406. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 192862/22772433. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> ((b (a (a a)))(a ((^y.y) a))) 8. ==[ alpha ]==> ((b (a (a a)))(a ((^x.x) a))) 9. ==[ beta ]==> ((b (a (a a)))(a a)) REDUCED to normal form. ------ 192863/22772460. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.a)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 192864/22772514. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.z)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)((a a) a))) 5. ==[ beta ]==> ((a a)((^y.y)((a a) a))) 6. ==[ alpha ]==> ((a a)((^x.x)((a a) a))) 7. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 192865/22772532. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((a a) a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((a a) a) a)) 3. ==[ beta ]==> ((a (^y.y))(((a a) a) a)) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a) a)) REDUCED to normal form. ------ 192866/22772937. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b ((a (^y.y))(^z.(z z)))) 6. ==[ alpha ]==> (b ((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 192867/22772964. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 192868/22772991. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((^x1.x1) a)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z) a)) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 192869/22773126. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 192870/22773144. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (a a))(a a))) 3. ==[ beta ]==> (b ((a (a a))(a a))) REDUCED to normal form. ------ 192871/22773288. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 192872/22773315. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 192873/22773369. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (a a)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a)) a)) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192874/22773396. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(((^z.z) a) b)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a b)) REDUCED to normal form. ------ 192875/22773414. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(c (a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(c (a (^x1.x1)))) REDUCED to normal form. ------ 192876/22773432. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 192877/22773459. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(x1 x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z z))) REDUCED to normal form. ------ 192878/22773540. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b (^x1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b (^x1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b (^z.a))) 5. ==[ beta ]==> (((^y.y) b)(b (^z.a))) 6. ==[ alpha ]==> (((^x.x) b)(b (^y.a))) 7. ==[ beta ]==> (b (b (^y.a))) 8. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 192879/22773567. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (^z.(z z)))) REDUCED to normal form. ------ 192880/22773594. ------ 1. ==[ start ]==> (((a b)(b a))((^b.a)(a a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.a)(a a))) 3. ==[ beta ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 192881/22773621. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 192882/22773648. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z) a)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y) a)) 7. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 192883/22773702. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 192884/22773729. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.a))) 7. ==[ beta ]==> ((b (^x.x))(^z.a)) 8. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 192885/22773810. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a (^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a (^x1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.a))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.a))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.a))) REDUCED to normal form. ------ 192886/22773828. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 192887/22773837. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 192888/22773864. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 192889/22773873. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a c)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a c)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a c)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192890/22773900. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(b (a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(b (a a))) 3. ==[ beta ]==> ((^y.y)(b (a a))) 4. ==[ alpha ]==> ((^x.x)(b (a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 192891/22774035. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a (a a))) 3. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 192892/22779429. ------ 1. ==[ start ]==> ((^a.(^b.b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192893/22779744. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(^c.(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192894/22785855. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192895/22785966. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 192896/22785975. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^z.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 192897/22786584. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192898/22786710. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192899/22786857. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (a (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(a (a (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 7. ==[ beta ]==> (^y.(a (a (^z.z)))) 8. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 192900/22787298. ------ 1. ==[ start ]==> ((((a a) a) a)(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 192901/22788042. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> (^y.(((^z.(z z))((^x1.x1) b))((^z.(z z))((^x1.x1) b)))) 4. ==[ alpha ]==> (^x.(((^y.(y y))((^z.z) b))((^x1.(x1 x1))((^y1.y1) b)))) 5. ==[ beta ]==> (^x.((((^z.z) b)((^z.z) b))((^x1.(x1 x1))((^y1.y1) b)))) 6. ==[ alpha ]==> (^x.((((^y.y) b)((^z.z) b))((^x1.(x1 x1))((^y1.y1) b)))) 7. ==[ beta ]==> (^x.((b ((^z.z) b))((^x1.(x1 x1))((^y1.y1) b)))) 8. ==[ alpha ]==> (^x.((b ((^y.y) b))((^z.(z z))((^x1.x1) b)))) 9. ==[ beta ]==> (^x.((b b)((^z.(z z))((^x1.x1) b)))) 10. ==[ alpha ]==> (^x.((b b)((^y.(y y))((^z.z) b)))) 11. ==[ beta ]==> (^x.((b b)(((^z.z) b)((^z.z) b)))) 12. ==[ alpha ]==> (^x.((b b)(((^y.y) b)((^z.z) b)))) 13. ==[ beta ]==> (^x.((b b)(b ((^z.z) b)))) 14. ==[ alpha ]==> (^x.((b b)(b ((^y.y) b)))) 15. ==[ beta ]==> (^x.((b b)(b b))) REDUCED to normal form. ------ 192902/22790052. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(^y.((a a)(a a)))) REDUCED to normal form. ------ 192903/22790229. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(a a))((a a) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192904/22790412. ------ 1. ==[ start ]==> (((a b)(a (a a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.(a a)))) REDUCED to normal form. ------ 192905/22791120. ------ 1. ==[ start ]==> ((^a.(^b.b))(a (^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192906/22791123. ------ 1. ==[ start ]==> ((a (^b.b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(y y)))) REDUCED to normal form. ------ 192907/22791435. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a a)(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a a)(^z.z))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192908/22791438. ------ 1. ==[ start ]==> ((a ((^a.a) b))(^c.(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.z))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 192909/22791447. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.x)(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192910/22791771. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 192911/22791780. ------ 1. ==[ start ]==> (((a a)(^b.b))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 192912/22792077. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (^y.y))(^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 192913/22792434. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((b a) b)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((b a) b)) 3. ==[ beta ]==> ((((b a) b)((b a) b))(((b a) b)((b a) b))) REDUCED to normal form. ------ 192914/22792968. ------ 1. ==[ start ]==> (((a b)(^a.b))(^c.(b a))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(b a))) REDUCED to normal form. ------ 192915/22793247. ------ 1. ==[ start ]==> (((a (a a))(b a))(^c.(^d.a))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.a))) REDUCED to normal form. ------ 192916/22794957. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192917/22795173. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.(z z)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.(z z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.(y y)))) 7. ==[ beta ]==> ((b b)(^y.(^z.(y y)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(x x)))) REDUCED to normal form. ------ 192918/22795362. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.(a z1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) a) 4. ==[ beta ]==> ((^y.(^z.z)) a) 5. ==[ alpha ]==> ((^x.(^y.y)) a) 6. ==[ beta ]==> (^y.y) 7. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192919/22795494. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 192920/22795917. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((a a) a) a)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((a a) a) a)) 3. ==[ beta ]==> ((((a a) a) a)((((a a) a) a)(^y.y))) 4. ==[ alpha ]==> ((((a a) a) a)((((a a) a) a)(^x.x))) REDUCED to normal form. ------ 192921/22796361. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^y.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 192922/22796505. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^z1.z1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 192923/22796631. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192924/22796790. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 192925/22797108. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.x1)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.x1)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.z)) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 192926/22797189. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.c)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.c)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.c)) 5. ==[ beta ]==> ((a (^y.y))(^z.c)) 6. ==[ alpha ]==> ((a (^x.x))(^y.c)) REDUCED to normal form. ------ 192927/22797240. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192928/22797252. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a (^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 192929/22797414. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (b (^y1.(^z1.z1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 192930/22797498. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 192931/22797552. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 192932/22797615. ------ 1. ==[ start ]==> (((a a) b)(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a) b)(c ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a a) b)(c (^y.y))) 4. ==[ alpha ]==> (((a a) b)(c (^x.x))) REDUCED to normal form. ------ 192933/22797633. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192934/22797642. ------ 1. ==[ start ]==> (((a (^a.a)) a)(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)(b (a (a (^y.y))))) REDUCED to normal form. ------ 192935/22797660. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 192936/22797669. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 192937/22797696. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a (^z.z)))(a a))) REDUCED to normal form. ------ 192938/22797750. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 192939/22797831. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 192940/22797858. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a) a)((b a)(a b))) 3. ==[ beta ]==> ((a a)((b a)(a b))) REDUCED to normal form. ------ 192941/22797885. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^x.a))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 192942/22797912. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1)(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((a a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a a)((a a)(^x1.x1)))) REDUCED to normal form. ------ 192943/22797939. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b)(b a))) 3. ==[ beta ]==> ((a (^y.y))((a b)(b a))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(b a))) REDUCED to normal form. ------ 192944/22798047. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a a)(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> ((a a)(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(a (b (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (b (^x.x)))) REDUCED to normal form. ------ 192945/22798092. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(b (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(b (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 192946/22798146. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 7. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 8. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 192947/22798254. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 192948/22798281. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 192949/22798299. ------ 1. ==[ start ]==> (((a a)(a (a a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(a (a a)))((b a)(^x.b))) REDUCED to normal form. ------ 192950/22798326. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 192951/22798407. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 192952/22798416. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192953/22798443. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192954/22798497. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(b (^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.a)(b (^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 7. ==[ beta ]==> ((^y.a)(b (^z.z))) 8. ==[ alpha ]==> ((^x.a)(b (^y.y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 192955/22798551. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a (a (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)((^z.z)(a (a (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 7. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 8. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 192956/22798578. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 7. ==[ beta ]==> ((^z.z)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192957/22798875. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192958/22798965. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y) b)(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.x) b)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (b (b ((^y.(^z.z)) a))) 6. ==[ alpha ]==> (b (b ((^x.(^y.y)) a))) 7. ==[ beta ]==> (b (b (^y.y))) 8. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 192959/22798992. ------ 1. ==[ start ]==> ((((a a) a) a)(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 192960/22799046. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 192961/22799073. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> ((a (^x.(x x)))(((a a)(a a)) a)) REDUCED to normal form. ------ 192962/22799100. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))(b (a (a a)))) REDUCED to normal form. ------ 192963/22799127. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192964/22799154. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((b a)((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((b a)((a a) a))) REDUCED to normal form. ------ 192965/22799343. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (b (((^y.y) a)((a a)(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)((a a)(a a)))) 5. ==[ beta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 192966/22799361. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.b)(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.b)(c (^y.(^z.z)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 192967/22799523. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.z)(a (a a)))) 3. ==[ beta ]==> (b ((^z.z)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 192968/22799550. ------ 1. ==[ start ]==> (((^a.a)(a b))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 192969/22799631. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a a)) REDUCED to normal form. ------ 192970/22799712. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192971/22799739. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((a (^x.(a a)))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(a a)))(b ((^z.z) b))) 6. ==[ alpha ]==> ((a (^x.(a a)))(b ((^y.y) b))) 7. ==[ beta ]==> ((a (^x.(a a)))(b b)) REDUCED to normal form. ------ 192972/22799757. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(a (^x.(a a)))) REDUCED to normal form. ------ 192973/22799838. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y) a)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x) a)) 5. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 192974/22799865. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((b (^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((b (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((b (^z.z)) b)) 5. ==[ beta ]==> (((^y.y) a)((b (^z.z)) b)) 6. ==[ alpha ]==> (((^x.x) a)((b (^y.y)) b)) 7. ==[ beta ]==> (a ((b (^y.y)) b)) 8. ==[ alpha ]==> (a ((b (^x.x)) b)) REDUCED to normal form. ------ 192975/22799955. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 192976/22800036. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> ((^y.(a a))(^z.(a a))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 192977/22800117. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192978/22800171. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((a a)((^y.a)(^z.(a a)))) 6. ==[ alpha ]==> ((a a)((^x.a)(^y.(a a)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 192979/22800180. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(c ((a a)(a a)))) REDUCED to normal form. ------ 192980/22800207. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(b (b (^z.z)))) REDUCED to normal form. ------ 192981/22800261. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b (^z.z))(a a))) REDUCED to normal form. ------ 192982/22800288. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(((a a)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(((a a)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(y y))(((a a)(a a))(a (^z.z)))) 6. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(a (^y.y)))) 7. ==[ beta ]==> ((((a a)(a a))(a (^y.y)))(((a a)(a a))(a (^y.y)))) 8. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 192983/22800315. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(b ((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(b ((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(^x.a))(b a)) REDUCED to normal form. ------ 192984/22800342. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) REDUCED to normal form. ------ 192985/22800369. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))((b a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 192986/22800558. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (b (((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (b (a ((^y.y) b))) 6. ==[ alpha ]==> (b (a ((^x.x) b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 192987/22800792. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 192988/22800900. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 192989/22800954. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.a)((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.a)((^y.y) b))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 192990/22801611. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(((a a) a)(a a))) REDUCED to normal form. ------ 192991/22801719. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(a a)))((a (^y.y)) b)) REDUCED to normal form. ------ 192992/22801737. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(b (^y.(a a)))) 3. ==[ beta ]==> (((a b)(a b))(b (^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(b (^x.(a a)))) REDUCED to normal form. ------ 192993/22801746. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a a)((a a)(a a)))) REDUCED to normal form. ------ 192994/22801818. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 192995/22801926. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))((a a) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 192996/22801944. ------ 1. ==[ start ]==> (((a a)(b a))((a b)(^a.b))) 2. ==[ alpha ]==> (((a a)(b a))((a b)(^x.b))) REDUCED to normal form. ------ 192997/22801971. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a) a)(^z.(a a)))) REDUCED to normal form. ------ 192998/22802052. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a) a)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(a (^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a a) a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 192999/22802079. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 193000/22802106. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a a)(^x.(a a)))) REDUCED to normal form. ------ 193001/22802133. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((a a)(a a)) a)) 3. ==[ beta ]==> (((a a)((^y.y) a))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)(a a)) a)) 5. ==[ beta ]==> (((a a) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 193002/22802160. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z) b) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(b b)) REDUCED to normal form. ------ 193003/22802304. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.b)(^x1.b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.b)(^x1.b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.b)(^x1.b))) 5. ==[ beta ]==> ((a a)((^z.b)(^x1.b))) 6. ==[ alpha ]==> ((a a)((^x.b)(^y.b))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 193004/22802502. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b (a a))) REDUCED to normal form. ------ 193005/22802529. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a (^x1.(^y1.y1)))(a (^z1.z1)))) REDUCED to normal form. ------ 193006/22802610. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(^x.(a a)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 193007/22802637. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a b)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a b)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a b)((a a) a))) 5. ==[ beta ]==> ((^y.b)((a b)((a a) a))) 6. ==[ alpha ]==> ((^x.b)((a b)((a a) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 193008/22802691. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(a a))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(a a))) 7. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 193009/22802718. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 193010/22802745. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a (b a))) REDUCED to normal form. ------ 193011/22802790. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(b (^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(b (^x1.x1))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193012/22802799. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a) b)) REDUCED to normal form. ------ 193013/22802817. ------ 1. ==[ start ]==> ((a (^b.b))(a (^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 193014/22802835. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(b (^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(b (^z.z))) REDUCED to normal form. ------ 193015/22802862. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 193016/22802889. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((b a)(^z.a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((b a)(^z.a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)(^y.a))) REDUCED to normal form. ------ 193017/22802916. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((a a)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 193018/22802943. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)((a a)(^y.(^z.z)))) 8. ==[ alpha ]==> ((a b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 193019/22802970. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)(^x.a))) REDUCED to normal form. ------ 193020/22802997. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((a a) a)(^z.b))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a) a)(^z.b))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a) a)(^y.b))) REDUCED to normal form. ------ 193021/22803024. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (((a a)(a (a a)))(^y.(a a))) 8. ==[ alpha ]==> (((a a)(a (a a)))(^x.(a a))) REDUCED to normal form. ------ 193022/22803105. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 193023/22803132. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a a)(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a a)(^y.y))) 3. ==[ beta ]==> ((a b)((a a)(^y.y))) 4. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 193024/22803141. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((^y.y)((^z.z) b)) 6. ==[ alpha ]==> ((^x.x)((^y.y) b)) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 193025/22803168. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1)(^x2.x2))) 3. ==[ beta ]==> ((^y.y)((^z1.z1)(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193026/22803303. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.b)(^x1.a))) 3. ==[ beta ]==> (b ((^z.b)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.b)(^y.a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 193027/22803420. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(c (b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(c (b a))) REDUCED to normal form. ------ 193028/22803447. ------ 1. ==[ start ]==> ((((^a.a) b) a)(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)(b (a (^y.(^z.z))))) 3. ==[ beta ]==> ((b a)(b (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((b a)(b (a (^x.(^y.y))))) REDUCED to normal form. ------ 193029/22803465. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193030/22803474. ------ 1. ==[ start ]==> (((a a)(^b.b))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y) b))) 3. ==[ beta ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 193031/22803501. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a a))) REDUCED to normal form. ------ 193032/22803582. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((^x1.x1)(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((^x1.x1)(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))(((^z.z)(a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.(a a))(((^y.y)(a a))(a (a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193033/22803609. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a b)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((a b)(^y.y))) REDUCED to normal form. ------ 193034/22803636. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 193035/22803663. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(a b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(a b))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a b))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 193036/22803690. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a (a a))(a a))) REDUCED to normal form. ------ 193037/22803744. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(b a))) REDUCED to normal form. ------ 193038/22803771. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b (^y.y))((a a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 193039/22803807. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a a) b)((a (^y.(^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 193040/22803834. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((b a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 193041/22803861. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> ((a (b a))(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> ((a (b a))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 193042/22803888. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 193043/22803915. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a b)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)((a b)(^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 193044/22803942. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((a a) a)(^x.a))) REDUCED to normal form. ------ 193045/22803969. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(^y.y))(^z.b))) 3. ==[ beta ]==> (((a b)((a a) a))((^y.y)(^z.b))) 4. ==[ alpha ]==> (((a b)((a a) a))((^x.x)(^y.b))) 5. ==[ beta ]==> (((a b)((a a) a))(^y.b)) 6. ==[ alpha ]==> (((a b)((a a) a))(^x.b)) REDUCED to normal form. ------ 193046/22803996. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (a a))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 193047/22804077. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 193048/22804104. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a (^y.(^z.z))) a)) 3. ==[ beta ]==> ((b (a a))((a (^y.(^z.z))) a)) 4. ==[ alpha ]==> ((b (a a))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 193049/22804131. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((b a) b)) REDUCED to normal form. ------ 193050/22804167. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193051/22804302. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (b ((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 193052/22804446. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((b b)(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((b b)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 193053/22804473. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a a)((^y.y) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a a)((^x.x) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a a) a)) REDUCED to normal form. ------ 193054/22804527. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a) a)(^z.z))) REDUCED to normal form. ------ 193055/22804554. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((a a) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))((a a) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)((a a) a))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)((a a) a))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 193056/22804635. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 193057/22804662. ------ 1. ==[ start ]==> (((a b)(^a.b))((a a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.b))((a a)(b a))) REDUCED to normal form. ------ 193058/22804761. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((^y1.(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193059/22804860. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a (a a))(^x.b))) REDUCED to normal form. ------ 193060/22804887. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(a (^z.(a a)))) 6. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.(a a)))) REDUCED to normal form. ------ 193061/22804968. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((b a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((b a) a)) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((b a) a)) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b a) a)) 5. ==[ beta ]==> (((a a)(^y.y))((b a) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((b a) a)) REDUCED to normal form. ------ 193062/22804995. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a)(^y.y)) b)) 3. ==[ beta ]==> ((((a a) a)(a a))(((a a)(^y.y)) b)) 4. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 193063/22805022. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a)) c)) 3. ==[ beta ]==> (((a b)(a b))((a a) c)) REDUCED to normal form. ------ 193064/22805598. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 193065/22805625. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193066/22805679. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.a)(a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.a)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.a)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) a) REDUCED to normal form. ------ 193067/22805760. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193068/22805868. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193069/22805994. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 193070/22806021. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 193071/22806048. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b) c)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b) c)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b) c)) 5. ==[ beta ]==> ((a b)((^y.b) c)) 6. ==[ alpha ]==> ((a b)((^x.b) c)) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 193072/22806264. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 193073/22806291. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((a a) a)(^y.a))) 5. ==[ beta ]==> ((b a)(((a a) a)(^y.a))) 6. ==[ alpha ]==> ((b a)(((a a) a)(^x.a))) REDUCED to normal form. ------ 193074/22806318. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(^z.(z z))) 6. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 193075/22806462. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.z))) 7. ==[ beta ]==> ((^y.(a a))(^z.z)) 8. ==[ alpha ]==> ((^x.(a a))(^y.y)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193076/22806543. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193077/22806651. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193078/22806768. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a (a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y) a)((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x) a)((a (a a))(a (a a)))) 5. ==[ beta ]==> (a ((a (a a))(a (a a)))) REDUCED to normal form. ------ 193079/22806813. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c (^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c (^x1.a))) 3. ==[ beta ]==> ((^y.y)(c (^x1.a))) 4. ==[ alpha ]==> ((^x.x)(c (^y.a))) 5. ==[ beta ]==> (c (^y.a)) 6. ==[ alpha ]==> (c (^x.a)) REDUCED to normal form. ------ 193080/22806867. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(a (^z.(a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(a (^z.(a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(a (^z.(a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))(a (^z.(a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(a (^y.(a a)))) 7. ==[ beta ]==> ((b b)(a (^y.(a a)))) 8. ==[ alpha ]==> ((b b)(a (^x.(a a)))) REDUCED to normal form. ------ 193081/22806948. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193082/22807056. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.z1)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193083/22807191. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 193084/22807263. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.b) a)) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.b) a)) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.b) a)) 5. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 193085/22807290. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^c.a) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a) b)) 3. ==[ beta ]==> (((a (a a)) b)((^y.a) b)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a) b)) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 193086/22807317. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1)) c)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1)) c)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1)) c)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1)) c)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) c)) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 193087/22807479. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.(^z1.z1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.y1))) REDUCED to normal form. ------ 193088/22807506. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (a a))(^y.a))) 3. ==[ beta ]==> ((b (a (a a)))((a (a a))(^y.a))) 4. ==[ alpha ]==> ((b (a (a a)))((a (a a))(^x.a))) REDUCED to normal form. ------ 193089/22807533. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y) a)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)(^y.(y y)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a (^y.(y y)))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.(x x)))) REDUCED to normal form. ------ 193090/22807614. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((a a) a) a)) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((a a) a) a)) REDUCED to normal form. ------ 193091/22808010. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c d)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c d)) 3. ==[ beta ]==> (((^y.y) b)(c d)) 4. ==[ alpha ]==> (((^x.x) b)(c d)) 5. ==[ beta ]==> (b (c d)) REDUCED to normal form. ------ 193092/22808028. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 7. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 8. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193093/22808055. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 193094/22808082. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193095/22808136. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a)(^y.a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 193096/22808172. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (a (a a)))) 5. ==[ beta ]==> ((^y.y)(b (a (a a)))) 6. ==[ alpha ]==> ((^x.x)(b (a (a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 193097/22808199. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 193098/22808280. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z)) a)) REDUCED to normal form. ------ 193099/22808325. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193100/22808460. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 193101/22808487. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 193102/22808559. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(z z)) a)) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(z z)) a)) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y)) a)) 5. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 193103/22808586. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^b.a) b)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.a) b)) 3. ==[ beta ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 193104/22808613. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) c)) 7. ==[ beta ]==> (b ((^y.(^z.z)) c)) 8. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193105/22808667. ------ 1. ==[ start ]==> (((a b)(b a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))(((^x.x) a)(^y.y))) 3. ==[ beta ]==> (((a b)(b a))(a (^y.y))) 4. ==[ alpha ]==> (((a b)(b a))(a (^x.x))) REDUCED to normal form. ------ 193106/22808694. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 193107/22808721. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a a)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a a)(^y.a))) REDUCED to normal form. ------ 193108/22808775. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a (^z.z)) b)) REDUCED to normal form. ------ 193109/22808802. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a) c)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a) c)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a) c)) 5. ==[ beta ]==> ((b (^y.y))((a a) c)) 6. ==[ alpha ]==> ((b (^x.x))((a a) c)) REDUCED to normal form. ------ 193110/22808829. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^b.a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.a) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (a a))) a) REDUCED to normal form. ------ 193111/22808901. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(c a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(c a)) 3. ==[ beta ]==> ((b (^y.y))(c a)) 4. ==[ alpha ]==> ((b (^x.x))(c a)) REDUCED to normal form. ------ 193112/22808910. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 193113/22808937. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 193114/22808946. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193115/22808973. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193116/22809108. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> (b ((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> (b ((^x.x)(^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193117/22821066. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 193118/22821108. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> (^y.((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> (^x.((^y.(y (^z.z))) b)) 5. ==[ beta ]==> (^x.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 193119/22821180. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((a a)(a a))(a (a a)))) 3. ==[ eta ]==> ((^y.y)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 193120/22821450. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((((^y.y) a)(b (^z.z)))((((^y.y) a)(b (^z.z)))(((^y.y) a)(b (^z.z))))) 4. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((((^z.z) a)(b (^x1.x1)))(((^y1.y1) a)(b (^z1.z1))))) 5. ==[ beta ]==> ((a (b (^y.y)))((((^z.z) a)(b (^x1.x1)))(((^y1.y1) a)(b (^z1.z1))))) 6. ==[ alpha ]==> ((a (b (^x.x)))((((^y.y) a)(b (^z.z)))(((^x1.x1) a)(b (^y1.y1))))) 7. ==[ beta ]==> ((a (b (^x.x)))((a (b (^z.z)))(((^x1.x1) a)(b (^y1.y1))))) 8. ==[ alpha ]==> ((a (b (^x.x)))((a (b (^y.y)))(((^z.z) a)(b (^x1.x1))))) 9. ==[ beta ]==> ((a (b (^x.x)))((a (b (^y.y)))(a (b (^x1.x1))))) 10. ==[ alpha ]==> ((a (b (^x.x)))((a (b (^y.y)))(a (b (^z.z))))) REDUCED to normal form. ------ 193121/22821525. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a b)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 193122/22821675. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193123/22821957. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 193124/22822389. ------ 1. ==[ start ]==> ((((a a) a) a)(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 193125/22822746. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y) a)((a a)(a a))) b) 4. ==[ alpha ]==> ((((^x.x) a)((a a)(a a))) b) 5. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 193126/22823133. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (a a))(^z.z))) 3. ==[ beta ]==> (^y.(((a (a a))(^z.z))((a (a a))(^z.z)))) 4. ==[ alpha ]==> (^x.(((a (a a))(^y.y))((a (a a))(^z.z)))) REDUCED to normal form. ------ 193127/22824015. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a a)(b (^z.z)))) 3. ==[ beta ]==> ((((a a)(b (^z.z)))((a a)(b (^z.z))))(^y.y)) 4. ==[ alpha ]==> ((((a a)(b (^x.x)))((a a)(b (^y.y))))(^z.z)) REDUCED to normal form. ------ 193128/22824414. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 193129/22824771. ------ 1. ==[ start ]==> ((^a.(b a))(b ((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(b x))(b ((a a)(a a)))) 3. ==[ eta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 193130/22826538. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193131/22826871. ------ 1. ==[ start ]==> (((a a)(^b.b))(^b.(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 193132/22828605. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(b ((a a)(^z.z)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193133/22829391. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 193134/22830273. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(y y)))) REDUCED to normal form. ------ 193135/22830462. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(a y1))) 3. ==[ eta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 193136/22830660. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.(y b))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(y b))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(x b))) REDUCED to normal form. ------ 193137/22830822. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^c.((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.((a a) a))) REDUCED to normal form. ------ 193138/22831002. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.((a a) a))) 3. ==[ beta ]==> ((a (^y.y))(^z.((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((a a) a))) REDUCED to normal form. ------ 193139/22831461. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 193140/22831596. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 193141/22831839. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193142/22831881. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(((^a.a) a) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 193143/22831956. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(z (z z)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(z (z z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(y (y y)))) REDUCED to normal form. ------ 193144/22832226. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.((^y.y) x))) 3. ==[ eta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 193145/22832298. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.z))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.z))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.y))) REDUCED to normal form. ------ 193146/22832331. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(b b)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193147/22832343. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193148/22832505. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^c.a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> (b (^y1.a)) 4. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 193149/22832607. ------ 1. ==[ start ]==> (((a a) a)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) a)((^x.b)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 193150/22832661. ------ 1. ==[ start ]==> (((^a.a) b)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193151/22832742. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 193152/22832769. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 193153/22832787. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193154/22832814. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.a))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> ((a (^x.a))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.a))(b (^y.y))) REDUCED to normal form. ------ 193155/22832832. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.y))) REDUCED to normal form. ------ 193156/22832859. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((b (^y.y)) a)) REDUCED to normal form. ------ 193157/22832886. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 193158/22833075. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a) a)(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a) a)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 193159/22833102. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1) b)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z) b)) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 193160/22833129. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 193161/22833156. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> ((a (a (a a)))(a (b (^y.y)))) 4. ==[ alpha ]==> ((a (a (a a)))(a (b (^x.x)))) REDUCED to normal form. ------ 193162/22833228. ------ 1. ==[ start ]==> ((((^a.a) a) b)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a b)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 193163/22833246. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 7. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 193164/22833255. ------ 1. ==[ start ]==> (((a (a a)) a)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a)) a)((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> (((a (a a)) a)((a a)(^y.y))) 4. ==[ alpha ]==> (((a (a a)) a)((a a)(^x.x))) REDUCED to normal form. ------ 193165/22833273. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 193166/22833300. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 193167/22833354. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(b (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 193168/22833363. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 193169/22833381. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 193170/22833471. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((b b)((^y.(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((b b)((^x.(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 193171/22833516. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193172/22833543. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193173/22833606. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.a)(b (^y.y)))) 3. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 193174/22833633. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (a ((^y.(^z.z))((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 193175/22833651. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 7. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 8. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 193176/22833660. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 193177/22833678. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a (a (^z.z))) a)) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z))) a)) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 5. ==[ beta ]==> ((a (a (^y.y))) a) 6. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 193178/22833687. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^y1.y1)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 193179/22833732. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((b (^z.z)) c)) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((b (^z.z)) c)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 193180/22834092. ------ 1. ==[ start ]==> ((((a a) a) a)((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((((a a) a) a)(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((((a a) a) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 193181/22834110. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a a) a)((^y.(y (^z.z))) a)) 4. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y))) a)) 5. ==[ beta ]==> (((a a) a)(a (^y.y))) 6. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 193182/22834290. ------ 1. ==[ start ]==> (((a a)((a a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)((a a) a))(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 193183/22834317. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 193184/22834344. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a b)((a a)(^y.y)))) 3. ==[ beta ]==> ((a (a (a a)))((a b)((a a)(^y.y)))) 4. ==[ alpha ]==> ((a (a (a a)))((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 193185/22834371. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((a a) a)(b a))) 3. ==[ beta ]==> (((a (a a)) a)(((a a) a)(b a))) REDUCED to normal form. ------ 193186/22834398. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.(^x1.x1))))) 9. ==[ beta ]==> ((a (^x.x))(a (^z.(^x1.x1)))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 193187/22834425. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a (a a))((^x.x) b))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (a a)) b)) REDUCED to normal form. ------ 193188/22834452. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (a b))(a ((a a)(a a)))) REDUCED to normal form. ------ 193189/22834542. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.(^x1.x1)) a)(^y1.y1))) IRREDUCIBLE: cycle. ------ 193190/22834605. ------ 1. ==[ start ]==> ((((a a) a) b)((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a) b)((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a) a) b)(a a)) REDUCED to normal form. ------ 193191/22834623. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> (b (b (^y.(y y)))) 6. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 193192/22834632. ------ 1. ==[ start ]==> (((a b) a)((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a b) a)((^x.x)(a (a a)))) 3. ==[ beta ]==> (((a b) a)(a (a a))) REDUCED to normal form. ------ 193193/22834650. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 193194/22834659. ------ 1. ==[ start ]==> (((a a)(^a.b))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 193195/22834677. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.a))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 193196/22834713. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 193197/22834731. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(^y.(a a)))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)(^x.(a a)))) REDUCED to normal form. ------ 193198/22834740. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a a)) REDUCED to normal form. ------ 193199/22834767. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 193200/22834812. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 193201/22834821. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 193202/22834839. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (a a))(^y.y))) REDUCED to normal form. ------ 193203/22835010. ------ 1. ==[ start ]==> (((^a.b) b)((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(a a))(^z.a))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 193204/22835226. ------ 1. ==[ start ]==> (((a b) b)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 193205/22835253. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a a) a)((^y.(y y))(^z.z))) 4. ==[ alpha ]==> (((a a) a)((^x.(x x))(^y.y))) 5. ==[ beta ]==> (((a a) a)((^y.y)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 193206/22835280. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 193207/22835505. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 193208/22835532. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(a b))((a a)(a b))) REDUCED to normal form. ------ 193209/22835559. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((a b)((^x.x)(a a)))) 5. ==[ beta ]==> ((a ((a a) a))((a b)(a a))) REDUCED to normal form. ------ 193210/22835586. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 193211/22835613. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(b a))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(b a))) 7. ==[ beta ]==> ((a (a a))((^y.y)(b a))) 8. ==[ alpha ]==> ((a (a a))((^x.x)(b a))) 9. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 193212/22835640. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> ((((a a) a) a)((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((((a a) a) a)((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 193213/22835658. ------ 1. ==[ start ]==> (((^a.b) c)(d (^b.b))) 2. ==[ alpha ]==> (((^x.b) c)(d (^y.y))) 3. ==[ beta ]==> (b (d (^y.y))) 4. ==[ alpha ]==> (b (d (^x.x))) REDUCED to normal form. ------ 193214/22835667. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a ((^z.z) b))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(a ((^y.y) b))) 5. ==[ beta ]==> (((a b)(a (^x.x)))(a b)) REDUCED to normal form. ------ 193215/22835694. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 193216/22835721. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(b (^y.y)))) REDUCED to normal form. ------ 193217/22835757. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 193218/22835892. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 193219/22835901. ------ 1. ==[ start ]==> (((a b) c)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 193220/22835928. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(a a))(a b))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(a b))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(a b))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 193221/22835955. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 193222/22836009. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 193223/22836036. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.b))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.b))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 193224/22836054. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) a)(^y.y))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a (^y.y))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(a (^x.x))) REDUCED to normal form. ------ 193225/22836090. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193226/22836117. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 193227/22836135. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((b (^z.z)) a)) 3. ==[ beta ]==> (b ((b (^z.z)) a)) 4. ==[ alpha ]==> (b ((b (^x.x)) a)) REDUCED to normal form. ------ 193228/22836198. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.a)) REDUCED to normal form. ------ 193229/22836477. ------ 1. ==[ start ]==> ((a (b a))(b ((a a)(a a)))) REDUCED to normal form. ------ 193230/22836567. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.z) c)) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.z) c)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z) c)) 5. ==[ beta ]==> (b ((^z.z) c)) 6. ==[ alpha ]==> (b ((^x.x) c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 193231/22836819. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(c (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(c (^z.z))) 3. ==[ beta ]==> ((a (^y.(a a)))(c (^z.z))) 4. ==[ alpha ]==> ((a (^x.(a a)))(c (^y.y))) REDUCED to normal form. ------ 193232/22836846. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(b (^y.(a a)))) REDUCED to normal form. ------ 193233/22836900. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 193234/22836918. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> (b (b (^y.(^z.z)))) 6. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 193235/22836927. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 193236/22836954. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 193237/22837305. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193238/22837620. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.b) b)) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 193239/22837647. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) c)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) c) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) c) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193240/22837899. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(b (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (^x1.x1))) REDUCED to normal form. ------ 193241/22838196. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193242/22838241. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z))) 3. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 193243/22838268. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1) b) a)) 3. ==[ beta ]==> ((^y.y)(((^z1.z1) b) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b) a)) 5. ==[ beta ]==> (((^y.y) b) a) 6. ==[ alpha ]==> (((^x.x) b) a) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 193244/22838547. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 193245/22838574. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 193246/22838592. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> ((^y.y)((^y1.y1) a)) 4. ==[ alpha ]==> ((^x.x)((^y.y) a)) 5. ==[ beta ]==> ((^y.y) a) 6. ==[ alpha ]==> ((^x.x) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 193247/22838871. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(b (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 193248/22839267. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a)(^x1.x1)) c)) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1)) c)) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y)) c)) 5. ==[ beta ]==> (((a a)(^y.y)) c) 6. ==[ alpha ]==> (((a a)(^x.x)) c) REDUCED to normal form. ------ 193249/22839510. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.(^x2.x2))) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2))) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193250/22839735. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(c (^y.(^z.z)))) REDUCED to normal form. ------ 193251/22839861. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1)(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193252/22839870. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a a)) REDUCED to normal form. ------ 193253/22839897. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.b)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.b)(a (a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y))) b) REDUCED to normal form. ------ 193254/22840311. ------ 1. ==[ start ]==> ((a (b (^a.a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(b ((a a)(^y.y)))) REDUCED to normal form. ------ 193255/22840401. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(a a)) c)) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(a a)) c)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(a a)) c)) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(a a)) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193256/22840626. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((b c)((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((b c)((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 193257/22840653. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a a)) REDUCED to normal form. ------ 193258/22840698. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> ((b (^y.y))(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 193259/22840725. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193260/22840761. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 193261/22840779. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)(^z1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^z1.b))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (^y1.b))) REDUCED to normal form. ------ 193262/22840788. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.a)(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 193263/22840860. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((a a)(^z.z)) a)) 3. ==[ beta ]==> (b (((a a)(^z.z)) a)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 193264/22840869. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 193265/22840896. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 193266/22840977. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 193267/22841004. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((b (^x.a))((^z.a)(^z.a))) 6. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.a))) 7. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 193268/22841031. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 193269/22841094. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 193270/22841121. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 193271/22841148. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((a ((^y.y) b))((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((a b)(a (^y.y)))) 5. ==[ beta ]==> ((a b)((a b)(a (^y.y)))) 6. ==[ alpha ]==> ((a b)((a b)(a (^x.x)))) REDUCED to normal form. ------ 193272/22841175. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(((a a) a) a)) REDUCED to normal form. ------ 193273/22841202. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(a (a a)))) 7. ==[ beta ]==> ((b a)((^y.y)(a (a a)))) 8. ==[ alpha ]==> ((b a)((^x.x)(a (a a)))) 9. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 193274/22841229. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 193275/22841256. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)((a a) a))) 5. ==[ beta ]==> (((a b)(a a))(a ((a a) a))) REDUCED to normal form. ------ 193276/22841283. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a (^y.y))(a b))) 3. ==[ beta ]==> (((a a)(a b))((a (^y.y))(a b))) 4. ==[ alpha ]==> (((a a)(a b))((a (^x.x))(a b))) REDUCED to normal form. ------ 193277/22841310. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((a a)(a a))) REDUCED to normal form. ------ 193278/22841562. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(a a)) a)) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a)) a)) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a)) a)) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a)) a)) 7. ==[ beta ]==> (((^y.y)(a a)) a) 8. ==[ alpha ]==> (((^x.x)(a a)) a) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 193279/22841643. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(^a.a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1)) d)) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1)) d)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) d)) 5. ==[ beta ]==> (b ((^y.y) d)) 6. ==[ alpha ]==> (b ((^x.x) d)) 7. ==[ beta ]==> (b d) REDUCED to normal form. ------ 193280/22841976. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 193281/22842003. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.b)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b)(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b)(a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193282/22842048. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.a))) 5. ==[ beta ]==> (b ((^y.y)(^z.a))) 6. ==[ alpha ]==> (b ((^x.x)(^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 193283/22842057. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 193284/22842084. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 193285/22842111. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 193286/22842156. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a a)(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193287/22842165. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a b)) REDUCED to normal form. ------ 193288/22842192. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.b)(^z.z))) 5. ==[ beta ]==> ((b (^x.(x x))) b) REDUCED to normal form. ------ 193289/22842219. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 193290/22842273. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(z z)))) 7. ==[ beta ]==> ((^y.(y y))(^z.(z z))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) 9. ==[ beta ]==> ((^y.(y y))(^y.(y y))) 10. ==[ alpha ]==> ((^x.(x x))(^y.(y y))) IRREDUCIBLE: cycle. ------ 193291/22842336. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 193292/22842363. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(a (a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(a (a b))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a (a b))) REDUCED to normal form. ------ 193293/22842390. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((a a) a)(a a))) 3. ==[ beta ]==> (((a (a a)) b)(((a a) a)(a a))) REDUCED to normal form. ------ 193294/22842417. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(a (^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (^x1.x1)))) 9. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 10. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 193295/22842444. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((a (a a))((^x.x) a))) 3. ==[ beta ]==> ((((a a) a)(b a))((a (a a)) a)) REDUCED to normal form. ------ 193296/22842471. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (a (a a)))) REDUCED to normal form. ------ 193297/22842498. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((a (^y.y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((a (^x.x))(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 193298/22842525. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a a)((a a) a))) REDUCED to normal form. ------ 193299/22842705. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.z)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((a a) a))) 5. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 193300/22842723. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((a a) a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((a a) a) a)) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((a a) a) a)) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a) a) a)) 5. ==[ beta ]==> ((((a a) a) a)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 193301/22843110. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)((^z.z) a))) 5. ==[ beta ]==> (b ((^y.a)((^z.z) a))) 6. ==[ alpha ]==> (b ((^x.a)((^y.y) a))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 193302/22843128. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((a (^y.y))(^z.(z z))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 193303/22843137. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 193304/22843155. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 193305/22843164. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 193306/22843182. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1)(^z1.z1)) a)) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1)) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) a)) 5. ==[ beta ]==> (((^y.y)(^z.z)) a) 6. ==[ alpha ]==> (((^x.x)(^y.y)) a) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 193307/22843272. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193308/22843299. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 193309/22843317. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z)) a)) 3. ==[ beta ]==> (b ((^y.(^z.z)) a)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193310/22843380. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c (^z.a))) REDUCED to normal form. ------ 193311/22843461. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))(a a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a)(a a))) REDUCED to normal form. ------ 193312/22843488. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 193313/22843542. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193314/22843560. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (a a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (a a)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a)) a)) REDUCED to normal form. ------ 193315/22843569. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 193316/22843587. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(((^a.a) a) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a) b)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a b)) REDUCED to normal form. ------ 193317/22843632. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b ((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b ((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(b a)) REDUCED to normal form. ------ 193318/22843659. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a (a (a a)))) 3. ==[ beta ]==> ((a (b (^y.y)))(a (a (a a)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (a (a a)))) REDUCED to normal form. ------ 193319/22843686. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(((^x.x) a)(a a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 193320/22843713. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((a (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(a (^z.z)))) 7. ==[ beta ]==> (b ((a (^y.y))(a (^z.z)))) 8. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 193321/22843740. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))((a a) a)) REDUCED to normal form. ------ 193322/22843821. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b c)) REDUCED to normal form. ------ 193323/22843902. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b (a (^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b (a (^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b (a (^z.z)))) 5. ==[ beta ]==> ((b (^y.y))(b (a (^z.z)))) 6. ==[ alpha ]==> ((b (^x.x))(b (a (^y.y)))) REDUCED to normal form. ------ 193324/22843929. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(a ((^x.x) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(a a)) REDUCED to normal form. ------ 193325/22843983. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(a (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(a (^y.y)))) REDUCED to normal form. ------ 193326/22844001. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a (^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a (^z.a))) 3. ==[ beta ]==> ((b (^y.y))(a (^z.a))) 4. ==[ alpha ]==> ((b (^x.x))(a (^y.a))) REDUCED to normal form. ------ 193327/22844037. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(b b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 193328/22844046. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193329/22844073. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a (^y1.y1)) a)) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.x)((a (^y.y)) a)) 5. ==[ beta ]==> ((a (^y.y)) a) 6. ==[ alpha ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 193330/22844208. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a a) a)) 3. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 193331/22849620. ------ 1. ==[ start ]==> ((^a.(^b.b))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193332/22854417. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^b.((a a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.((a a) a))) 3. ==[ beta ]==> ((^z.((a a) a))((^z.((a a) a))(^y.y))) 4. ==[ alpha ]==> ((^x.((a a) a))((^y.((a a) a))(^z.z))) 5. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 193333/22856028. ------ 1. ==[ start ]==> ((^a.b)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.b)((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 193334/22856202. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 193335/22856226. ------ 1. ==[ start ]==> ((^a.(^b.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.x))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> (^y.((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> (^x.((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 193336/22856469. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a b)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a b)(b a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 193337/22856919. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.b)(b a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193338/22857075. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 193339/22857525. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> (((a a) a)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> (((a a) a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 193340/22857684. ------ 1. ==[ start ]==> ((^a.(^a.b))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))((b a)((a a) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 193341/22858353. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^x.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 193342/22858458. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.(x1 x1)))((^z.z)(^x1.(x1 x1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.(z z)))((^x1.x1)(^y1.(y1 y1))))) 5. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.x1)(^y1.(y1 y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(x1 x1)))) 7. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.(z z)))) 9. ==[ beta ]==> (((^y.y)(^z.(z z)))((^y.y)(^z.(z z)))) 10. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.z)(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 193343/22858767. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> (((^x.(x x))((^y.y)(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.z1))) 7. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(^z1.z1))) 8. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(^y1.y1))) 9. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.y1))) 10. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.x1))) 11. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 12. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 13. ==[ beta ]==> (^y.(^z.z)) 14. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193344/22859889. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))(^x1.(a a)))) 3. ==[ eta ]==> (b ((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193345/22860648. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(^y.((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)(^y.((a a)(a a)))) 6. ==[ alpha ]==> (((a a) a)(^x.((a a)(a a)))) REDUCED to normal form. ------ 193346/22860726. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (((^x1.(^y1.(^z1.z1)))(^x2.a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193347/22861008. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(^y1.((y1 y1)(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((y1 y1)(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((z z)(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193348/22861329. ------ 1. ==[ start ]==> ((^a.(^b.b))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z) b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193349/22861332. ------ 1. ==[ start ]==> ((a (^b.b))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) b))) 3. ==[ beta ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 193350/22861644. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 193351/22862007. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(^y1.((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) b))) 5. ==[ beta ]==> (^y.((^z.z) b)) 6. ==[ alpha ]==> (^x.((^y.y) b)) 7. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 193352/22862322. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^a.(^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(^z.z))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 193353/22862619. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b (a a))(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b (a a))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 193354/22862643. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((((^y.(^z.(^x1.x1)))(^y1.y1))((^y.(^z.(^x1.x1)))(^y1.y1)))(((^y.(^z.(^x1.x1)))(^y1.y1))((^y.(^z.(^x1.x1)))(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.(^x2.x2)))(^y2.y2)))(((^z2.(^x3.(^y3.y3)))(^z3.z3))((^x4.(^y4.(^z4.z4)))(^x5.x5)))) 5. ==[ beta ]==> (((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.y2)))(((^z2.(^x3.(^y3.y3)))(^z3.z3))((^x4.(^y4.(^z4.z4)))(^x5.x5)))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1)))(((^x2.(^y2.(^z2.z2)))(^x3.x3))((^y3.(^z3.(^x4.x4)))(^y4.y4)))) 7. ==[ beta ]==> ((^y.y)(((^x2.(^y2.(^z2.z2)))(^x3.x3))((^y3.(^z3.(^x4.x4)))(^y4.y4)))) 8. ==[ alpha ]==> ((^x.x)(((^y.(^z.(^x1.x1)))(^y1.y1))((^z1.(^x2.(^y2.y2)))(^z2.z2)))) 9. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.y1))((^z1.(^x2.(^y2.y2)))(^z2.z2))) 10. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 11. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 12. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193355/22862925. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.(y1 (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(y1 (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193356/22863483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(^x1.(x1 a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(^x1.(x1 a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.(z a))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(z a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y a))) REDUCED to normal form. ------ 193357/22863723. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193358/22864509. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 193359/22864884. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193360/22865382. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^c.(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(a b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(a b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(a b))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(a b))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(a b))) 7. ==[ beta ]==> ((b b)(^y.(a b))) 8. ==[ alpha ]==> ((b b)(^x.(a b))) REDUCED to normal form. ------ 193361/22865580. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.b))) REDUCED to normal form. ------ 193362/22865778. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.(^z.y))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.y))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.x))) REDUCED to normal form. ------ 193363/22866126. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.z)((a a) a))) 3. ==[ beta ]==> (((^z.z)((a a) a))(((^z.z)((a a) a))(^y.y))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y)((a a) a))(^z.z))) 5. ==[ beta ]==> (((a a) a)(((^y.y)((a a) a))(^z.z))) 6. ==[ alpha ]==> (((a a) a)(((^x.x)((a a) a))(^y.y))) 7. ==[ beta ]==> (((a a) a)(((a a) a)(^y.y))) 8. ==[ alpha ]==> (((a a) a)(((a a) a)(^x.x))) REDUCED to normal form. ------ 193364/22866129. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^b.((a a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.((a a) a))) REDUCED to normal form. ------ 193365/22866732. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 193366/22867074. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 193367/22867182. ------ 1. ==[ start ]==> (((a b)(b a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 193368/22867344. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.a))) REDUCED to normal form. ------ 193369/22867416. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.c)) 3. ==[ beta ]==> ((b (^y.y))(^z.c)) 4. ==[ alpha ]==> ((b (^x.x))(^y.c)) REDUCED to normal form. ------ 193370/22867425. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(^z.y))) REDUCED to normal form. ------ 193371/22867449. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193372/22867623. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.b)) 3. ==[ beta ]==> (b (^y1.b)) 4. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 193373/22867743. ------ 1. ==[ start ]==> ((a b)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a b)((^x.b)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 193374/22867797. ------ 1. ==[ start ]==> (((a a)(a a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))(^y.y)) 4. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 193375/22867887. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (a (a (^z.z))))) 3. ==[ beta ]==> ((a (^y.y))(b (a (a (^z.z))))) 4. ==[ alpha ]==> ((a (^x.x))(b (a (a (^y.y))))) REDUCED to normal form. ------ 193376/22867914. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 193377/22867923. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 193378/22867941. ------ 1. ==[ start ]==> ((a (^b.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.a))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 193379/22868022. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.a)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.a)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 193380/22868049. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) b)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193381/22868103. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((b a)(a b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((b a)(a b))) 3. ==[ beta ]==> (((^y.y) a)((b a)(a b))) 4. ==[ alpha ]==> (((^x.x) a)((b a)(a b))) 5. ==[ beta ]==> (a ((b a)(a b))) REDUCED to normal form. ------ 193382/22868130. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((a a)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 193383/22868184. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a b)(b a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a b)(b a))) REDUCED to normal form. ------ 193384/22868292. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> ((((^y.y) a)(b (^z.z)))(((^y.y) a)(b (^z.z)))) 6. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(((^z.z) a)(b (^x1.x1)))) 7. ==[ beta ]==> ((a (b (^y.y)))(((^z.z) a)(b (^x1.x1)))) 8. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(b (^z.z)))) 9. ==[ beta ]==> ((a (b (^x.x)))(a (b (^z.z)))) 10. ==[ alpha ]==> ((a (b (^x.x)))(a (b (^y.y)))) REDUCED to normal form. ------ 193385/22868319. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 193386/22868382. ------ 1. ==[ start ]==> (((a (a a)) a)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a)) a)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 193387/22868409. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 193388/22868436. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 193389/22868463. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(^z.(z z)))) REDUCED to normal form. ------ 193390/22868490. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 193391/22868526. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 193392/22868598. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((b b)((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((b b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 193393/22868607. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 193394/22868634. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(b a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(b a))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 193395/22868787. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 193396/22868814. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 193397/22868841. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((a (^y.a))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((a (^x.a))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> ((a (^x.a))((^z.z) b)) 6. ==[ alpha ]==> ((a (^x.a))((^y.y) b)) 7. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 193398/22868868. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((b (^z.z)) c)) REDUCED to normal form. ------ 193399/22868931. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 193400/22869039. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 193401/22869237. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(a (a (a (^y.y))))) 3. ==[ beta ]==> (((a a) a)(a (a (a (^y.y))))) 4. ==[ alpha ]==> (((a a) a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 193402/22869264. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.(^z1.z1)) a)(a a))) 3. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a)(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a a)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a a)) 7. ==[ beta ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193403/22869318. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((a a)(a a))((^z.z) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((a a)(a a))((^y.y) a))) 7. ==[ beta ]==> ((a a)(((a a)(a a))((^y.y) a))) 8. ==[ alpha ]==> ((a a)(((a a)(a a))((^x.x) a))) 9. ==[ beta ]==> ((a a)(((a a)(a a)) a)) REDUCED to normal form. ------ 193404/22869327. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.(a a)) d)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(a a)) d)) 3. ==[ beta ]==> (((a (a a))(^x.a))(a a)) REDUCED to normal form. ------ 193405/22869399. ------ 1. ==[ start ]==> ((a (^a.b))((b a)((a a) a))) 2. ==[ alpha ]==> ((a (^x.b))((b a)((a a) a))) REDUCED to normal form. ------ 193406/22869588. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.b)(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 193407/22869732. ------ 1. ==[ start ]==> ((((a a) a) b)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a) b)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 193408/22869759. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b) a)(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> (((a b) a)(b (^y.(y y)))) 4. ==[ alpha ]==> (((a b) a)(b (^x.(x x)))) REDUCED to normal form. ------ 193409/22869786. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 193410/22869840. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 193411/22869867. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 193412/22869894. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.a)((a b)(^y.(^z.z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 193413/22869948. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.x))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 193414/22869984. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(x x))((^y.y) b))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> (((a a)(a b))(b ((^y.y) b))) 6. ==[ alpha ]==> (((a a)(a b))(b ((^x.x) b))) 7. ==[ beta ]==> (((a a)(a b))(b b)) REDUCED to normal form. ------ 193415/22870011. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) a) REDUCED to normal form. ------ 193416/22870038. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(b (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(b (^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 193417/22870065. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 193418/22870137. ------ 1. ==[ start ]==> (((^a.b) b)(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b) b)(((a a)(a a)) c)) 3. ==[ beta ]==> (b (((a a)(a a)) c)) REDUCED to normal form. ------ 193419/22870146. ------ 1. ==[ start ]==> (((a b)(a a))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 193420/22870173. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(y y)))) 5. ==[ beta ]==> ((a (a a))(^y.(y y))) 6. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 193421/22870425. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))(c ((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(c ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(c ((a a)(a a)))) 5. ==[ beta ]==> (c ((a a)(a a))) REDUCED to normal form. ------ 193422/22870479. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(a ((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(a ((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(a ((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a ((^x1.(^y1.y1)) a))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a ((^z.(^x1.x1)) a))) 9. ==[ beta ]==> ((^y.y)(a ((^z.(^x1.x1)) a))) 10. ==[ alpha ]==> ((^x.x)(a ((^y.(^z.z)) a))) 11. ==[ beta ]==> (a ((^y.(^z.z)) a)) 12. ==[ alpha ]==> (a ((^x.(^y.y)) a)) 13. ==[ beta ]==> (a (^y.y)) 14. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 193423/22870542. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.(a a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 193424/22870560. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (b (((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (b (((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (b (b ((^y.y) a))) 6. ==[ alpha ]==> (b (b ((^x.x) a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 193425/22871028. ------ 1. ==[ start ]==> (((a b) c)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b) c)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 193426/22871055. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (((a a) b)((a a)(^y.b))) 6. ==[ alpha ]==> (((a a) b)((a a)(^x.b))) REDUCED to normal form. ------ 193427/22871082. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)(^y.(a a)))) REDUCED to normal form. ------ 193428/22871163. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.b))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.b))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 193429/22871217. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193430/22871271. ------ 1. ==[ start ]==> (((a b)(^b.a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.a))((b (^y.y)) a)) REDUCED to normal form. ------ 193431/22871298. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(a a)) b)) REDUCED to normal form. ------ 193432/22871325. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) b) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b c)) REDUCED to normal form. ------ 193433/22871361. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 193434/22871415. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 193435/22871442. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(a a))(^y.b))) 3. ==[ beta ]==> (((a (a a))((a a) a))(a a)) REDUCED to normal form. ------ 193436/22871469. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(^y1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(^y1.(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.(a a)))) 7. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(a a)))) 8. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(a a)))) 9. ==[ beta ]==> ((^y.b)(^z.(a a))) 10. ==[ alpha ]==> ((^x.b)(^y.(a a))) 11. ==[ beta ]==> b REDUCED to normal form. ------ 193437/22871550. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(a (^x.x)))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 7. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 193438/22871577. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 193439/22871604. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 193440/22871694. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) b)(a (^x1.x1)))) 5. ==[ beta ]==> (b (((^z.z) b)(a (^x1.x1)))) 6. ==[ alpha ]==> (b (((^x.x) b)(a (^y.y)))) 7. ==[ beta ]==> (b (b (a (^y.y)))) 8. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 193441/22871775. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 193442/22871883. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b a)(((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((b a)((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> ((b a)((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> ((b a)((a a)(^y.y))) 8. ==[ alpha ]==> ((b a)((a a)(^x.x))) REDUCED to normal form. ------ 193443/22871910. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (a a))(b a))) 3. ==[ beta ]==> ((^y.y)((a (a a))(b a))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(b a))) 5. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 193444/22871964. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.y))((^z.z) b))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> (((a b)(a b))((a (^x.x)) b)) REDUCED to normal form. ------ 193445/22872027. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(a a))(^z.z))) REDUCED to normal form. ------ 193446/22872054. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 193447/22872081. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 193448/22872108. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 193449/22872171. ------ 1. ==[ start ]==> (((a a)(b a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(a a))((a a) a))) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 193450/22872198. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 193451/22872252. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 193452/22872279. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(z z))(b a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(y y))(b a))) 5. ==[ beta ]==> (((a a) a)((^y.(y y))(b a))) 6. ==[ alpha ]==> (((a a) a)((^x.(x x))(b a))) 7. ==[ beta ]==> (((a a) a)((b a)(b a))) REDUCED to normal form. ------ 193453/22872306. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((((a a) a)(^x.x)) a) REDUCED to normal form. ------ 193454/22872333. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 193455/22872360. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.y)((a a)(a a)))) 5. ==[ beta ]==> (((a a) a)((^y.y)((a a)(a a)))) 6. ==[ alpha ]==> (((a a) a)((^x.x)((a a)(a a)))) 7. ==[ beta ]==> (((a a) a)((a a)(a a))) REDUCED to normal form. ------ 193456/22872441. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 193457/22872720. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(a ((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193458/22872747. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 193459/22872756. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.b) b)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1) b)) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 193460/22872774. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 193461/22872828. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a)(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a)(^z.z))(a (a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(^y.y))(a (a a)))) 7. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))(a (a a)))) 8. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 193462/22872909. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((a a) a)(a b))) 3. ==[ beta ]==> (b (((a a) a)(a b))) REDUCED to normal form. ------ 193463/22873017. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193464/22873044. ------ 1. ==[ start ]==> ((a (^b.b))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) b))) 3. ==[ beta ]==> ((a (^x.x))((a a) b)) REDUCED to normal form. ------ 193465/22873089. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((^b.b)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)(a a))) 3. ==[ beta ]==> (((a (^x.x))(b a))(a a)) REDUCED to normal form. ------ 193466/22873116. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 193467/22873170. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (a a)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 193468/22873197. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 193469/22873224. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.b)((a a) a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.b)((a a) a))) 5. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 193470/22873278. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.y)) REDUCED to normal form. ------ 193471/22873332. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.a)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) a) REDUCED to normal form. ------ 193472/22873359. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 193473/22873692. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y) b)(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x) b)(b (a (^y.(^z.z))))) 5. ==[ beta ]==> (b (b (a (^y.(^z.z))))) 6. ==[ alpha ]==> (b (b (a (^x.(^y.y))))) REDUCED to normal form. ------ 193474/22873719. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(a ((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)(a ((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y) b))) 5. ==[ beta ]==> (a ((^y.y) b)) 6. ==[ alpha ]==> (a ((^x.x) b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 193475/22873728. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) a) REDUCED to normal form. ------ 193476/22873773. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((b a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((b a)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((b a)(a (^z.z)))) REDUCED to normal form. ------ 193477/22873809. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1)) d)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1)) d)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1)) d)) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1)) d)) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z)) d)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193478/22873854. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (b ((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((a b)(^y.y))) 6. ==[ alpha ]==> (b ((a b)(^x.x))) REDUCED to normal form. ------ 193479/22873962. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^y1.y1) a)((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193480/22874034. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(a (^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(a (^y.y))) 3. ==[ beta ]==> (((a a) b)(a (^y.y))) 4. ==[ alpha ]==> (((a a) b)(a (^x.x))) REDUCED to normal form. ------ 193481/22874061. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 193482/22874142. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(a (a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(a (a a)))) 7. ==[ beta ]==> ((a a)((^y.(a a))(a (a a)))) 8. ==[ alpha ]==> ((a a)((^x.(a a))(a (a a)))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 193483/22874169. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a b)) b) REDUCED to normal form. ------ 193484/22874196. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.a)((a a) a))) 3. ==[ beta ]==> (((a b)((a a) a)) a) REDUCED to normal form. ------ 193485/22874223. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(a b))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 193486/22874250. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(((^z.z)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 193487/22874304. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.x1)) REDUCED to normal form. ------ 193488/22874331. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b (a a))((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b (a a))((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((b (a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 193489/22874358. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 193490/22874637. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(a (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193491/22874718. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((a a)((^y.y) a))) 6. ==[ alpha ]==> (((a a)(a a))((a a)((^x.x) a))) 7. ==[ beta ]==> (((a a)(a a))((a a) a)) REDUCED to normal form. ------ 193492/22874745. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((a b)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(a (a a)))) 5. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 193493/22874799. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> (((b a)(b a))((^y.y)((a a) a))) 6. ==[ alpha ]==> (((b a)(b a))((^x.x)((a a) a))) 7. ==[ beta ]==> (((b a)(b a))((a a) a)) REDUCED to normal form. ------ 193494/22874880. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (b ((a (^y.y))((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 193495/22874943. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((b a)(^x1.x1))) REDUCED to normal form. ------ 193496/22874997. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)(^x1.a))) REDUCED to normal form. ------ 193497/22875024. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a b)(^z.(z z)))) REDUCED to normal form. ------ 193498/22875051. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 193499/22875087. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 193500/22875114. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(z z))(a b))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(z z))(a b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y y))(a b))) 5. ==[ beta ]==> (((a (^x.x)) b)((a b)(a b))) REDUCED to normal form. ------ 193501/22875141. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 193502/22875168. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 193503/22875195. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.x1)(b a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.x1)(b a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.z)(b a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(b a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(b a))) 7. ==[ beta ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 193504/22875249. ------ 1. ==[ start ]==> (((a b)(a b))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 193505/22875276. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(a a))(^z.a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(a a))(^y.a))) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 193506/22875303. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 193507/22875357. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 193508/22875384. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(z z))(^x1.b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(y y))(^z.b))) 5. ==[ beta ]==> ((b (a (^x.x)))((^z.b)(^z.b))) 6. ==[ alpha ]==> ((b (a (^x.x)))((^y.b)(^z.b))) 7. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 193509/22875411. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.a)(^y.(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 193510/22875438. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 193511/22875528. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(a a))(a (^y2.y2)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x2.x2)(a a))(a (^y2.y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193512/22875609. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193513/22875717. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193514/22875753. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a)(^y.y))(^z.z))) 3. ==[ beta ]==> ((b c)(((a a)(^y.y))(^z.z))) 4. ==[ alpha ]==> ((b c)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 193515/22875780. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 193516/22875888. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))(^z.a))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.a))) REDUCED to normal form. ------ 193517/22875915. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^y1.b))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(a (^x1.b))) REDUCED to normal form. ------ 193518/22875996. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 193519/22876023. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(a a)) b)) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a)) b)) 5. ==[ beta ]==> (((a a)(^x.b))((a a) b)) REDUCED to normal form. ------ 193520/22876221. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 193521/22876410. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(c (^y.b))) 3. ==[ beta ]==> (((a a)(a b))(c (^y.b))) 4. ==[ alpha ]==> (((a a)(a b))(c (^x.b))) REDUCED to normal form. ------ 193522/22876437. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(b (^y.(a a)))) REDUCED to normal form. ------ 193523/22876491. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a a)) REDUCED to normal form. ------ 193524/22876518. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((b a)((^y.b)(a (^z.z)))) 6. ==[ alpha ]==> ((b a)((^x.b)(a (^y.y)))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 193525/22876599. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(((^z.z)(^x1.x1))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 9. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 10. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 11. ==[ beta ]==> ((a (^x.x))(^z.z)) 12. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 193526/22876878. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(b (a b))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193527/22877013. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a (a a))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a (a a)))) 7. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 193528/22877040. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.z))) 7. ==[ beta ]==> (a ((^y.y)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 193529/22877094. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a a)(a b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a a)(a b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a a)(a b))) 5. ==[ beta ]==> ((b ((^y.y) b))((a a)(a b))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a a)(a b))) 7. ==[ beta ]==> ((b b)((a a)(a b))) REDUCED to normal form. ------ 193530/22877130. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a b)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a b)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a b)(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a b)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(^x1.x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193531/22877184. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.a)) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 193532/22877211. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 193533/22877238. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 193534/22877292. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(^y1.b))) REDUCED to normal form. ------ 193535/22877319. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a b) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a b) a)) 3. ==[ beta ]==> ((b (^y.(y y)))((a b) a)) 4. ==[ alpha ]==> ((b (^x.(x x)))((a b) a)) REDUCED to normal form. ------ 193536/22877346. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((a a) a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((a a) a) b)) REDUCED to normal form. ------ 193537/22877436. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 193538/22877463. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 193539/22877490. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.y)(^z.b))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(^z.b))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(^y.b))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.b)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.b)) REDUCED to normal form. ------ 193540/22877652. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b (^y.a))) REDUCED to normal form. ------ 193541/22877733. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 193542/22877760. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(y y))((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y) a)((^y.y) a))) 6. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> ((((a a)(a a)) a)(a ((^y.y) a))) 8. ==[ alpha ]==> ((((a a)(a a)) a)(a ((^x.x) a))) 9. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 193543/22877814. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 193544/22877841. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.a)((a a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)((a a) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a a) a)) REDUCED to normal form. ------ 193545/22878237. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.a))) 5. ==[ beta ]==> (b (((^y.y) a)(^z.a))) 6. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 7. ==[ beta ]==> (b (a (^y.a))) 8. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 193546/22878264. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 193547/22878291. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 193548/22878444. ------ 1. ==[ start ]==> (((^a.b)(b a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> (b (a ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (b (a ((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 193549/22878507. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 193550/22878552. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193551/22878588. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a))(^z.z))) REDUCED to normal form. ------ 193552/22878615. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 193553/22878669. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193554/22878696. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (a a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (a a)) a)) REDUCED to normal form. ------ 193555/22878732. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 193556/22878759. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 193557/22878786. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.(z z))) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.(y y))) REDUCED to normal form. ------ 193558/22878840. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(c (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)(c (^y.(^z.z)))) 7. ==[ beta ]==> (b (c (^y.(^z.z)))) 8. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 193559/22878867. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b (^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b (^z.a))) REDUCED to normal form. ------ 193560/22878894. ------ 1. ==[ start ]==> (((a b)(b a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a b)(b a))(a (^x.(x x)))) REDUCED to normal form. ------ 193561/22878921. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.a)(a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.a)(a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a)(a a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 193562/22878948. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 193563/22879002. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a)) a) REDUCED to normal form. ------ 193564/22879029. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 193565/22879056. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x)(^y.a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.a)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.a)) REDUCED to normal form. ------ 193566/22879110. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 193567/22879128. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a) c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.z) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.y) c)) 5. ==[ beta ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 193568/22879137. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a (^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a (^y.a))) REDUCED to normal form. ------ 193569/22879164. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 193570/22879173. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193571/22879335. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a b)) 3. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 193572/22891347. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 193573/22891356. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^z.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 193574/22891788. ------ 1. ==[ start ]==> ((((^a.a) a) b)(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((a b)(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((a b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 193575/22891806. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 193576/22891938. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193577/22892238. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 5. ==[ beta ]==> (^y.(a (a (^z.z)))) 6. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 193578/22892670. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 193579/22893102. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) IRREDUCIBLE: cycle. ------ 193580/22893396. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(a (^y1.(^z1.z1))))((^z.(^x1.x1))(a (^y1.(^z1.z1)))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(a (^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.(^z2.z2)))))) 5. ==[ beta ]==> (^x.((^z.z)((^z1.(^x2.x2))(a (^y2.(^z2.z2)))))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(a (^y1.(^z1.z1)))))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(a (^x1.(^y1.y1))))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193581/22893921. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((a (a a))(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 193582/22894695. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 193583/22896153. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(^y1.(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193584/22896162. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.((z z)(z z)))) REDUCED to normal form. ------ 193585/22896474. ------ 1. ==[ start ]==> ((^a.(^b.b))(b (^b.b))) 2. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193586/22896789. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 193587/22896828. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.((^x2.x2) z1))) 3. ==[ eta ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^x2.x2)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(^z1.z1)) 5. ==[ beta ]==> ((^y.y)(^z1.z1)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193588/22897152. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193589/22897161. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.b)) REDUCED to normal form. ------ 193590/22897764. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b (a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 193591/22897788. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a (^y.(^z.z))) a)) 3. ==[ beta ]==> ((((a (^y.(^z.z))) a)((a (^y.(^z.z))) a))(((a (^y.(^z.z))) a)((a (^y.(^z.z))) a))) 4. ==[ alpha ]==> ((((a (^x.(^y.y))) a)((a (^z.(^x1.x1))) a))(((a (^y1.(^z1.z1))) a)((a (^x2.(^y2.y2))) a))) REDUCED to normal form. ------ 193592/22898070. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193593/22899420. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.((a a)(^y.y)))) REDUCED to normal form. ------ 193594/22900029. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (a a))(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^y.(^z.z))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193595/22900122. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(a a)))) 7. ==[ beta ]==> (^y.((^z.z)(a a))) 8. ==[ alpha ]==> (^x.((^y.y)(a a))) 9. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 193596/22900536. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^c.(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(a b))) REDUCED to normal form. ------ 193597/22900848. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 193598/22901283. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^b.((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.((a a) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.((a a) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.((a a) a))) 5. ==[ beta ]==> ((^z.((a a) a))(^y.y)) 6. ==[ alpha ]==> ((^x.((a a) a))(^y.y)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 193599/22901742. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193600/22901877. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 193601/22902120. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (a a)))) REDUCED to normal form. ------ 193602/22902144. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.z1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 193603/22902219. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.d)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.d)) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.d)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.d)) REDUCED to normal form. ------ 193604/22902561. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(a (^z.z)))) REDUCED to normal form. ------ 193605/22902570. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.c)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.c)) REDUCED to normal form. ------ 193606/22902594. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193607/22902633. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.z)))) 5. ==[ beta ]==> (^y.(a (^z.z))) 6. ==[ alpha ]==> (^x.(a (^y.y))) REDUCED to normal form. ------ 193608/22902768. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^b.(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> (b (^y1.(a a))) 4. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 193609/22902906. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)((^y.b)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)((^x.b)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 193610/22903041. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 193611/22903050. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (a (a (^z.z))))) REDUCED to normal form. ------ 193612/22903068. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 193613/22903077. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 193614/22903113. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (((a a)(a (^x.x)))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(b (^y.y))) REDUCED to normal form. ------ 193615/22903131. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 193616/22903212. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) b)(b (^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.y))) REDUCED to normal form. ------ 193617/22903239. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 193618/22903266. ------ 1. ==[ start ]==> (((a a)(^b.a))((b a)(a b))) 2. ==[ alpha ]==> (((a a)(^x.a))((b a)(a b))) REDUCED to normal form. ------ 193619/22903293. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(a a))) REDUCED to normal form. ------ 193620/22903320. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a a)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 193621/22903428. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 193622/22903509. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((a b)((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> ((a b)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 193623/22903527. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 193624/22903554. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((a (a a))((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a a))((a a)(^y.y))) 6. ==[ alpha ]==> ((a (a a))((a a)(^x.x))) REDUCED to normal form. ------ 193625/22903662. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 193626/22903707. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((b a)(^z.b))) 3. ==[ beta ]==> (((a (^x.x)) a)((b a)(^z.b))) 4. ==[ alpha ]==> (((a (^x.x)) a)((b a)(^y.b))) REDUCED to normal form. ------ 193627/22903734. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 193628/22903797. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193629/22903878. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 7. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 8. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 9. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 193630/22903932. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193631/22903959. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 193632/22904256. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 193633/22904310. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (a ((^z.(z z))(^x1.(a a)))) 6. ==[ alpha ]==> (a ((^x.(x x))(^y.(a a)))) 7. ==[ beta ]==> (a ((^y.(a a))(^y.(a a)))) 8. ==[ alpha ]==> (a ((^x.(a a))(^y.(a a)))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 193634/22904346. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)(c (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)(c (b (^z.z)))) 3. ==[ beta ]==> (((^y.y) b)(c (b (^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)(c (b (^y.y)))) 5. ==[ beta ]==> (b (c (b (^y.y)))) 6. ==[ alpha ]==> (b (c (b (^x.x)))) REDUCED to normal form. ------ 193635/22904373. ------ 1. ==[ start ]==> ((((a a) a) a)(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) a)(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> ((((a a) a) a)(b (^y.y))) 4. ==[ alpha ]==> ((((a a) a) a)(b (^x.x))) REDUCED to normal form. ------ 193636/22904391. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(y (^z.z))))) 5. ==[ beta ]==> (((a a) a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> (((a a) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 193637/22904427. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 193638/22904454. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 193639/22904481. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(((a a)(a a)) a)) REDUCED to normal form. ------ 193640/22904508. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193641/22904535. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 193642/22904724. ------ 1. ==[ start ]==> (((^a.b) a)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) a)((a (a a))((^y.y) b))) 3. ==[ beta ]==> (b ((a (a a))((^y.y) b))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x) b))) 5. ==[ beta ]==> (b ((a (a a)) b)) REDUCED to normal form. ------ 193643/22904823. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(a (^z.(z (^x1.x1))))) IRREDUCIBLE: cycle. ------ 193644/22904904. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 193645/22904931. ------ 1. ==[ start ]==> (((^a.a)(a b))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a b)((^y.y)(a (a a)))) 4. ==[ alpha ]==> ((a b)((^x.x)(a (a a)))) 5. ==[ beta ]==> ((a b)(a (a a))) REDUCED to normal form. ------ 193646/22904958. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193647/22905093. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.a)(b a))) 3. ==[ beta ]==> (b ((^y.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 193648/22905120. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 193649/22905138. ------ 1. ==[ start ]==> (((a a)(a b))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(a b))((a (a a))(^x.x))) REDUCED to normal form. ------ 193650/22905246. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.(^x1.x1)) a) a)) 5. ==[ beta ]==> (((^y.y) a)(((^z.(^x1.x1)) a) a)) 6. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a) a)) 7. ==[ beta ]==> (a (((^y.(^z.z)) a) a)) 8. ==[ alpha ]==> (a (((^x.(^y.y)) a) a)) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193651/22905273. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((b (^y.y)) b)) REDUCED to normal form. ------ 193652/22905300. ------ 1. ==[ start ]==> (((a b)(a a))(((a a)(a a)) c)) REDUCED to normal form. ------ 193653/22905336. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193654/22905363. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193655/22905417. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.b))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.b))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193656/22905498. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 193657/22905552. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((a a)((^y.(y y))(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(^y.y))) 7. ==[ beta ]==> ((a a)((^y.y)(^y.y))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 193658/22905579. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(a a))) 6. ==[ alpha ]==> ((^x.a)(^y.(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 193659/22905588. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))(c ((a a)(a a)))) REDUCED to normal form. ------ 193660/22905642. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 193661/22905669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((b (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((b (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b (^z.z))(a a))) 5. ==[ beta ]==> ((^y.(y y))((b (^z.z))(a a))) 6. ==[ alpha ]==> ((^x.(x x))((b (^y.y))(a a))) 7. ==[ beta ]==> (((b (^y.y))(a a))((b (^y.y))(a a))) 8. ==[ alpha ]==> (((b (^x.x))(a a))((b (^y.y))(a a))) REDUCED to normal form. ------ 193662/22905696. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 193663/22905723. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b ((^z.z) a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(b a)) REDUCED to normal form. ------ 193664/22905750. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 193665/22905939. ------ 1. ==[ start ]==> (((^a.b) c)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) c)((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> (b ((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (b ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 193666/22906254. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 193667/22906335. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 193668/22906416. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (b (b (^y.y))) 6. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 193669/22906992. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a b)(a b))) REDUCED to normal form. ------ 193670/22907100. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.(a a)))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a (^x.(a a)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 193671/22907118. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(c (^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(c (^y.y))) 3. ==[ beta ]==> (((a b)(a b))(c (^y.y))) 4. ==[ alpha ]==> (((a b)(a b))(c (^x.x))) REDUCED to normal form. ------ 193672/22907127. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a (^y.y)) b)) REDUCED to normal form. ------ 193673/22907199. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((^y.(a a))(a a))) 3. ==[ beta ]==> (b ((^y.(a a))(a a))) 4. ==[ alpha ]==> (b ((^x.(a a))(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 193674/22907325. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> (((a a)(b a))((a a)(^y.a))) 4. ==[ alpha ]==> (((a a)(b a))((a a)(^x.a))) REDUCED to normal form. ------ 193675/22907352. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a b)(^z.b))) REDUCED to normal form. ------ 193676/22907379. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a) a)(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(((a a) a)(^y.(a a)))) 6. ==[ alpha ]==> ((a (a a))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 193677/22907406. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a b))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 193678/22907460. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 193679/22907487. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 193680/22907541. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((a a)(a a)) a)) REDUCED to normal form. ------ 193681/22907604. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))(^y2.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193682/22907685. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((a a)((^z.(a a))(^x1.a))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.a))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 193683/22907766. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193684/22907883. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 193685/22907910. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(b (a a))) REDUCED to normal form. ------ 193686/22907991. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 193687/22908018. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.b)(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 193688/22908072. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(a b))) REDUCED to normal form. ------ 193689/22908099. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)(a a))) 8. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)(a a))) 9. ==[ beta ]==> (((a a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 193690/22908126. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (a a))((a a)(^z.z)))) REDUCED to normal form. ------ 193691/22908180. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 193692/22908198. ------ 1. ==[ start ]==> ((a (^b.b))(b (^b.b))) 2. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 193693/22908243. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(b a))(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(b a))(b (^y.y))) REDUCED to normal form. ------ 193694/22908270. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 193695/22908297. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((b a)(^y.a))) 3. ==[ beta ]==> (((a (a a))(a a))((b a)(^y.a))) 4. ==[ alpha ]==> (((a (a a))(a a))((b a)(^x.a))) REDUCED to normal form. ------ 193696/22908324. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a b)(((a a)(^y.y))(^z.(z z)))) 6. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 193697/22908351. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 193698/22908378. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a b)(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a b)(^z.a))) 3. ==[ beta ]==> (((a b)(^y.y))((a b)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.x))((a b)(^y.a))) REDUCED to normal form. ------ 193699/22908405. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((a a) a)(^y.b))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a) a)(^y.b))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((a a) a)(^x.b))) REDUCED to normal form. ------ 193700/22908432. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(^z.(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(a a))) 8. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(a a))) REDUCED to normal form. ------ 193701/22908513. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a b)((a (^y.y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a b)((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 193702/22908522. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193703/22908549. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1)((^x2.x2) b))) 3. ==[ beta ]==> ((^y.y)((^z1.z1)((^x2.x2) b))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) b))) 5. ==[ beta ]==> ((^y.y)((^z.z) b)) 6. ==[ alpha ]==> ((^x.x)((^y.y) b)) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 193704/22908684. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 193705/22908828. ------ 1. ==[ start ]==> ((((^a.a) b) a)(c (b a))) 2. ==[ alpha ]==> ((((^x.x) b) a)(c (b a))) 3. ==[ beta ]==> ((b a)(c (b a))) REDUCED to normal form. ------ 193706/22908846. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193707/22908855. ------ 1. ==[ start ]==> (((a a)(^b.b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 193708/22908873. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193709/22908882. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a ((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a b)) REDUCED to normal form. ------ 193710/22908963. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(((a a)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(((a a)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(a a))(((a a)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(a a))(((a a)(^y.y))((^z.z) a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193711/22908990. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((a a)(a (a a)))) REDUCED to normal form. ------ 193712/22909017. ------ 1. ==[ start ]==> (((a b)(^c.a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a))((a b)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.a))((a b)(^y.y))) REDUCED to normal form. ------ 193713/22909044. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 193714/22909071. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((^x1.x1)(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a b)) REDUCED to normal form. ------ 193715/22909125. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1) a)((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((a a)(^y1.y1)))) REDUCED to normal form. ------ 193716/22909152. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a (^z.z))(b a))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(b a))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(b a))) REDUCED to normal form. ------ 193717/22909215. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (^x1.(^y1.y1)))(^z1.z1))) REDUCED to normal form. ------ 193718/22909242. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (b a))((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((a (b a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 193719/22909269. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 193720/22909296. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(a a))(^z.(z z)))) 7. ==[ beta ]==> ((a a)(((^y.y)(a a))(^z.(z z)))) 8. ==[ alpha ]==> ((a a)(((^x.x)(a a))(^y.(y y)))) 9. ==[ beta ]==> ((a a)((a a)(^y.(y y)))) 10. ==[ alpha ]==> ((a a)((a a)(^x.(x x)))) REDUCED to normal form. ------ 193721/22909323. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 193722/22909350. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a) a)(^x.a))) REDUCED to normal form. ------ 193723/22909377. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.b))) 7. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.b))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.b))) 9. ==[ beta ]==> (((a a)(^x.x))(^z.b)) 10. ==[ alpha ]==> (((a a)(^x.x))(^y.b)) REDUCED to normal form. ------ 193724/22909404. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 193725/22909485. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b (a a))((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b (a a))((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 193726/22909512. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 193727/22909683. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193728/22909791. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193729/22909827. ------ 1. ==[ start ]==> ((((^a.a) b) b)((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((b a)(a a))) 3. ==[ beta ]==> ((b b)((b a)(a a))) REDUCED to normal form. ------ 193730/22909854. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 193731/22909908. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((a b)(a (a a)))) REDUCED to normal form. ------ 193732/22909935. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 193733/22910016. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))(a (a a))) REDUCED to normal form. ------ 193734/22910034. ------ 1. ==[ start ]==> (((^a.b)(a b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(c (^y.(^z.z)))) 3. ==[ beta ]==> (b (c (^y.(^z.z)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 193735/22910043. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 193736/22910268. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (a a))(^z.b))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (a a))(^z.b))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (a a))(^y.b))) REDUCED to normal form. ------ 193737/22910295. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (^x1.(a a)))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (^z.(a a)))) REDUCED to normal form. ------ 193738/22910322. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 193739/22910376. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((b a) a)) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((b a) a)) 3. ==[ beta ]==> ((((a a) a)(a a))((b a) a)) REDUCED to normal form. ------ 193740/22910403. ------ 1. ==[ start ]==> (((a b)(a b))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 193741/22910871. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193742/22910979. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.b)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 193743/22911060. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(y1 y1))((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a) a)((a a) a))) REDUCED to normal form. ------ 193744/22911141. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)((a a)(^y.y)))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 193745/22911429. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(a a)) b)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(a a)) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a)) b)) 5. ==[ beta ]==> ((a b)((^y.(a a)) b)) 6. ==[ alpha ]==> ((a b)((^x.(a a)) b)) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 193746/22911456. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b) c)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b) c)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 193747/22911483. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a) d)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a) d)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a) d)) 5. ==[ beta ]==> ((b a)((^y.a) d)) 6. ==[ alpha ]==> ((b a)((^x.a) d)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 193748/22911645. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a a)(^z.z))) REDUCED to normal form. ------ 193749/22911672. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)((a b)(^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 193750/22911699. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((a a) a)(^y.a))) REDUCED to normal form. ------ 193751/22911753. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 193752/22911843. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.z)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(a a)))) 7. ==[ beta ]==> ((^y.y)((^z.z)(a a))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(a a))) 9. ==[ beta ]==> ((^y.y)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193753/22911924. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 193754/22912032. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193755/22912149. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))((^x1.x1) a))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))((^z.z) a))) 7. ==[ beta ]==> (a ((^y.y)((^z.z) a))) 8. ==[ alpha ]==> (a ((^x.x)((^y.y) a))) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193756/22912248. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b (^z.b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b (^z.b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b (^z.b))) 5. ==[ beta ]==> ((b ((^y.y) b))(b (^z.b))) 6. ==[ alpha ]==> ((b ((^x.x) b))(b (^y.b))) 7. ==[ beta ]==> ((b b)(b (^y.b))) 8. ==[ alpha ]==> ((b b)(b (^x.b))) REDUCED to normal form. ------ 193757/22912257. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(a b))) REDUCED to normal form. ------ 193758/22912329. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 193759/22912437. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193760/22912572. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 193761/22912671. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.b) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.b) a)) 3. ==[ beta ]==> (((a (a a)) b)((^y.b) a)) 4. ==[ alpha ]==> (((a (a a)) b)((^x.b) a)) 5. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 193762/22912725. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y)) c)) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 193763/22912860. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((a a) a)(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 193764/22912887. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (a a)))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (a (a a)))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((b (a (a a)))(^y.(^z.z))) 8. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 193765/22912914. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (a a))(^y.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (a a))(^y.a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (a a))(^x.a))) REDUCED to normal form. ------ 193766/22912968. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((a (^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 193767/22913004. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.x1)((a a) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.x1)((a a) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)((a a) a))) 5. ==[ beta ]==> (((^z.z)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((^x.x)((a a) a))(^y.y)) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 193768/22913409. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) a))) 7. ==[ beta ]==> ((^y.a)((^z.z) a)) 8. ==[ alpha ]==> ((^x.a)((^y.y) a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 193769/22913436. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 193770/22913463. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.y1)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193771/22913517. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 193772/22913553. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(c ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c ((^z.z) a))) 5. ==[ beta ]==> ((^y.y)(c ((^z.z) a))) 6. ==[ alpha ]==> ((^x.x)(c ((^y.y) a))) 7. ==[ beta ]==> (c ((^y.y) a)) 8. ==[ alpha ]==> (c ((^x.x) a)) 9. ==[ beta ]==> (c a) REDUCED to normal form. ------ 193773/22913580. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(b (a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(b (a (a a)))) REDUCED to normal form. ------ 193774/22913598. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 193775/22913661. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (a (^z.z)))) REDUCED to normal form. ------ 193776/22913706. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193777/22913841. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (a a))) REDUCED to normal form. ------ 193778/22913868. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 193779/22913886. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(((^y.y) a) b)) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a b)) REDUCED to normal form. ------ 193780/22913967. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(x x)) a)) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 193781/22913994. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.a) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.a) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a) b)) 5. ==[ beta ]==> (((^y.y) b)((^z.a) b)) 6. ==[ alpha ]==> (((^x.x) b)((^y.a) b)) 7. ==[ beta ]==> (b ((^y.a) b)) 8. ==[ alpha ]==> (b ((^x.a) b)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 193782/22914075. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 193783/22914102. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 193784/22914156. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(((^z.z) a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(a a)) REDUCED to normal form. ------ 193785/22914183. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a (^x1.x1)) b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a (^x1.x1)) b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a (^z.z)) b)) 5. ==[ beta ]==> ((b (^y.y))((a (^z.z)) b)) 6. ==[ alpha ]==> ((b (^x.x))((a (^y.y)) b)) REDUCED to normal form. ------ 193786/22914264. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) b)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) b)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 193787/22914282. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a)(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.y))((a a)(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(a (^y.y)))) REDUCED to normal form. ------ 193788/22914318. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 193789/22914327. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193790/22914354. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(a (^z.z))) 6. ==[ alpha ]==> ((^x.x)(a (^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 193791/22914489. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.y1)(a a))) 3. ==[ beta ]==> (b ((^y1.y1)(a a))) 4. ==[ alpha ]==> (b ((^x.x)(a a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 193792/22926528. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 193793/22926543. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (^y.((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 193794/22926615. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((b (^z.z))((^x1.x1) a))) 3. ==[ eta ]==> ((^y.y)((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 193795/22926885. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(((a (a a))((a a)(a a)))((a (a a))((a a)(a a))))) REDUCED to normal form. ------ 193796/22926987. ------ 1. ==[ start ]==> (((a (a a)) a)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 193797/22927110. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193798/22927419. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 193799/22928181. ------ 1. ==[ start ]==> ((^a.(a b))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x b))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a (a a))((^y.y) b)) b) 4. ==[ alpha ]==> (((a (a a))((^x.x) b)) b) 5. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 193800/22928568. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.((((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2)))))) 4. ==[ alpha ]==> (^x.((((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(^z2.(^x3.(^y3.y3)))))) 5. ==[ beta ]==> (^x.(((^z.z)(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(^z2.(^x3.(^y3.y3)))))) 6. ==[ alpha ]==> (^x.(((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.(^z2.(^x3.x3)))))) 7. ==[ beta ]==> (^x.((^z.(^x1.(^y1.y1)))(((^z1.z1)(^x2.x2))(^y2.(^z2.(^x3.x3)))))) 8. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2)))))) 9. ==[ beta ]==> (^x.(^z.(^x1.x1))) 10. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 193801/22929450. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((((a (^z.z))((a a)(a a)))((a (^z.z))((a a)(a a))))(^y.y)) 4. ==[ alpha ]==> ((((a (^x.x))((a a)(a a)))((a (^y.y))((a a)(a a))))(^z.z)) REDUCED to normal form. ------ 193802/22929867. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 193803/22929876. ------ 1. ==[ start ]==> (((a b)(^b.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 193804/22930206. ------ 1. ==[ start ]==> ((^a.(b a))(c ((^a.a) b))) 2. ==[ alpha ]==> ((^x.(b x))(c ((^y.y) b))) 3. ==[ eta ]==> (b (c ((^y.y) b))) 4. ==[ alpha ]==> (b (c ((^x.x) b))) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 193805/22930755. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 193806/22931334. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(^x1.(a a)))) REDUCED to normal form. ------ 193807/22932333. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) REDUCED to normal form. ------ 193808/22932639. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 193809/22933548. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 193810/22934040. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(c ((^z.z)(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 193811/22934358. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^a.(^d.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.y))) 3. ==[ beta ]==> ((b c)(^y.(^z.y))) 4. ==[ alpha ]==> ((b c)(^x.(^y.x))) REDUCED to normal form. ------ 193812/22934592. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 193813/22934601. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 193814/22934853. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 193815/22935294. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(a a)))) 7. ==[ beta ]==> (^y.(^z.(a a))) 8. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 193816/22935735. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(x1 x1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193817/22935924. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(a z))) 3. ==[ eta ]==> ((((^x.x) b)(^y.(y y))) a) 4. ==[ beta ]==> ((b (^y.(y y))) a) 5. ==[ alpha ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 193818/22936122. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^a.(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(y b))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(y b))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(x b))) REDUCED to normal form. ------ 193819/22937193. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 193820/22937301. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(a (a a)))) REDUCED to normal form. ------ 193821/22937316. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (a a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (a a)) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 193822/22937418. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(x (x x)))) REDUCED to normal form. ------ 193823/22937499. ------ 1. ==[ start ]==> (((a b)(b a))(^c.((^a.a) a))) 2. ==[ alpha ]==> (((a b)(b a))(^x.((^y.y) a))) 3. ==[ beta ]==> (((a b)(b a))(^x.a)) REDUCED to normal form. ------ 193824/22937940. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^c.(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (b (^y1.(^z1.z1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 193825/22938096. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 193826/22938123. ------ 1. ==[ start ]==> (((^a.a) b)((^c.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.z))) 3. ==[ beta ]==> (b ((^y.a)(^z.z))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 193827/22938150. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193828/22938231. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 193829/22938258. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 193830/22938276. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a (^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 193831/22938294. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 193832/22938321. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 193833/22938348. ------ 1. ==[ start ]==> ((a ((^a.a) a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a a)((b (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((a a)((b (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((a a)((b (^x.x)) a)) REDUCED to normal form. ------ 193834/22938537. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a b)(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a b)(b a))) 3. ==[ beta ]==> (((a a) a)((a b)(b a))) REDUCED to normal form. ------ 193835/22938564. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 193836/22938591. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (a a))((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a (a a))((^y.y) b)) 8. ==[ alpha ]==> ((a (a a))((^x.x) b)) 9. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 193837/22938618. ------ 1. ==[ start ]==> ((a (a (a a)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 193838/22938690. ------ 1. ==[ start ]==> ((((^a.a) a) b)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a b)(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a b)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 193839/22938717. ------ 1. ==[ start ]==> (((a (a a)) a)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 193840/22938735. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a (a a))((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> ((a (a a))((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 193841/22938744. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 193842/22938762. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193843/22938816. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 193844/22938843. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 193845/22938933. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 193846/22939005. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 193847/22939068. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a)) b)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 193848/22939095. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> (a ((^y.a)(b (^z.z)))) 6. ==[ alpha ]==> (a ((^x.a)(b (^y.y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 193849/22939122. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 193850/22939140. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 193851/22939149. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(a (a (^z.z)))) REDUCED to normal form. ------ 193852/22939176. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.a))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.a))((^x1.x1)(^z.z))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.a))(^z.z)) 8. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 193853/22939194. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(^x1.x1)) a) b)) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1) b)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z) b)) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 193854/22939599. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 (^z1.z1))) a)) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 (^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((^y.(y (^z.z))) a) 6. ==[ alpha ]==> ((^x.(x (^y.y))) a) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 193855/22939752. ------ 1. ==[ start ]==> (((a a)((a a) a))((b a)((a a) a))) REDUCED to normal form. ------ 193856/22939779. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(a b))) REDUCED to normal form. ------ 193857/22939806. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a (a a)))((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> ((a (a (a a)))((a a)((^x.x)(a a)))) 7. ==[ beta ]==> ((a (a (a a)))((a a)(a a))) REDUCED to normal form. ------ 193858/22939833. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a b)((a a)(^y.y)))) 3. ==[ beta ]==> (((a (a a)) a)((a b)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a (a a)) a)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 193859/22939860. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((a a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a) a)(b a))) 5. ==[ beta ]==> ((a (^y.y))(((a a) a)(b a))) 6. ==[ alpha ]==> ((a (^x.x))(((a a) a)(b a))) REDUCED to normal form. ------ 193860/22939887. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a)(a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((((a a) a)(a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 193861/22939914. ------ 1. ==[ start ]==> ((a (a b))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a b))((a (a a))((^x.x) b))) 3. ==[ beta ]==> ((a (a b))((a (a a)) b)) REDUCED to normal form. ------ 193862/22940085. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (b (((a a)(a a))(^z.a))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.a))) REDUCED to normal form. ------ 193863/22940094. ------ 1. ==[ start ]==> (((a b) a)((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b) a)((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 193864/22940112. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((a b)(((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> ((a b)(((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> ((a b)(b (^y.(y y)))) 6. ==[ alpha ]==> ((a b)(b (^x.(x x)))) REDUCED to normal form. ------ 193865/22940121. ------ 1. ==[ start ]==> (((a a)(^a.b))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(a (a a))) REDUCED to normal form. ------ 193866/22940139. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 193867/22940193. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 193868/22940229. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.a)((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 193869/22940256. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y))) b) REDUCED to normal form. ------ 193870/22940283. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.a)(b a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.a)(b a))) 3. ==[ beta ]==> (((a b)(^x.x)) a) REDUCED to normal form. ------ 193871/22940301. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(a a)))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 193872/22940688. ------ 1. ==[ start ]==> (((a b) b)((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a b) b)((^x.a)(^y.a))) 3. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 193873/22940715. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 193874/22940742. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 193875/22940769. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 193876/22940895. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> (b ((^z.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 193877/22940967. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(a a))((b a)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))((b a)(^x.x))) REDUCED to normal form. ------ 193878/22940994. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 193879/22941021. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x)(a a))(a b))) 5. ==[ beta ]==> ((a ((a a) a))((a a)(a b))) REDUCED to normal form. ------ 193880/22941048. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a b)((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.x))((a b)(a a))) REDUCED to normal form. ------ 193881/22941075. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((a a) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a) a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a))(((a a) a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a (a a))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 193882/22941102. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> ((((a a) a) a)((^y.y)(b a))) 6. ==[ alpha ]==> ((((a a) a) a)((^x.x)(b a))) 7. ==[ beta ]==> ((((a a) a) a)(b a)) REDUCED to normal form. ------ 193883/22941129. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 193884/22941156. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (((a a)(a a))(a ((^y.y) b))) 6. ==[ alpha ]==> (((a a)(a a))(a ((^x.x) b))) 7. ==[ beta ]==> (((a a)(a a))(a b)) REDUCED to normal form. ------ 193885/22941183. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 193886/22941354. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 193887/22941363. ------ 1. ==[ start ]==> (((a b) c)((^d.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 193888/22941390. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 193889/22941417. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 193890/22941435. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.(a a)))) REDUCED to normal form. ------ 193891/22941471. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 193892/22941498. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 193893/22941516. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a (a a))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (a a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 193894/22941552. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((^y1.y1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1) b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193895/22941579. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 193896/22941606. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a))(b (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 193897/22941939. ------ 1. ==[ start ]==> ((a (b a))(c ((^a.a) b))) 2. ==[ alpha ]==> ((a (b a))(c ((^x.x) b))) 3. ==[ beta ]==> ((a (b a))(c b)) REDUCED to normal form. ------ 193898/22942029. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a)) b)) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a)) b)) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a)) b)) 5. ==[ beta ]==> (b ((^z.(a a)) b)) 6. ==[ alpha ]==> (b ((^x.(a a)) b)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 193899/22942308. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(c (^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(c (^y.y))) REDUCED to normal form. ------ 193900/22942380. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((a a)(a a))(^y.y))) 3. ==[ beta ]==> (b (((a a)(a a))(^y.y))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.x))) REDUCED to normal form. ------ 193901/22942389. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.(a a))(a a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a a)) REDUCED to normal form. ------ 193902/22942416. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.a))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 193903/22942443. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 193904/22942488. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 193905/22942767. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193906/22943109. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.z) b)) 3. ==[ beta ]==> ((^y.y)((^z.z) b)) 4. ==[ alpha ]==> ((^x.x)((^y.y) b)) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 193907/22943397. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)((^z.z) b))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a) b)) REDUCED to normal form. ------ 193908/22943658. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(x1 x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193909/22943703. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 193910/22943730. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a a)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((a a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 193911/22943982. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 193912/22944036. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 193913/22944063. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 193914/22944108. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 193915/22944333. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(c (^d.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(c (^z.a))) 3. ==[ beta ]==> ((b (^y.y))(c (^z.a))) 4. ==[ alpha ]==> ((b (^x.x))(c (^y.a))) REDUCED to normal form. ------ 193916/22944369. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a) b)((a a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a) b)((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 193917/22944729. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((b a) b)) 3. ==[ beta ]==> ((^y.y)((b a) b)) 4. ==[ alpha ]==> ((^x.x)((b a) b)) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 193918/22945224. ------ 1. ==[ start ]==> (((a b)(^a.b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 193919/22945278. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 193920/22945323. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193921/22945332. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.x1)) REDUCED to normal form. ------ 193922/22945359. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 193923/22945386. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x)) b) REDUCED to normal form. ------ 193924/22945773. ------ 1. ==[ start ]==> ((a (b (^a.a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))(c ((^y.y)(a a)))) 3. ==[ beta ]==> ((a (b (^x.x)))(c (a a))) REDUCED to normal form. ------ 193925/22946088. ------ 1. ==[ start ]==> ((((^a.a) b) c)(a (^d.a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(a (^y.a))) 3. ==[ beta ]==> ((b c)(a (^y.a))) 4. ==[ alpha ]==> ((b c)(a (^x.a))) REDUCED to normal form. ------ 193926/22946115. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y))(a a))) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 193927/22946160. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b)(^z.a))) 3. ==[ beta ]==> ((b (^y.y))((a b)(^z.a))) 4. ==[ alpha ]==> ((b (^x.x))((a b)(^y.a))) REDUCED to normal form. ------ 193928/22946187. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(y y)))) 5. ==[ beta ]==> (((a a) a)(^y.(y y))) 6. ==[ alpha ]==> (((a a) a)(^x.(x x))) REDUCED to normal form. ------ 193929/22946223. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 193930/22946250. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(((a a) a)((a a) a))) REDUCED to normal form. ------ 193931/22946322. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 193932/22946331. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 193933/22946358. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 193934/22946466. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 193935/22946556. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(b (a a))) REDUCED to normal form. ------ 193936/22946583. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 193937/22946610. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((a b)(((^y.y)(a a))(a a))) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a))(a a))) 7. ==[ beta ]==> ((a b)((a a)(a a))) REDUCED to normal form. ------ 193938/22946637. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a b)(a (^z.z)))) REDUCED to normal form. ------ 193939/22946664. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (((^y.y)(b a))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> (((^x.x)(b a))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((b a)(((a a) a)((^y.y) a))) 6. ==[ alpha ]==> ((b a)(((a a) a)((^x.x) a))) 7. ==[ beta ]==> ((b a)(((a a) a) a)) REDUCED to normal form. ------ 193940/22946691. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 193941/22946718. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))((a (a a))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))((a (a a))((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a b)(a a))((a (a a))(^y.y))) 6. ==[ alpha ]==> (((a b)(a a))((a (a a))(^x.x))) REDUCED to normal form. ------ 193942/22946745. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y) a)((a a) a))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x) a)((a a) a))) 5. ==[ beta ]==> (((a a)(a b))(a ((a a) a))) REDUCED to normal form. ------ 193943/22946772. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a (^y.y))(a b))) REDUCED to normal form. ------ 193944/22947024. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(a a)))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.(a a)))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(a a)))) 7. ==[ beta ]==> ((a a)(^y.(a a))) 8. ==[ alpha ]==> ((a a)(^x.(a a))) REDUCED to normal form. ------ 193945/22947105. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a) c)) 3. ==[ beta ]==> (b (((a a) a) c)) REDUCED to normal form. ------ 193946/22947438. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b (^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.b))) REDUCED to normal form. ------ 193947/22947465. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(a (^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(a (^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (^y1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193948/22947510. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 193949/22947519. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 193950/22947546. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 193951/22947573. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((a (a a))(a (a a)))) REDUCED to normal form. ------ 193952/22947627. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 193953/22947654. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.z)(a b))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.z)(a b))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(a b))) 5. ==[ beta ]==> ((b (^x.(x x)))(a b)) REDUCED to normal form. ------ 193954/22947681. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.b)(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) b) REDUCED to normal form. ------ 193955/22947735. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193956/22947798. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(c (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(c (^z.z))) REDUCED to normal form. ------ 193957/22947825. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(b ((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(b ((a a) a))) REDUCED to normal form. ------ 193958/22947852. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(a (a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(a (a b))) 3. ==[ beta ]==> (((a (a a)) b)(a (a b))) REDUCED to normal form. ------ 193959/22947879. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((a a) a)(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((a a) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a) a)(a a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(a a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 193960/22947906. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y)(a (^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(a (^y.y)))) 5. ==[ beta ]==> ((((a a) a)(b a))(a (^y.y))) 6. ==[ alpha ]==> ((((a a) a)(b a))(a (^x.x))) REDUCED to normal form. ------ 193961/22947933. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((a (a a))((^y.y) a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((a (a a)) a)) REDUCED to normal form. ------ 193962/22947960. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(a (a a)))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(a (a a)))) 7. ==[ beta ]==> (((a a)(a a))(a (a (a a)))) REDUCED to normal form. ------ 193963/22947987. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 193964/22948167. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 193965/22948572. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> (b ((^y.(y y))(a (^z.z)))) 6. ==[ alpha ]==> (b ((^x.(x x))(a (^y.y)))) 7. ==[ beta ]==> (b ((a (^y.y))(a (^y.y)))) 8. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 193966/22948590. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.a))) 7. ==[ beta ]==> (((^y.y) a)(^z.a)) 8. ==[ alpha ]==> (((^x.x) a)(^y.a)) 9. ==[ beta ]==> (a (^y.a)) 10. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 193967/22948599. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.a)((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a) a) REDUCED to normal form. ------ 193968/22948617. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.(z z)))) REDUCED to normal form. ------ 193969/22948626. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 193970/22948644. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 193971/22948698. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (a a)) b)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (a a)) b)) REDUCED to normal form. ------ 193972/22948734. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 7. ==[ beta ]==> ((^y.a)(^z.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 193973/22948761. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 193974/22948923. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 193975/22948950. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(y y))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))((a a)(a a))) REDUCED to normal form. ------ 193976/22949004. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193977/22949022. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 193978/22949031. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a (a a))) REDUCED to normal form. ------ 193979/22949049. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (a a)) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a)) a)) REDUCED to normal form. ------ 193980/22949121. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b ((^z.z) a))) 3. ==[ beta ]==> ((a (b (^y.y)))(b ((^z.z) a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(b ((^y.y) a))) 5. ==[ beta ]==> ((a (b (^x.x)))(b a)) REDUCED to normal form. ------ 193981/22949148. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a (a (a a)))) REDUCED to normal form. ------ 193982/22949175. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a)(a a))) 5. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(a a))) 6. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(a a))) 7. ==[ beta ]==> (b (((^y.y) a)(a a))) 8. ==[ alpha ]==> (b (((^x.x) a)(a a))) 9. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 193983/22949202. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 193984/22949229. ------ 1. ==[ start ]==> (((a b)(b a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(b a))((a a)((^x.x) a))) 3. ==[ beta ]==> (((a b)(b a))((a a) a)) REDUCED to normal form. ------ 193985/22949364. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(c (a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(c (a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(c (a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(c (a a))) 5. ==[ beta ]==> ((b (^y.y))(c (a a))) 6. ==[ alpha ]==> ((b (^x.x))(c (a a))) REDUCED to normal form. ------ 193986/22949391. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(b (a (^x.x)))) REDUCED to normal form. ------ 193987/22949445. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a (^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(a a))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a a))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 193988/22949463. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 193989/22949472. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a a)(a (^y.y)))) REDUCED to normal form. ------ 193990/22949508. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193991/22949535. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 193992/22949670. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a a)(^y1.y1))) 3. ==[ beta ]==> (b ((a a)(^y1.y1))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 193993/22950006. ------ 1. ==[ start ]==> ((^a.(^b.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (^x.(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^x.(^y.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 193994/22956423. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.(a (^z.(^x1.x1))))(^y.(a (^z.(^x1.x1)))))((^y.(a (^z.(^x1.x1))))(^y.(a (^z.(^x1.x1)))))) 4. ==[ alpha ]==> (((^x.(a (^y.(^z.z))))(^x1.(a (^y1.(^z1.z1)))))((^x2.(a (^y2.(^z2.z2))))(^x3.(a (^y3.(^z3.z3)))))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x2.(a (^y2.(^z2.z2))))(^x3.(a (^y3.(^z3.z3)))))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a (^x1.(^y1.y1))))(^z1.(a (^x2.(^y2.y2)))))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 193995/22961229. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(^z1.y1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 193996/22961625. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y1.(a a)))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^x1.x1)) 5. ==[ beta ]==> ((^y.y)(^x1.x1)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 193997/22961742. ------ 1. ==[ start ]==> ((^a.(^b.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (^x.(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(a (^y.(^z.z)))) REDUCED to normal form. ------ 193998/22961745. ------ 1. ==[ start ]==> ((a (^b.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.a))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 193999/22961985. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 194000/22962435. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194001/22962867. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.(a a))(^z.(^x1.x1)))((^y.(a a))(^z.(^x1.x1))))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.(a a))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1))))((^x2.(a a))(^y2.(^z2.z2)))) 5. ==[ beta ]==> (((a a)((^x1.(a a))(^y1.(^z1.z1))))((^x2.(a a))(^y2.(^z2.z2)))) 6. ==[ alpha ]==> (((a a)((^x.(a a))(^y.(^z.z))))((^x1.(a a))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a a)(a a))((^x1.(a a))(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(^z.z)))) 9. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 194002/22963068. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.(y1 (y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^y1.(y1 (y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (y (^z.z))))) 5. ==[ beta ]==> (^y.(y (y (^z.z)))) 6. ==[ alpha ]==> (^x.(x (x (^y.y)))) REDUCED to normal form. ------ 194003/22963200. ------ 1. ==[ start ]==> ((^a.(^a.b))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 194004/22963896. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((^y.y) a)(^z.((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> (((^x.x) a)(^y.((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (a (^y.((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> (a (^x.((^y.(^z.z)) a))) 9. ==[ beta ]==> (a (^x.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 194005/22964688. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 194006/22965075. ------ 1. ==[ start ]==> (((a b)(^b.a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194007/22965405. ------ 1. ==[ start ]==> ((^a.(b a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(^z.z))) 3. ==[ eta ]==> (b ((^y.a)(^z.z))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 194008/22966191. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.((a a)(a a)))) REDUCED to normal form. ------ 194009/22966242. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^x1.x1)(^y1.(^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194010/22966551. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((x1 x1)(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((z z)(z z)))) REDUCED to normal form. ------ 194011/22966845. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194012/22966893. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.(^z.(y y)))) REDUCED to normal form. ------ 194013/22967160. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.a)(b a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a)(b a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 194014/22967865. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 194015/22968159. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.y)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((^y.y)(a (^z.(^x1.x1))))((^y.y)(a (^z.(^x1.x1)))))(((^y.y)(a (^z.(^x1.x1))))((^y.y)(a (^z.(^x1.x1)))))) 4. ==[ alpha ]==> ((((^x.x)(a (^y.(^z.z))))((^x1.x1)(a (^y1.(^z1.z1)))))(((^x2.x2)(a (^y2.(^z2.z2))))((^x3.x3)(a (^y3.(^z3.z3)))))) 5. ==[ beta ]==> (((a (^y.(^z.z)))((^x1.x1)(a (^y1.(^z1.z1)))))(((^x2.x2)(a (^y2.(^z2.z2))))((^x3.x3)(a (^y3.(^z3.z3)))))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(a (^x1.(^y1.y1)))))(((^z1.z1)(a (^x2.(^y2.y2))))((^z2.z2)(a (^x3.(^y3.y3)))))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^x1.(^y1.y1))))(((^z1.z1)(a (^x2.(^y2.y2))))((^z2.z2)(a (^x3.(^y3.y3)))))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(a (^z1.(^x2.x2))))((^y2.y2)(a (^z2.(^x3.x3)))))) 9. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^z1.(^x2.x2)))((^y2.y2)(a (^z2.(^x3.x3)))))) 10. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))((^x2.x2)(a (^y2.(^z2.z2)))))) 11. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a (^y2.(^z2.z2))))) 12. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.(^z1.z1)))(a (^x2.(^y2.y2))))) REDUCED to normal form. ------ 194016/22968162. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 194017/22969026. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(^b.(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(^y.(y a))) 3. ==[ beta ]==> ((((a a) a)(a a))(^y.(y a))) 4. ==[ alpha ]==> ((((a a) a)(a a))(^x.(x a))) REDUCED to normal form. ------ 194018/22969239. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194019/22969800. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194020/22970052. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194021/22970400. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(^y1.y1))(a (a a)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194022/22971123. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.b))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.b))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.b))) REDUCED to normal form. ------ 194023/22971321. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.y))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.y))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.x))) REDUCED to normal form. ------ 194024/22971510. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(^z1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.b))) REDUCED to normal form. ------ 194025/22971642. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^z.(^x1.x1))((^y1.y1)(^z1.z1)))(((^z.(^x1.x1))((^y1.y1)(^z1.z1)))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))(^z2.z2))) 5. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))(^z2.z2))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))((^x1.x1)(^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(^y1.y1)))(^z1.z1)) 8. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.y1)) 9. ==[ beta ]==> ((^y.y)(^y1.y1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194026/22972617. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 194027/22972725. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 194028/22972806. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^z.a)) REDUCED to normal form. ------ 194029/22972965. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a (^y1.a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194030/22972968. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(^y1.x1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 194031/22973367. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 194032/22973457. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))(b (a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)(b (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 194033/22973484. ------ 1. ==[ start ]==> ((a (^b.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 194034/22973520. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((^y.(y (^z.z))) b) 6. ==[ alpha ]==> ((^x.(x (^y.y))) b) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194035/22973565. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.a)((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.a)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 194036/22973592. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 194037/22973646. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> (a ((a (^y.(^z.z)))((a a) a))) 6. ==[ alpha ]==> (a ((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 194038/22973673. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((b a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((b a)(a b))) 3. ==[ beta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 194039/22973727. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.(x x)))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 194040/22973835. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.(y y))((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))((a (a a))((a a)(a a)))) 5. ==[ beta ]==> (((a (a a))((a a)(a a)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 194041/22973862. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 194042/22973916. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(a (a (^z.z))))) 5. ==[ beta ]==> ((^y.y)((a a)(a (a (^z.z))))) 6. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 7. ==[ beta ]==> ((a a)(a (a (^y.y)))) 8. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 194043/22973952. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 194044/22973979. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 194045/22974006. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 194046/22974033. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 194047/22974069. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 194048/22974096. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 194049/22974141. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a)(^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((b b)(((a a)(^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((b b)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 194050/22974177. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 194051/22974276. ------ 1. ==[ start ]==> (((a (a a)) b)((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 194052/22974357. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 194053/22974384. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (a (^z.z))) a)) 3. ==[ beta ]==> ((a (^y.a))((a (a (^z.z))) a)) 4. ==[ alpha ]==> ((a (^x.a))((a (a (^y.y))) a)) REDUCED to normal form. ------ 194054/22974411. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1) b)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z) b)) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 194055/22974438. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((b (^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))((b (^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z)) c)) 5. ==[ beta ]==> ((^y.y)((b (^z.z)) c)) 6. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 7. ==[ beta ]==> ((b (^y.y)) c) 8. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 194056/22974501. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(^z.z))) REDUCED to normal form. ------ 194057/22974609. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(a a)) REDUCED to normal form. ------ 194058/22974780. ------ 1. ==[ start ]==> (((^a.a)((a a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)((a a) a))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a) a)(b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a a) a)(b ((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 194059/22974807. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(a (a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a (a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (a (a (^y.y))))) 5. ==[ beta ]==> (a (a (a (^y.y)))) 6. ==[ alpha ]==> (a (a (a (^x.x)))) REDUCED to normal form. ------ 194060/22974816. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.x1))) REDUCED to normal form. ------ 194061/22974861. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((b (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a a)((b (^y.y))(a (^z.z)))) 8. ==[ alpha ]==> ((a a)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 194062/22974942. ------ 1. ==[ start ]==> ((a (^a.b))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.b))((a (^y.(^z.z)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 194063/22975131. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((^y.b)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((^x.b)((a (a a))((^y.y) b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 194064/22975212. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a a)((^z.(^x1.x1)) a))) IRREDUCIBLE: cycle. ------ 194065/22975275. ------ 1. ==[ start ]==> ((((a a) a) b)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 194066/22975302. ------ 1. ==[ start ]==> (((a b) a)(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a b) a)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 194067/22975329. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.b))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.b))(b (^y.(y y)))) REDUCED to normal form. ------ 194068/22975383. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 194069/22975410. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 194070/22975437. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.a)(((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.a)(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 194071/22975464. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 194072/22975527. ------ 1. ==[ start ]==> (((a a)(a b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 194073/22975554. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(b ((^z.z) b))) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))(b ((^y.y) b))) 7. ==[ beta ]==> (((a (^x.x))((a a) a))(b b)) REDUCED to normal form. ------ 194074/22975581. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)((a a)(a a)))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 194075/22975608. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 194076/22975635. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((^y.y) a)((^z.z)((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (a ((^y.y)((^z.(^x1.x1)) a))) 8. ==[ alpha ]==> (a ((^x.x)((^y.(^z.z)) a))) 9. ==[ beta ]==> (a ((^y.(^z.z)) a)) 10. ==[ alpha ]==> (a ((^x.(^y.y)) a)) 11. ==[ beta ]==> (a (^y.y)) 12. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 194077/22975680. ------ 1. ==[ start ]==> (((^a.b) b)((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b) b)((b (^y.y)) b)) 3. ==[ beta ]==> (b ((b (^y.y)) b)) 4. ==[ alpha ]==> (b ((b (^x.x)) b)) REDUCED to normal form. ------ 194078/22976022. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))(b (b (^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(b (b (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(b (b (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(b (b (^x1.x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(b (b (^x1.x1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(b (b (^z.z)))) 9. ==[ beta ]==> ((^y.y)(b (b (^z.z)))) 10. ==[ alpha ]==> ((^x.x)(b (b (^y.y)))) 11. ==[ beta ]==> (b (b (^y.y))) 12. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 194079/22976103. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> (b (((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (b (((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 194080/22976112. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a)) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 194081/22976427. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 194082/22976571. ------ 1. ==[ start ]==> (((a b) c)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 194083/22976598. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 194084/22976625. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(^z.b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)(^y.b))) REDUCED to normal form. ------ 194085/22976679. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 194086/22976760. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194087/22976841. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((b (^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b (^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 194088/22976868. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(a a)) b)) REDUCED to normal form. ------ 194089/22976904. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.a)) REDUCED to normal form. ------ 194090/22976931. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 194091/22977012. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(^z1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(^y1.b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.b))) 7. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.b))) 8. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.b))) 9. ==[ beta ]==> ((^y.(a a))(^z.b)) 10. ==[ alpha ]==> ((^x.(a a))(^y.b)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194092/22977039. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.b)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (a a))) b) REDUCED to normal form. ------ 194093/22977066. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b) a) a) REDUCED to normal form. ------ 194094/22977120. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(^x1.(^y1.y1)))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 194095/22977147. ------ 1. ==[ start ]==> ((a (b a))((^b.a)(^b.b))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(^y.y))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 194096/22977237. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(((a a)(a a))(a a))) 3. ==[ beta ]==> (((^y.b)(^y.b))(((a a)(a a))(a a))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(a a))(a a))) 5. ==[ beta ]==> (b (((a a)(a a))(a a))) REDUCED to normal form. ------ 194097/22977318. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((b a)(a (a a)))) 3. ==[ beta ]==> (b ((b a)(a (a a)))) REDUCED to normal form. ------ 194098/22977426. ------ 1. ==[ start ]==> (((^a.a)(b a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> ((b a)(((a a) a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((b a)(((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> ((b a)(((a a) a)(a a))) REDUCED to normal form. ------ 194099/22977453. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.z))) 7. ==[ beta ]==> ((^y.y)((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 194100/22977507. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a b)(a b))(a (a (^y.(^z.z))))) 6. ==[ alpha ]==> (((a b)(a b))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 194101/22977597. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 194102/22977624. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 194103/22977651. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) REDUCED to normal form. ------ 194104/22977714. ------ 1. ==[ start ]==> (((a a)(b a))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b a))(^y.y)) 4. ==[ alpha ]==> (((a a)(b a))(^x.x)) REDUCED to normal form. ------ 194105/22977741. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 194106/22977768. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.b)(a b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.b)(a b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.b)(a b))) 5. ==[ beta ]==> ((a (a a))((^y.b)(a b))) 6. ==[ alpha ]==> ((a (a a))((^x.b)(a b))) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 194107/22977795. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(a b)) a) REDUCED to normal form. ------ 194108/22977822. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 194109/22977849. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(z z))(b a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(y y))(b a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))((b a)(b a))) REDUCED to normal form. ------ 194110/22977876. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 194111/22977903. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((^z.z) b))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 194112/22977930. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((a a)(a a))) REDUCED to normal form. ------ 194113/22977975. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1) b) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194114/22977984. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.x1))) REDUCED to normal form. ------ 194115/22978263. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))(b ((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194116/22978290. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(a ((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a ((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 194117/22978317. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a a))) 5. ==[ beta ]==> (((^y.y) b)(a a)) 6. ==[ alpha ]==> (((^x.x) b)(a a)) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 194118/22978371. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((b a)((^z.z) a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((b a)((^z.z) a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((b a)((^z.z) a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((b a)((^z.z) a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b a)((^y.y) a))) 7. ==[ beta ]==> (((a a)(a a))((b a)((^y.y) a))) 8. ==[ alpha ]==> (((a a)(a a))((b a)((^x.x) a))) 9. ==[ beta ]==> (((a a)(a a))((b a) a)) REDUCED to normal form. ------ 194119/22978452. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a b)((a a) a))) 3. ==[ beta ]==> (b ((a b)((a a) a))) REDUCED to normal form. ------ 194120/22978560. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194121/22978587. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 194122/22978605. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(b (^b.b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(b (^z.z))) REDUCED to normal form. ------ 194123/22978632. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(a (^y.(a a)))) REDUCED to normal form. ------ 194124/22978659. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((^z.z)(a a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(a a))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 194125/22978686. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 194126/22978767. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 194127/22978794. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.b)((a a) a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.b)((a a) a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.b)((a a) a))) 5. ==[ beta ]==> (((a a)(a (a a))) b) REDUCED to normal form. ------ 194128/22978866. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194129/22978875. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(((a a)(^x1.x1))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((a a)(^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 194130/22978902. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.a)(b a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(b a))) 3. ==[ beta ]==> ((a b)((^y.a)(b a))) 4. ==[ alpha ]==> ((a b)((^x.a)(b a))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 194131/22979235. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))(c (b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))(c (b a))) 3. ==[ beta ]==> (((^y.y) b)(c (b a))) 4. ==[ alpha ]==> (((^x.x) b)(c (b a))) 5. ==[ beta ]==> (b (c (b a))) REDUCED to normal form. ------ 194132/22979262. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))(b (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(b (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(b (a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 194133/22979316. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 194134/22979379. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z)) d)) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 194135/22979397. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (b (((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> (b ((a a)(a (a a)))) REDUCED to normal form. ------ 194136/22979505. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a (a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194137/22979577. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b)(b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a) b)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 194138/22979604. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 194139/22979631. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 194140/22979712. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a b))(a a)) REDUCED to normal form. ------ 194141/22979739. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)((a a) a)) b) REDUCED to normal form. ------ 194142/22979793. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 194143/22979847. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) a) REDUCED to normal form. ------ 194144/22979874. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 194145/22979901. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a (^y.(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 194146/22980180. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(b (b a))) 3. ==[ beta ]==> ((^y.(^z.z))(b (b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194147/22980216. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((b b)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((b b)((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 194148/22980261. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 194149/22980288. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((^z.z) a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.z) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.y) a)) 7. ==[ beta ]==> ((a a)((^y.y) a)) 8. ==[ alpha ]==> ((a a)((^x.x) a)) 9. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 194150/22980342. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((b a)(b a))(((a a) a)(^y.y))) 6. ==[ alpha ]==> (((b a)(b a))(((a a) a)(^x.x))) REDUCED to normal form. ------ 194151/22980423. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> (b (((^y.y) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y)(a a)))) 5. ==[ beta ]==> (b (a ((^y.y)(a a)))) 6. ==[ alpha ]==> (b (a ((^x.x)(a a)))) 7. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 194152/22980540. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a)(^x1.x1))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 194153/22980567. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a a)(^x1.a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 194154/22980594. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a b)(^y.(y y)))) REDUCED to normal form. ------ 194155/22980657. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 194156/22980684. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))(a b))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a b)(a b))) REDUCED to normal form. ------ 194157/22980711. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 194158/22980738. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((a a)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 194159/22980765. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.y)(b a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.y)(b a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.x)(b a))) 5. ==[ beta ]==> ((((a a) a)(a a))(b a)) REDUCED to normal form. ------ 194160/22980846. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 194161/22980927. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 194162/22980954. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(x x))(^y.b))) 3. ==[ beta ]==> ((((a a)(a a))(a a))((^y.b)(^y.b))) 4. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b)(^y.b))) 5. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 194163/22980981. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 194164/22981071. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(((a a)(^x2.x2))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x2.x2))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194165/22981152. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> (b (((a a) a)(a (a a)))) REDUCED to normal form. ------ 194166/22981260. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194167/22981323. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 194168/22981431. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 194169/22981539. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 194170/22981566. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a)(^z.z)) a)) 3. ==[ beta ]==> (((a a)(^y.b))(((a a)(^z.z)) a)) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 194171/22981764. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 194172/22982061. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(a a))(a a))) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(a a))(a a))) 5. ==[ beta ]==> ((b a)((^y.(a a))(a a))) 6. ==[ alpha ]==> ((b a)((^x.(a a))(a a))) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 194173/22982088. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 194174/22982142. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 194175/22982421. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(c ((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194176/22982556. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) a)) 9. ==[ beta ]==> ((^y.y)((^z.z) a)) 10. ==[ alpha ]==> ((^x.x)((^y.y) a)) 11. ==[ beta ]==> ((^y.y) a) 12. ==[ alpha ]==> ((^x.x) a) 13. ==[ beta ]==> a REDUCED to normal form. ------ 194177/22982583. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a (a a)))) 5. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 194178/22982637. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (^z.z))((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (^z.z))((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (^y.y))((a a) a))) 7. ==[ beta ]==> ((b b)((a (^y.y))((a a) a))) 8. ==[ alpha ]==> ((b b)((a (^x.x))((a a) a))) REDUCED to normal form. ------ 194179/22982727. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 194180/22982754. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(^z.a)) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.a)) REDUCED to normal form. ------ 194181/22982781. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 194182/22982835. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))(^z1.a))) REDUCED to normal form. ------ 194183/22982862. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)(^z.b))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)(^z.b))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)(^y.b))) REDUCED to normal form. ------ 194184/22982889. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a b) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a b) a)) REDUCED to normal form. ------ 194185/22982979. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.(z z))(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 194186/22983006. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 194187/22983060. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.y)(^z.b))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(^z.b))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.b))) 5. ==[ beta ]==> (((a (a a)) b)(^y.b)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.b)) REDUCED to normal form. ------ 194188/22983195. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 194189/22983249. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a (^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a (^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a (^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.b))) REDUCED to normal form. ------ 194190/22983276. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^c.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a)(a a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.a)(a a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a)(a a))) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 194191/22983303. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 194192/22983357. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((a a)((^y.a)(a (a a)))) 6. ==[ alpha ]==> ((a a)((^x.a)(a (a a)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 194193/22983375. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 194194/22983384. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 194195/22983780. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a (a a))(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 194196/22983807. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a (^z.a))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(a (^y.a))) REDUCED to normal form. ------ 194197/22983834. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 194198/22983942. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a) c)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a) c)) 5. ==[ beta ]==> ((^y.y)(((^z.z) a) c)) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a) c)) 7. ==[ beta ]==> (((^y.y) a) c) 8. ==[ alpha ]==> (((^x.x) a) c) 9. ==[ beta ]==> (a c) REDUCED to normal form. ------ 194199/22983987. ------ 1. ==[ start ]==> (((^a.b)(b a))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(b (a (a a)))) 3. ==[ beta ]==> (b (b (a (a a)))) REDUCED to normal form. ------ 194200/22984050. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(z z)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(b b)) REDUCED to normal form. ------ 194201/22984095. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194202/22984158. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 194203/22984212. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194204/22984239. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a)(^z.(z z)))) REDUCED to normal form. ------ 194205/22984275. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 6. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 194206/22984302. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 194207/22984329. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 194208/22984356. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.(y y))) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(x x))) REDUCED to normal form. ------ 194209/22984437. ------ 1. ==[ start ]==> (((a b)(b a))(b (^b.a))) 2. ==[ alpha ]==> (((a b)(b a))(b (^x.a))) REDUCED to normal form. ------ 194210/22984464. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a (^z.(z z)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a (^z.(z z)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.(y y)))) REDUCED to normal form. ------ 194211/22984491. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.a)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 194212/22984545. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a)) a) REDUCED to normal form. ------ 194213/22984572. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))((^z.a)(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.z))) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 194214/22984599. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 194215/22984671. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 194216/22984680. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(b (^y.(^z.z)))) REDUCED to normal form. ------ 194217/22984707. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a (^x1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.a))) REDUCED to normal form. ------ 194218/22984716. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(c a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(c a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(c a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(c a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194219/22984743. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(b b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(b b)) 3. ==[ beta ]==> ((^y.y)(b b)) 4. ==[ alpha ]==> ((^x.x)(b b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194220/22984878. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(b a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(b a)) 3. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 194221/22985223. ------ 1. ==[ start ]==> ((^a.(^b.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 194222/22995996. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(a (a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194223/22996446. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194224/22996806. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194225/22996968. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^x.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194226/22996971. ------ 1. ==[ start ]==> ((a (^b.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 194227/22997430. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 194228/22997535. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194229/22998294. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 194230/22998303. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) REDUCED to normal form. ------ 194231/22998993. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.a)(b a))) 3. ==[ beta ]==> (^y.(((^z.a)(b a))((^z.a)(b a)))) 4. ==[ alpha ]==> (^x.(((^y.a)(b a))((^z.a)(b a)))) 5. ==[ beta ]==> (^x.(a ((^z.a)(b a)))) 6. ==[ alpha ]==> (^x.(a ((^y.a)(b a)))) 7. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 194232/22999545. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.((^y1.(^z1.z1)) x1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(^z.(z z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> (((^y.y)(^z.(z z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.(y y)))(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 9. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194233/23001057. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.((a a)(a a)))) REDUCED to normal form. ------ 194234/23001468. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a) b) b)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1) b) b)) 3. ==[ beta ]==> ((((^x1.x1) b) b)(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x) b) b)(^y.(^z.z))) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 194235/23001777. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 194236/23001786. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.((x1 x1)(x1 x1)))) REDUCED to normal form. ------ 194237/23002071. ------ 1. ==[ start ]==> ((^a.(^b.b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194238/23003385. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^y.(^z.(^x1.x1))))((a a)(^y.(^z.(^x1.x1)))))(((a a)(^y.(^z.(^x1.x1))))((a a)(^y.(^z.(^x1.x1)))))) 4. ==[ alpha ]==> ((((a a)(^x.(^y.(^z.z))))((a a)(^x1.(^y1.(^z1.z1)))))(((a a)(^x2.(^y2.(^z2.z2))))((a a)(^x3.(^y3.(^z3.z3)))))) REDUCED to normal form. ------ 194239/23003703. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> ((b b)(^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b b)(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 194240/23003973. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(^c.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.(b a))) REDUCED to normal form. ------ 194241/23004783. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.((a a)(^z.z)))) 3. ==[ beta ]==> ((b c)(^y.((a a)(^z.z)))) 4. ==[ alpha ]==> ((b c)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 194242/23005626. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194243/23006445. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 194244/23006868. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^z.z))(^x1.(^y1.y1)))(((a (^z.z))(^x1.(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a (^x1.x1))(^y1.(^z1.z1)))(^x2.x2))) REDUCED to normal form. ------ 194245/23007618. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^c.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(a (a a)))) REDUCED to normal form. ------ 194246/23007741. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(a (a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194247/23007744. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(a (a a)))) REDUCED to normal form. ------ 194248/23008194. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.c)) REDUCED to normal form. ------ 194249/23008203. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194250/23008365. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b (^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 194251/23008557. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 194252/23008611. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194253/23008692. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194254/23008701. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (a (a (^z.z))))) REDUCED to normal form. ------ 194255/23008719. ------ 1. ==[ start ]==> ((a (^b.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194256/23008737. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 194257/23008755. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((a (a (^z.z)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a (^y.y)))(a a)) 6. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 194258/23008764. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.y))) REDUCED to normal form. ------ 194259/23008836. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 194260/23008863. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 194261/23008890. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 194262/23008917. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b a)(a b))) REDUCED to normal form. ------ 194263/23008944. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 194264/23009052. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a a)(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a a)((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a a)((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a a)((^y.y) b)) 8. ==[ alpha ]==> ((a a)((^x.x) b)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 194265/23009133. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a b)((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a b)((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a b)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((a b)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 194266/23009151. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(b (^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 7. ==[ beta ]==> (b (^y.(y (^z.z)))) 8. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 194267/23009160. ------ 1. ==[ start ]==> (((a (a a)) a)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 194268/23009178. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 194269/23009205. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(a a)) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(a a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 194270/23009286. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(a (a a)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 194271/23009304. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 194272/23009358. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((b a)(^z.b))) 3. ==[ beta ]==> ((a (a (^y.y)))((b a)(^z.b))) 4. ==[ alpha ]==> ((a (a (^x.x)))((b a)(^y.b))) REDUCED to normal form. ------ 194273/23009385. ------ 1. ==[ start ]==> (((a (a a))(a a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 194274/23009421. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194275/23009448. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 194276/23009502. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))((^x2.x2) b))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194277/23009556. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 7. ==[ beta ]==> ((^y.a)(b (^z.z))) 8. ==[ alpha ]==> ((^x.a)(b (^y.y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 194278/23009583. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194279/23009637. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^y1.y1)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 194280/23009934. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 194281/23010042. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 7. ==[ beta ]==> (^y.(y (^z.z))) 8. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 194282/23010051. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (a (a (^x1.x1))))) REDUCED to normal form. ------ 194283/23010078. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((a (^y.(y y)))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a)(a a))) 5. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 194284/23010105. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 194285/23010132. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))((^z.z) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194286/23010159. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(b (a (a a)))) REDUCED to normal form. ------ 194287/23010348. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 194288/23010555. ------ 1. ==[ start ]==> (((^a.a)(a b))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a b))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((a b)((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((a b)((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 194289/23010582. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (a a)))) 5. ==[ beta ]==> ((^y.y)(a (a a))) 6. ==[ alpha ]==> ((^x.x)(a (a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 194290/23010717. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (b ((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194291/23010744. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.a)(b a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.a)(b a))) 3. ==[ beta ]==> ((a (^x.(a a))) a) REDUCED to normal form. ------ 194292/23010762. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a b))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a b))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 194293/23010789. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (a a))(^y.y))) REDUCED to normal form. ------ 194294/23010897. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((^z.z) a)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y) a)) 5. ==[ beta ]==> ((((a a) a)(a (^x.x))) a) REDUCED to normal form. ------ 194295/23010924. ------ 1. ==[ start ]==> (((a b)(a a))((b (^a.a)) b)) 2. ==[ alpha ]==> (((a b)(a a))((b (^x.x)) b)) REDUCED to normal form. ------ 194296/23010960. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.(a a))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(a a))(^z.a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194297/23010987. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(z z))) 6. ==[ alpha ]==> ((^x.x)(^y.(y y))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 194298/23011122. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194299/23011176. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 194300/23011203. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((^y.(y y))(^z.z)) 6. ==[ alpha ]==> ((^x.(x x))(^y.y)) 7. ==[ beta ]==> ((^y.y)(^y.y)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194301/23011266. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(b (b (^z.z)))) REDUCED to normal form. ------ 194302/23011293. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(a ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(a ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(a ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.(y y))(a ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((^x.(x x))(a ((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a ((^y.(^z.z)) a))(a ((^y.(^z.z)) a))) 8. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(a ((^z.(^x1.x1)) a))) 9. ==[ beta ]==> ((a (^y.y))(a ((^z.(^x1.x1)) a))) 10. ==[ alpha ]==> ((a (^x.x))(a ((^y.(^z.z)) a))) 11. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 12. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 194303/23011320. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((b (^y.y))(a a))) REDUCED to normal form. ------ 194304/23011347. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(a a))(a (^z.z)))) REDUCED to normal form. ------ 194305/23011374. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))(b ((^z.z) a))) 6. ==[ alpha ]==> (((a a)(^x.x))(b ((^y.y) a))) 7. ==[ beta ]==> (((a a)(^x.x))(b a)) REDUCED to normal form. ------ 194306/23011563. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (b ((^y.y)(b a))) 6. ==[ alpha ]==> (b ((^x.x)(b a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 194307/23011797. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 194308/23011878. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(a b))) 5. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 194309/23011905. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 194310/23011959. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.x)) REDUCED to normal form. ------ 194311/23012040. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194312/23012139. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) b) c)) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(b c)) REDUCED to normal form. ------ 194313/23012616. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((a a)((a a) a))) REDUCED to normal form. ------ 194314/23012724. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (a a))(b a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (a a))(b a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (a a))(b a))) REDUCED to normal form. ------ 194315/23012751. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^x.b))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 194316/23012805. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 194317/23012949. ------ 1. ==[ start ]==> (((a a)(b a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 194318/23013003. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a b)(^z.b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a b)(^z.b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a b)(^y.b))) 5. ==[ beta ]==> ((a (a a))((a b)(^y.b))) 6. ==[ alpha ]==> ((a (a a))((a b)(^x.b))) REDUCED to normal form. ------ 194319/23013030. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 194320/23013111. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x) a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a (a a)))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(a (a a)))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 194321/23013138. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.y))(^z.z))) 5. ==[ beta ]==> (((a a) a)((a (^y.y))(^z.z))) 6. ==[ alpha ]==> (((a a) a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 194322/23013219. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a) b) b)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) b) b)) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(b b)) REDUCED to normal form. ------ 194323/23013228. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194324/23013309. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 194325/23013390. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 194326/23013498. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194327/23013507. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)(b ((^z.z) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(b b)) REDUCED to normal form. ------ 194328/23013534. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(a ((a a)(a a)))) REDUCED to normal form. ------ 194329/23013615. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((b a)((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))((b a) a)) REDUCED to normal form. ------ 194330/23013642. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.b)(((a a)(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(a (a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 194331/23013696. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)((a a) a))) REDUCED to normal form. ------ 194332/23013723. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((a a) a)(a b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a) a)(a b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)(a b))) REDUCED to normal form. ------ 194333/23013750. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(a a))) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 194334/23013804. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (b a))) REDUCED to normal form. ------ 194335/23013822. ------ 1. ==[ start ]==> ((a (^b.b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 194336/23013894. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(b (^z.z))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 194337/23013921. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 194338/23013948. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((b a)(^z.a))) 3. ==[ beta ]==> (((^y.y)(a b))((b a)(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a b))((b a)(^y.a))) 5. ==[ beta ]==> ((a b)((b a)(^y.a))) 6. ==[ alpha ]==> ((a b)((b a)(^x.a))) REDUCED to normal form. ------ 194339/23013975. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 194340/23014002. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.x))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 194341/23014029. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a b)(^y.a))) 3. ==[ beta ]==> (((a a)(a (a a)))((a b)(^y.a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a b)(^x.a))) REDUCED to normal form. ------ 194342/23014056. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((a a) a)(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a) a)(^z.b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a) a)(^y.b))) REDUCED to normal form. ------ 194343/23014146. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(b a))) 3. ==[ beta ]==> ((^y.y)((^z.a)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b a))) 5. ==[ beta ]==> ((^y.a)(b a)) 6. ==[ alpha ]==> ((^x.a)(b a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 194344/23014173. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))(a (^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194345/23014308. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194346/23014416. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194347/23014479. ------ 1. ==[ start ]==> (((a a)(^b.b))(c (b a))) 2. ==[ alpha ]==> (((a a)(^x.x))(c (b a))) REDUCED to normal form. ------ 194348/23014497. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194349/23014506. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(b (a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 194350/23014587. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((b a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((b a)(a (^z.z)))) 6. ==[ alpha ]==> ((^x.(a a))((b a)(a (^y.y)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194351/23014614. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 194352/23014641. ------ 1. ==[ start ]==> (((a b)(^c.a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.a))((a a)(a (a a)))) REDUCED to normal form. ------ 194353/23014668. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a b)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 194354/23014695. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 194355/23014749. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))(a a))) REDUCED to normal form. ------ 194356/23014776. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)((a a)(^z.z)))) 5. ==[ beta ]==> ((b (^x.x))(a ((a a)(^z.z)))) 6. ==[ alpha ]==> ((b (^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 194357/23014866. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (b a))((a (^y.(^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a (b a))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 194358/23014893. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 194359/23014920. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a)(^z.z))(^x1.a))) 6. ==[ alpha ]==> (((^x.x)(a a))(((a a)(^y.y))(^z.a))) 7. ==[ beta ]==> ((a a)(((a a)(^y.y))(^z.a))) 8. ==[ alpha ]==> ((a a)(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 194360/23014947. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(a b))((a a)(^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a)(a b))((a a)(^x.(x x)))) REDUCED to normal form. ------ 194361/23014974. ------ 1. ==[ start ]==> (((a b)((a a) a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 194362/23015028. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((^z.z)(^x1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.y)(^z.b))) 5. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.b)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.b)) REDUCED to normal form. ------ 194363/23015136. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 194364/23015172. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194365/23015307. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b ((^z.a)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 194366/23015451. ------ 1. ==[ start ]==> ((((^a.a) b) b)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) b)(a (a (^y.(^z.z))))) 3. ==[ beta ]==> ((b b)(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> ((b b)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 194367/23015478. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((b a)(a a))) REDUCED to normal form. ------ 194368/23015532. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a) a)) REDUCED to normal form. ------ 194369/23015559. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((a b)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((a b)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a b)(a (a a)))) REDUCED to normal form. ------ 194370/23015640. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a (a a))(a b))) REDUCED to normal form. ------ 194371/23015667. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.b))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((a b)(^x.b))(a ((^y.y)(a a)))) 5. ==[ beta ]==> (((a b)(^x.b))(a (a a))) REDUCED to normal form. ------ 194372/23015721. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(b a))) REDUCED to normal form. ------ 194373/23015865. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 194374/23015892. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(^x1.a))) 6. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.a))) 7. ==[ beta ]==> (((a (^x.x)) b)(^z.a)) 8. ==[ alpha ]==> (((a (^x.x)) b)(^y.a)) REDUCED to normal form. ------ 194375/23015919. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a (a a))(^x1.b))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (a a))(^x1.b))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (a a))(^z.b))) REDUCED to normal form. ------ 194376/23015946. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> (((a (a a))(b a))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a (a a))(b a))(a (^x.(a a)))) REDUCED to normal form. ------ 194377/23016027. ------ 1. ==[ start ]==> (((a b)(a b))((b a) a)) REDUCED to normal form. ------ 194378/23016054. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((a a)(^y.y)) b)) 3. ==[ beta ]==> (((a a)((a a) a))(((a a)(^y.y)) b)) 4. ==[ alpha ]==> (((a a)((a a) a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 194379/23016531. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a a)((a a)(^y.y)))) 3. ==[ beta ]==> ((b c)((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((b c)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 194380/23016603. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 194381/23016630. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.y)((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z) a))) 5. ==[ beta ]==> ((^y.b)((^z.z) a)) 6. ==[ alpha ]==> ((^x.b)((^y.y) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 194382/23016684. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2)(^y2.y2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.z1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 194383/23016765. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194384/23016873. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194385/23017053. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a b)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a b)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 194386/23017080. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(a a)) b)) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 194387/23017107. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.b) c)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.b) c)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.b) c)) 5. ==[ beta ]==> ((b a)((^y.b) c)) 6. ==[ alpha ]==> ((b a)((^x.b) c)) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 194388/23017296. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> ((b a)(((^y.y)(a a))(^z.z))) 6. ==[ alpha ]==> ((b a)(((^x.x)(a a))(^y.y))) 7. ==[ beta ]==> ((b a)((a a)(^y.y))) 8. ==[ alpha ]==> ((b a)((a a)(^x.x))) REDUCED to normal form. ------ 194389/23017323. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 194390/23017377. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 194391/23017467. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a b))) 7. ==[ beta ]==> ((^y.(^z.z))(a b)) 8. ==[ alpha ]==> ((^x.(^y.y))(a b)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194392/23017548. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194393/23017656. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194394/23017773. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(a (^y.y)))) 5. ==[ beta ]==> (a (((a a) a)(a (^y.y)))) 6. ==[ alpha ]==> (a (((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 194395/23017872. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c (^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c (^z.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c (^z.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c (^z.a))) 5. ==[ beta ]==> ((b ((^y.y) b))(c (^z.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(c (^y.a))) 7. ==[ beta ]==> ((b b)(c (^y.a))) 8. ==[ alpha ]==> ((b b)(c (^x.a))) REDUCED to normal form. ------ 194396/23017881. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 194397/23017908. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a a)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(a b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(a b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(a b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194398/23017953. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.b)(a a))) 3. ==[ beta ]==> (b ((^z.b)(a a))) 4. ==[ alpha ]==> (b ((^x.b)(a a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194399/23018061. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.a)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194400/23018196. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 194401/23018322. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.b) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.b) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.b) a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b) a)) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 194402/23018349. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^c.a) b)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a) b)) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 194403/23018376. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 194404/23018511. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((a a) a)(^y.y))) 3. ==[ beta ]==> ((b (a (a a)))(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((b (a (a a)))(((a a) a)(^x.x))) REDUCED to normal form. ------ 194405/23018538. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.z))) 8. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 194406/23018592. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(^z.(z z)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(a (^y.(y y)))) 8. ==[ alpha ]==> ((a a)(a (^x.(x x)))) REDUCED to normal form. ------ 194407/23018619. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 194408/23018628. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((^z.(^x1.x1))((^y1.y1)(^z1.z1)))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(^y1.y1)) 7. ==[ beta ]==> ((^y.y)(^y1.y1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194409/23019033. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.z)))) 7. ==[ beta ]==> ((^y.(y y))(a (^z.z))) 8. ==[ alpha ]==> ((^x.(x x))(a (^y.y))) 9. ==[ beta ]==> ((a (^y.y))(a (^y.y))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 194410/23019060. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 194411/23019087. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194412/23019141. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 194413/23019222. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194414/23019285. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (a a))(a a))) REDUCED to normal form. ------ 194415/23019366. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(a (a a)))) REDUCED to normal form. ------ 194416/23019465. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 194417/23019492. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (a a))) REDUCED to normal form. ------ 194418/23019510. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (a a)) a)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (a a)) a)) REDUCED to normal form. ------ 194419/23019537. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(((^x1.x1) a) b)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a) b)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a) b)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a b)) REDUCED to normal form. ------ 194420/23019564. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z)) c)) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z)) c)) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y)) c)) REDUCED to normal form. ------ 194421/23019618. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(z z)) a)) 5. ==[ beta ]==> (((^y.y) b)((^z.(z z)) a)) 6. ==[ alpha ]==> (((^x.x) b)((^y.(y y)) a)) 7. ==[ beta ]==> (b ((^y.(y y)) a)) 8. ==[ alpha ]==> (b ((^x.(x x)) a)) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 194422/23019645. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^b.a) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.a) b)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 194423/23019672. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y)) c)) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 194424/23019726. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 194425/23019780. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a a)(^z.a))) REDUCED to normal form. ------ 194426/23019807. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(((^x1.x1) a) a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(((^x1.x1) a) a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(((^z.z) a) a)) 5. ==[ beta ]==> ((b (^y.y))(((^z.z) a) a)) 6. ==[ alpha ]==> ((b (^x.x))(((^y.y) a) a)) 7. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 194427/23019834. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a (^x.x)) b)) REDUCED to normal form. ------ 194428/23019888. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^b.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.a) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.a) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a) a)) 5. ==[ beta ]==> ((a (^y.y))((^z.a) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.a) a)) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 194429/23019906. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a (^z.z))(a a))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(a a))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 194430/23019915. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 194431/23019951. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a (^y1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194432/23019978. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(a a)) 6. ==[ alpha ]==> ((^x.(^y.y))(a a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194433/23020113. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 194434/23031240. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194435/23032242. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194436/23032293. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ eta ]==> ((^y.y)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 194437/23032563. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^x1.x1) b))((((^y.y)(^z.z))((^x1.x1) b))(((^y.y)(^z.z))((^x1.x1) b)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((((^x1.x1)(^y1.y1))((^z1.z1) b))(((^x2.x2)(^y2.y2))((^z2.z2) b)))) 5. ==[ beta ]==> (((^y.y)((^z.z) b))((((^x1.x1)(^y1.y1))((^z1.z1) b))(((^x2.x2)(^y2.y2))((^z2.z2) b)))) 6. ==[ alpha ]==> (((^x.x)((^y.y) b))((((^z.z)(^x1.x1))((^y1.y1) b))(((^z1.z1)(^x2.x2))((^y2.y2) b)))) 7. ==[ beta ]==> (((^y.y) b)((((^z.z)(^x1.x1))((^y1.y1) b))(((^z1.z1)(^x2.x2))((^y2.y2) b)))) 8. ==[ alpha ]==> (((^x.x) b)((((^y.y)(^z.z))((^x1.x1) b))(((^y1.y1)(^z1.z1))((^x2.x2) b)))) 9. ==[ beta ]==> (b ((((^y.y)(^z.z))((^x1.x1) b))(((^y1.y1)(^z1.z1))((^x2.x2) b)))) 10. ==[ alpha ]==> (b ((((^x.x)(^y.y))((^z.z) b))(((^x1.x1)(^y1.y1))((^z1.z1) b)))) 11. ==[ beta ]==> (b (((^y.y)((^z.z) b))(((^x1.x1)(^y1.y1))((^z1.z1) b)))) 12. ==[ alpha ]==> (b (((^x.x)((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) b)))) 13. ==[ beta ]==> (b (((^y.y) b)(((^z.z)(^x1.x1))((^y1.y1) b)))) 14. ==[ alpha ]==> (b (((^x.x) b)(((^y.y)(^z.z))((^x1.x1) b)))) 15. ==[ beta ]==> (b (b (((^y.y)(^z.z))((^x1.x1) b)))) 16. ==[ alpha ]==> (b (b (((^x.x)(^y.y))((^z.z) b)))) 17. ==[ beta ]==> (b (b ((^y.y)((^z.z) b)))) 18. ==[ alpha ]==> (b (b ((^x.x)((^y.y) b)))) 19. ==[ beta ]==> (b (b ((^y.y) b))) 20. ==[ alpha ]==> (b (b ((^x.x) b))) 21. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 194438/23032692. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 194439/23032788. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194440/23033124. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.a))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 194441/23033556. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) REDUCED to normal form. ------ 194442/23033859. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))(a (^x1.(^y1.y1)))) b) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1)))) b) 5. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1)))) b) 6. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z)))) b) 7. ==[ beta ]==> ((a (^y.(^z.z))) b) 8. ==[ alpha ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 194443/23035128. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (((((^z.z) a)((^x1.x1) b))(((^z.z) a)((^x1.x1) b)))(^y.y)) 4. ==[ alpha ]==> (((((^x.x) a)((^y.y) b))(((^z.z) a)((^x1.x1) b)))(^y1.y1)) 5. ==[ beta ]==> (((a ((^y.y) b))(((^z.z) a)((^x1.x1) b)))(^y1.y1)) 6. ==[ alpha ]==> (((a ((^x.x) b))(((^y.y) a)((^z.z) b)))(^x1.x1)) 7. ==[ beta ]==> (((a b)(((^y.y) a)((^z.z) b)))(^x1.x1)) 8. ==[ alpha ]==> (((a b)(((^x.x) a)((^y.y) b)))(^z.z)) 9. ==[ beta ]==> (((a b)(a ((^y.y) b)))(^z.z)) 10. ==[ alpha ]==> (((a b)(a ((^x.x) b)))(^y.y)) 11. ==[ beta ]==> (((a b)(a b))(^y.y)) 12. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 194444/23035581. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 194445/23036433. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((b a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194446/23037039. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(^y1.(a a)))) REDUCED to normal form. ------ 194447/23037372. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a (^x.x))(b a))(^y.b)) REDUCED to normal form. ------ 194448/23038956. ------ 1. ==[ start ]==> ((((^a.a) b) b)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b b)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 194449/23040036. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^d.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b c)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 194450/23040306. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 194451/23040558. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.((y y)(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.((y y)(^z.z)))) 6. ==[ alpha ]==> ((a b)(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 194452/23041629. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^b.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(a y))) 3. ==[ eta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 194453/23041827. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.(y1 b))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(y1 b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(x1 b))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z b))) REDUCED to normal form. ------ 194454/23042898. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194455/23042994. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194456/23042997. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(y1 y1)))) REDUCED to normal form. ------ 194457/23043123. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(z (z z)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(z (z z)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(y (y y)))) 7. ==[ beta ]==> (b (^y.(y (y y)))) 8. ==[ alpha ]==> (b (^x.(x (x x)))) REDUCED to normal form. ------ 194458/23043393. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.x1)) 5. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.z)) 7. ==[ beta ]==> ((a (^y.y))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 194459/23043444. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194460/23043456. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.c)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.c)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194461/23043618. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^b.b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> (b (^y1.y1)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194462/23043828. ------ 1. ==[ start ]==> (((^a.a) b)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) b)((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^y.b)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194463/23043882. ------ 1. ==[ start ]==> (((a a) b)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(a a)))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 194464/23043963. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 194465/23043999. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 194466/23044026. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 194467/23044053. ------ 1. ==[ start ]==> ((a ((^a.a) a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a (^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 194468/23044242. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) a)(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a) a)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 194469/23044269. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a b)(b a))) REDUCED to normal form. ------ 194470/23044296. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (a a))(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (a a))(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 194471/23044323. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)((^z.z) b))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)((^y.y) b))) 5. ==[ beta ]==> ((a (a (a a)))((^y.y) b)) 6. ==[ alpha ]==> ((a (a (a a)))((^x.x) b)) 7. ==[ beta ]==> ((a (a (a a))) b) REDUCED to normal form. ------ 194472/23044422. ------ 1. ==[ start ]==> (((a (a a)) a)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 194473/23044449. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 194474/23044467. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(^z.z))) 5. ==[ beta ]==> ((a (a (^y.y)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 194475/23044476. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a)(^z.z))) REDUCED to normal form. ------ 194476/23044521. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((b (^y.y))(^z.a))) 3. ==[ beta ]==> (((a a)(a a))((b (^y.y))(^z.a))) 4. ==[ alpha ]==> (((a a)(a a))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 194477/23044548. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(^z.(z z)))) REDUCED to normal form. ------ 194478/23044683. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194479/23044764. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194480/23044773. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 194481/23044800. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> (a ((^y.(y y))((a a)(a a)))) 6. ==[ alpha ]==> (a ((^x.(x x))((a a)(a a)))) 7. ==[ beta ]==> (a (((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 194482/23044827. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 194483/23044854. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 194484/23044881. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.a))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.a))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((a (^x.a))(a (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.a))(a (a (^y.y)))) REDUCED to normal form. ------ 194485/23044899. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a (a (^z.z))) a)) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a (a (^z.z))) a)) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 194486/23044908. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^y1.y1)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 194487/23045232. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.(y y))(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.(a a)))) 7. ==[ beta ]==> (b ((^y.(a a))(^y.(a a)))) 8. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 194488/23045313. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(x1 (^y1.y1)))) REDUCED to normal form. ------ 194489/23045457. ------ 1. ==[ start ]==> (((a a)((a a) a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))((a (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 194490/23045484. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)((a a) a))) REDUCED to normal form. ------ 194491/23045511. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((a a)(^y.y))(a b))) 3. ==[ beta ]==> ((a (a (a a)))(((a a)(^y.y))(a b))) 4. ==[ alpha ]==> ((a (a (a a)))(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 194492/23045538. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (((a (a a)) a)((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> (((a (a a)) a)((a a)((^x.x)(a a)))) 7. ==[ beta ]==> (((a (a a)) a)((a a)(a a))) REDUCED to normal form. ------ 194493/23045565. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a b)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a b)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^y.y))((a b)((a a)(^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))((a b)((a a)(^y.y)))) REDUCED to normal form. ------ 194494/23045592. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((a a) a)(b a))) REDUCED to normal form. ------ 194495/23045619. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a b))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a b))(a (^x.(^y.y)))) REDUCED to normal form. ------ 194496/23045790. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 194497/23045817. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a b))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> ((a b)(((a a)(a a))(^y.a))) 4. ==[ alpha ]==> ((a b)(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 194498/23045826. ------ 1. ==[ start ]==> (((a a)(^a.b))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 194499/23045844. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(z z))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(y y))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 194500/23045880. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 194501/23045898. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((b a)(^y.a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b a)(^y.a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)(^x.a))) REDUCED to normal form. ------ 194502/23045934. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(a b))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(a b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 194503/23045961. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 194504/23045979. ------ 1. ==[ start ]==> (((^a.b)(a a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 194505/23045988. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.x)) b) REDUCED to normal form. ------ 194506/23046222. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((a a)(a a)) c)) 3. ==[ beta ]==> ((^y.(a a))(((a a)(a a)) c)) 4. ==[ alpha ]==> ((^x.(a a))(((a a)(a a)) c)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194507/23046393. ------ 1. ==[ start ]==> (((a b) b)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b) b) b) REDUCED to normal form. ------ 194508/23046447. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 194509/23046474. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 194510/23046672. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 194511/23046699. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a b))((b a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((b a)(^y.y))) REDUCED to normal form. ------ 194512/23046726. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> ((a ((a a) a))(((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> ((a ((a a) a))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 194513/23046753. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(a a))(a b))) 5. ==[ beta ]==> (((a (a a))(^x.x))((a a)(a b))) REDUCED to normal form. ------ 194514/23046780. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a b)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a a))((a b)((^y.y)(a a)))) 6. ==[ alpha ]==> ((a (a a))((a b)((^x.x)(a a)))) 7. ==[ beta ]==> ((a (a a))((a b)(a a))) REDUCED to normal form. ------ 194515/23046807. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a) a)(((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((((a a) a) a)(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 194516/23046834. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((^z.z)(b a))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.y)(b a))) 5. ==[ beta ]==> (((a b)(a (^x.x)))(b a)) REDUCED to normal form. ------ 194517/23046861. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a (a a))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 194518/23046888. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(a ((^y.y) b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a b)) REDUCED to normal form. ------ 194519/23047059. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 194520/23047068. ------ 1. ==[ start ]==> (((a b) c)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a b) c)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) c)(^x.(^y.y))) REDUCED to normal form. ------ 194521/23047140. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.b))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 194522/23047167. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(a a)))) 5. ==[ beta ]==> ((a b)(^y.(a a))) 6. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 194523/23047176. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a))) b) REDUCED to normal form. ------ 194524/23047203. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 194525/23047257. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194526/23047284. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) a) REDUCED to normal form. ------ 194527/23047302. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 194528/23047311. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 194529/23047338. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(b (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)(b (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(b (^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (^z.z))) REDUCED to normal form. ------ 194530/23048067. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b (^z.(a a)))) REDUCED to normal form. ------ 194531/23048121. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((^c.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((^z.(a a))(a a))) 3. ==[ beta ]==> (((a a)(^y.a))((^z.(a a))(a a))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.(a a))(a a))) 5. ==[ beta ]==> (((a a)(^x.a))(a a)) REDUCED to normal form. ------ 194532/23048148. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (^x1.x1))) REDUCED to normal form. ------ 194533/23048193. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 194534/23048490. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) b) b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) b) b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) b) b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194535/23048769. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 194536/23048814. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(a a)) a)) 3. ==[ beta ]==> ((^y.y)((^z.(a a)) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(a a)) a)) 5. ==[ beta ]==> ((^y.(a a)) a) 6. ==[ alpha ]==> ((^x.(a a)) a) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194537/23049102. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a (^z.z))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 194538/23049129. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a (^x.x))(b a))((a a) b)) REDUCED to normal form. ------ 194539/23049363. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194540/23049435. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.z1))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> ((^y.y)((a (^z1.z1))(^x2.(^y2.(^z2.z2))))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194541/23049570. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((a a)(^a.a)) d)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(^z.z)) d)) 3. ==[ beta ]==> (b (((a a)(^z.z)) d)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) d)) REDUCED to normal form. ------ 194542/23049687. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 194543/23049714. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 194544/23049768. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 194545/23049813. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z) a)) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) a) REDUCED to normal form. ------ 194546/23049894. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z)) d)) 3. ==[ beta ]==> (b ((^y.(^z.z)) d)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) d)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194547/23050074. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (^y.y))(b a))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))(b a))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))(b a))) REDUCED to normal form. ------ 194548/23050101. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 194549/23050434. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z))) a)) 5. ==[ beta ]==> ((a (^y.(^z.z))) a) 6. ==[ alpha ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 194550/23050713. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b b)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b b)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((b b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 194551/23050785. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) c)) 5. ==[ beta ]==> ((^y.(^z.z)) c) 6. ==[ alpha ]==> ((^x.(^y.y)) c) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194552/23051028. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((b a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((b a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194553/23051064. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 194554/23051091. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a a)) REDUCED to normal form. ------ 194555/23051793. ------ 1. ==[ start ]==> ((((^a.a) b) c)(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(b (^y.(^z.z)))) 3. ==[ beta ]==> ((b c)(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((b c)(b (^x.(^y.y)))) REDUCED to normal form. ------ 194556/23051865. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 194557/23051892. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a b)(^z.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.a))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 194558/23051928. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 194559/23051946. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^z1.z1)(^x2.(^y2.y2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^z1.(^x2.x2))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(^y1.(^z1.z1))) REDUCED to normal form. ------ 194560/23051955. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 194561/23052027. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 194562/23052036. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 194563/23052063. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.b))((a a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 194564/23052135. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a b) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a b) c)) 3. ==[ beta ]==> ((^y.(^z.z))((a b) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194565/23052144. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) b) REDUCED to normal form. ------ 194566/23052171. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 194567/23052198. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 194568/23052261. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(c (a b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(c (a b))) REDUCED to normal form. ------ 194569/23052288. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(b (a a))) REDUCED to normal form. ------ 194570/23052315. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(a ((a a)(^z.z)))) 3. ==[ beta ]==> ((a ((^y.y) b))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(a ((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)(a ((a a)(^y.y)))) 6. ==[ alpha ]==> ((a b)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 194571/23052342. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 194572/23052369. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((a b)(a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(b a))((a b)(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(b a))((a b)(a (^y.y)))) 5. ==[ beta ]==> ((b a)((a b)(a (^y.y)))) 6. ==[ alpha ]==> ((b a)((a b)(a (^x.x)))) REDUCED to normal form. ------ 194573/23052396. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 194574/23052423. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a b)(a a))((^y.y)(a (a a)))) 6. ==[ alpha ]==> (((a b)(a a))((^x.x)(a (a a)))) 7. ==[ beta ]==> (((a b)(a a))(a (a a))) REDUCED to normal form. ------ 194575/23052450. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a b))((a (a a))((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))((a (a a))((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(a b))((a (a a))(^y.y))) 6. ==[ alpha ]==> (((a a)(a b))((a (a a))(^x.x))) REDUCED to normal form. ------ 194576/23052477. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a ((a a) a))) REDUCED to normal form. ------ 194577/23052531. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 194578/23052729. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.b))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.b))) 7. ==[ beta ]==> ((a (^y.y))(^z.b)) 8. ==[ alpha ]==> ((a (^x.x))(^y.b)) REDUCED to normal form. ------ 194579/23052810. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b) b)) 3. ==[ beta ]==> (b ((a b) b)) REDUCED to normal form. ------ 194580/23053143. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c (^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c (^y.a))) REDUCED to normal form. ------ 194581/23053170. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(b (^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b (^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (^y1.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (^y1.b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194582/23053215. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a b)(^z.z))) 3. ==[ beta ]==> (b ((a b)(^z.z))) 4. ==[ alpha ]==> (b ((a b)(^x.x))) REDUCED to normal form. ------ 194583/23053224. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 194584/23053251. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 194585/23053278. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 194586/23053323. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1) a)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194587/23053332. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 194588/23053359. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 194589/23053386. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(a b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a b)) REDUCED to normal form. ------ 194590/23053557. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(b ((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(b ((a a) a))) 3. ==[ beta ]==> (((a (a a)) b)(b ((a a) a))) REDUCED to normal form. ------ 194591/23053584. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(a (a b))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(a (a b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(a (a b))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(a (a b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (a b))) REDUCED to normal form. ------ 194592/23053611. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((a a) a)(a a))) REDUCED to normal form. ------ 194593/23053638. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a b)((a a)(^x.x)))(a (^z.z))) 6. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 194594/23053665. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))((a (a a))((^y.y) a))) 6. ==[ alpha ]==> (((a a)(a a))((a (a a))((^x.x) a))) 7. ==[ beta ]==> (((a a)(a a))((a (a a)) a)) REDUCED to normal form. ------ 194595/23053692. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(a (a (a a)))) REDUCED to normal form. ------ 194596/23053746. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a a)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)((a a) a))) REDUCED to normal form. ------ 194597/23053872. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.a)(a (a a)))) 5. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 194598/23053890. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^z.z))(^x1.(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 194599/23054277. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(a a))) 5. ==[ beta ]==> (b ((^y.(^z.z))(a a))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194600/23054295. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 194601/23054304. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((a (^z.z))(a (^z.z)))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 194602/23054322. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)(^z.a))) 5. ==[ beta ]==> ((a (a (^x.x)))(a (^z.a))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.a))) REDUCED to normal form. ------ 194603/23054331. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y)))) a) REDUCED to normal form. ------ 194604/23054349. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(z z))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 194605/23054403. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x)(^y.y)) a)) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y) a)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x) a)) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 194606/23054439. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 9. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194607/23054466. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 194608/23054592. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.a) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194609/23054628. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 194610/23054655. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 194611/23054709. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.a)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194612/23054727. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 194613/23054736. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 194614/23054754. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 194615/23054826. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(c (a (^z.z)))) 3. ==[ beta ]==> ((a (b (^y.y)))(c (a (^z.z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(c (a (^y.y)))) REDUCED to normal form. ------ 194616/23054853. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(b ((^x.x) a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(b a)) REDUCED to normal form. ------ 194617/23054880. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a (a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a (a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (a (a a)))) 5. ==[ beta ]==> (((^y.y) b)(a (a (a a)))) 6. ==[ alpha ]==> (((^x.x) b)(a (a (a a)))) 7. ==[ beta ]==> (b (a (a (a a)))) REDUCED to normal form. ------ 194618/23054907. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 194619/23054934. ------ 1. ==[ start ]==> (((a b)(b a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 194620/23054961. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a)((^z.z) a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)((^y.y) a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))((a a) a)) REDUCED to normal form. ------ 194621/23055042. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b c)) REDUCED to normal form. ------ 194622/23055150. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a ((^z.z) a))) 5. ==[ beta ]==> ((a (^y.y))(a ((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 194623/23055168. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(c (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(c (^z.z))) 3. ==[ beta ]==> ((b (^y.y))(c (^z.z))) 4. ==[ alpha ]==> ((b (^x.x))(c (^y.y))) REDUCED to normal form. ------ 194624/23055177. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a (^y.y))(a a))) REDUCED to normal form. ------ 194625/23055204. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a (^z.z)))) REDUCED to normal form. ------ 194626/23055213. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1) c)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1) c)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1) c)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194627/23055240. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.z))) 5. ==[ beta ]==> ((a (^y.y))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 194628/23055375. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.y1) b)) 3. ==[ beta ]==> (b ((^y1.y1) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194629/23055482. ------ 1. ==[ start ]==> (^a.((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> (^x.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194630/23055483. ------ 1. ==[ start ]==> (a ((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.b))) 3. ==[ beta ]==> (a (^y.(^z.z))) 4. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 194631/23067243. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b)) a) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b)) a) 3. ==[ beta ]==> ((^y.(^z.z)) a) 4. ==[ alpha ]==> ((^x.(^y.y)) a) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194632/23067249. ------ 1. ==[ start ]==> ((^a.a)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194633/23067303. ------ 1. ==[ start ]==> ((^a.b)((^c.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 194634/23067501. ------ 1. ==[ start ]==> ((^a.(^b.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))(b (a (a (^z.z))))) 3. ==[ beta ]==> (^y.(b (a (a (^z.z))))) 4. ==[ alpha ]==> (^x.(b (a (a (^y.y))))) REDUCED to normal form. ------ 194635/23067522. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 194636/23067744. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 194637/23068404. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(^c.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 194638/23068959. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 194639/23069682. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 194640/23071164. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(y y))(^z.(^x1.(^y1.y1))))) 3. ==[ eta ]==> (b ((^y.(y y))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 194641/23071257. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(b (^x1.x1)))) 5. ==[ beta ]==> (b (^z.(b (^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 194642/23071608. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(^y.((a a)(a a)))) 3. ==[ beta ]==> (b (^y.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 194643/23072337. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(^z.((z z)(z z)))) 3. ==[ beta ]==> ((^y.y)(^z.((z z)(z z)))) 4. ==[ alpha ]==> ((^x.x)(^y.((y y)(y y)))) 5. ==[ beta ]==> (^y.((y y)(y y))) 6. ==[ alpha ]==> (^x.((x x)(x x))) REDUCED to normal form. ------ 194644/23072604. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(b a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194645/23072919. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 194646/23073336. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.((^x1.x1) b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.b)) REDUCED to normal form. ------ 194647/23073651. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^a.(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(^z.z))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 194648/23073918. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((((^y.(^z.z))(b a))((^y.(^z.z))(b a)))(((^y.(^z.z))(b a))((^y.(^z.z))(b a)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(b a))((^z.(^x1.x1))(b a)))(((^y1.(^z1.z1))(b a))((^x2.(^y2.y2))(b a)))) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1))(b a)))(((^y1.(^z1.z1))(b a))((^x2.(^y2.y2))(b a)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(b a)))(((^x1.(^y1.y1))(b a))((^z1.(^x2.x2))(b a)))) 7. ==[ beta ]==> (((^y.(^z.z))(b a))(((^x1.(^y1.y1))(b a))((^z1.(^x2.x2))(b a)))) 8. ==[ alpha ]==> (((^x.(^y.y))(b a))(((^z.(^x1.x1))(b a))((^y1.(^z1.z1))(b a)))) 9. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(b a))((^y1.(^z1.z1))(b a)))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(b a))((^x1.(^y1.y1))(b a)))) 11. ==[ beta ]==> (((^y.(^z.z))(b a))((^x1.(^y1.y1))(b a))) 12. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(b a))) 13. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(b a))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 15. ==[ beta ]==> ((^y.(^z.z))(b a)) 16. ==[ alpha ]==> ((^x.(^y.y))(b a)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194649/23074812. ------ 1. ==[ start ]==> (((a b)(a b))(^b.(b a))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(x a))) REDUCED to normal form. ------ 194650/23074998. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194651/23075091. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(^y1.(b y1))) 3. ==[ eta ]==> (((^x.(x x))(^y.(^z.(^x1.x1)))) b) 4. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1)))) b) 5. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) b) 6. ==[ beta ]==> ((^y.(^z.z)) b) 7. ==[ alpha ]==> ((^x.(^y.y)) b) 8. ==[ beta ]==> (^y.y) 9. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194652/23075586. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194653/23075838. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 194654/23076081. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 194655/23076909. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.b))) REDUCED to normal form. ------ 194656/23077107. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.(^z1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(^y1.(^z1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(^x1.(^y1.x1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.z))) REDUCED to normal form. ------ 194657/23077296. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.b))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.b))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.b))) REDUCED to normal form. ------ 194658/23077401. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((^z.a)(a (a a)))(((^z.a)(a (a a)))(^y.y))) 4. ==[ alpha ]==> (((^x.a)(a (a a)))(((^y.a)(a (a a)))(^z.z))) 5. ==[ beta ]==> (a (((^y.a)(a (a a)))(^z.z))) 6. ==[ alpha ]==> (a (((^x.a)(a (a a)))(^y.y))) 7. ==[ beta ]==> (a (a (^y.y))) 8. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 194659/23078295. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(a (a a)))) REDUCED to normal form. ------ 194660/23078403. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z)))) 7. ==[ beta ]==> (b (^y.(^z.(z z)))) 8. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 194661/23078511. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.(z z)))) REDUCED to normal form. ------ 194662/23078592. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((b (^y.y))(^z.((^x1.x1) a))) 6. ==[ alpha ]==> ((b (^x.x))(^y.((^z.z) a))) 7. ==[ beta ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 194663/23078673. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.a))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 194664/23078724. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194665/23078736. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a (^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194666/23078898. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^c.(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(a a))) 3. ==[ beta ]==> (b (^y1.(a a))) 4. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 194667/23079006. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^a.a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.y1)) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194668/23079018. ------ 1. ==[ start ]==> ((a a)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.b))) 3. ==[ beta ]==> ((a a)(^y.(^z.z))) 4. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 194669/23079072. ------ 1. ==[ start ]==> ((a b)((^c.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)(^y.y)) 4. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 194670/23079126. ------ 1. ==[ start ]==> (((a a)(a a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 194671/23079270. ------ 1. ==[ start ]==> ((a (^b.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))(b (a (a (^y.y))))) REDUCED to normal form. ------ 194672/23079288. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194673/23079306. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194674/23079351. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.a)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.a)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 194675/23079378. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 194676/23079432. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a (((^y.y) b)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.x) b)((^y.y)(^z.z)))) 7. ==[ beta ]==> (a (b ((^y.y)(^z.z)))) 8. ==[ alpha ]==> (a (b ((^x.x)(^y.y)))) 9. ==[ beta ]==> (a (b (^y.y))) 10. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 194677/23079459. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 194678/23079513. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(x x)))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 194679/23079621. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((((^y.y)(^z.z))((^x1.x1) b))(((^y.y)(^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 7. ==[ beta ]==> (((^y.y)((^z.z) b))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 8. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) b))) 9. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))((^y1.y1) b))) 10. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))((^x1.x1) b))) 11. ==[ beta ]==> (b (((^y.y)(^z.z))((^x1.x1) b))) 12. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z) b))) 13. ==[ beta ]==> (b ((^y.y)((^z.z) b))) 14. ==[ alpha ]==> (b ((^x.x)((^y.y) b))) 15. ==[ beta ]==> (b ((^y.y) b)) 16. ==[ alpha ]==> (b ((^x.x) b)) 17. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194680/23079648. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 194681/23079702. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 9. ==[ beta ]==> ((a (^x.x))(^z.z)) 10. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 194682/23079729. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((a (a a))((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> ((a (a a))((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 194683/23079765. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 194684/23079792. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 194685/23079819. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 194686/23079882. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.z))) 7. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 8. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 194687/23079909. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 194688/23079927. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x)) b)((b a)(^y.b))) 3. ==[ beta ]==> ((b b)((b a)(^y.b))) 4. ==[ alpha ]==> ((b b)((b a)(^x.b))) REDUCED to normal form. ------ 194689/23080062. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y))(^z.z))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 194690/23080170. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.a))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.a))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 194691/23080197. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a (a (^z.z))) a)) REDUCED to normal form. ------ 194692/23080224. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.(^y1.y1)) a) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.(^y1.y1)) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.(^x1.x1)) a) b)) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a) b)) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 7. ==[ beta ]==> (((^y.(^z.z)) a) b) 8. ==[ alpha ]==> (((^x.(^y.y)) a) b) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 194693/23080314. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 194694/23080593. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))(b ((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)(b ((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194695/23080629. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y (^z.z))) a)) 5. ==[ beta ]==> ((a (^x.(x x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 194696/23080647. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.(^x1.x1)) a)(a a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a)(a a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a)(a a))) 7. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(a a))) 8. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a a))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 194697/23080728. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((a (^x.b))(b (a (a a)))) REDUCED to normal form. ------ 194698/23080917. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 194699/23080998. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (^z.z))(b (^x1.x1)))) IRREDUCIBLE: cycle. ------ 194700/23081061. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.(^y.y)) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a) b)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)((^x.x)(^y.y))) 5. ==[ beta ]==> ((((a a) a) b)(^y.y)) 6. ==[ alpha ]==> ((((a a) a) b)(^x.x)) REDUCED to normal form. ------ 194701/23081088. ------ 1. ==[ start ]==> (((a b) a)((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 194702/23081115. ------ 1. ==[ start ]==> (((a a)(^a.b))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.b))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 194703/23081169. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 194704/23081196. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b a)(^y.a))) REDUCED to normal form. ------ 194705/23081223. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.a)(((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((^x.a)(((a a)(^y.y))(^z.b))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 194706/23081250. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(^x1.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.(a a)))) REDUCED to normal form. ------ 194707/23081277. ------ 1. ==[ start ]==> (((a b)(^a.a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 194708/23081313. ------ 1. ==[ start ]==> (((a a)(a b))((^c.a)(b a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.a)(b a))) 3. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 194709/23081340. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 194710/23081367. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> ((a (^x.x))(((^z.z) b)((^z.z) b))) 8. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)((^z.z) b))) 9. ==[ beta ]==> ((a (^x.x))(b ((^z.z) b))) 10. ==[ alpha ]==> ((a (^x.x))(b ((^y.y) b))) 11. ==[ beta ]==> ((a (^x.x))(b b)) REDUCED to normal form. ------ 194711/23081394. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a))) a) REDUCED to normal form. ------ 194712/23081421. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(b (^y1.y1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(b (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(b (^x1.x1)))) 7. ==[ beta ]==> (a ((^y.(^z.z))(b (^x1.x1)))) 8. ==[ alpha ]==> (a ((^x.(^y.y))(b (^z.z)))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 194713/23081448. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 194714/23081466. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.b) b)(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> (b (((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 194715/23081889. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((b (^z.z))(a a))) 3. ==[ beta ]==> (b ((b (^z.z))(a a))) 4. ==[ alpha ]==> (b ((b (^x.x))(a a))) REDUCED to normal form. ------ 194716/23082213. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a (^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((a a)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 194717/23082357. ------ 1. ==[ start ]==> (((a b) c)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b) c)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 194718/23082384. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((b a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 194719/23082465. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a b)(^z.(a a)))) REDUCED to normal form. ------ 194720/23082492. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 194721/23082546. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (a a))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194722/23082573. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 194723/23082600. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 194724/23082654. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((b (^z.z)) a)) REDUCED to normal form. ------ 194725/23082717. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.a)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.a)) REDUCED to normal form. ------ 194726/23082744. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (a b))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a b))(^x.(^y.y))) REDUCED to normal form. ------ 194727/23082825. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(a a))(^y.b))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(a a)) REDUCED to normal form. ------ 194728/23082852. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> (((a b) a)((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (((a b) a)((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (((a b) a) b) REDUCED to normal form. ------ 194729/23082933. ------ 1. ==[ start ]==> ((a (b a))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (b a))((^x.(x x))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 194730/23083023. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(a (b (^z.z)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(a (b (^z.z)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(a (b (^z.z)))) 5. ==[ beta ]==> (b (a (b (^z.z)))) 6. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 194731/23083104. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 194732/23083212. ------ 1. ==[ start ]==> (((^a.a)(b a))((a b)(a b))) 2. ==[ alpha ]==> (((^x.x)(b a))((a b)(a b))) 3. ==[ beta ]==> ((b a)((a b)(a b))) REDUCED to normal form. ------ 194733/23083239. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((a a) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a a))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 194734/23083293. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (a a))(b a))) 3. ==[ beta ]==> (((a b)(a b))((a (a a))(b a))) REDUCED to normal form. ------ 194735/23083374. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a a)((a a)(a a)))) 3. ==[ beta ]==> (b ((a a)((a a)(a a)))) REDUCED to normal form. ------ 194736/23083410. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a)(a a))(^y.y))) REDUCED to normal form. ------ 194737/23083437. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 194738/23083554. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(a a))((a a) a))) 5. ==[ beta ]==> ((a (a a))((^y.(a a))((a a) a))) 6. ==[ alpha ]==> ((a (a a))((^x.(a a))((a a) a))) 7. ==[ beta ]==> ((a (a a))(a a)) REDUCED to normal form. ------ 194739/23083581. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.b)(a b))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.b)(a b))) 3. ==[ beta ]==> (((a (a a))(a b)) b) REDUCED to normal form. ------ 194740/23083635. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 194741/23083662. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(x x))(b a))) 3. ==[ beta ]==> (((a b)(a (a a)))((b a)(b a))) REDUCED to normal form. ------ 194742/23083689. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)((^y.a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a) a)((^x.a)(a (^y.(^z.z))))) 7. ==[ beta ]==> (((a a) a) a) REDUCED to normal form. ------ 194743/23083716. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 194744/23083761. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((a a)(a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194745/23084076. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b ((^x1.x1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b ((^x1.x1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((^z.z) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 194746/23084103. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(a ((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(a ((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(a ((a a)(a a)))) 5. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 194747/23084157. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((a (^y.(^z.z)))(a (^x1.x1)))) 7. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(a (^x1.x1)))) 8. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 194748/23084166. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 194749/23084238. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b (((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b ((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 194750/23084346. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194751/23084373. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(b a))) 3. ==[ beta ]==> ((a (^x.x))(a (b a))) REDUCED to normal form. ------ 194752/23084418. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(b (^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(b (^y.y))) REDUCED to normal form. ------ 194753/23084472. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((^y.y)(a a))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(a a))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(a a))) 5. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 194754/23084499. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(a (^x1.x1)))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 194755/23084553. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 194756/23084580. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 194757/23084607. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.b)((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.b)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.b)((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a) b) REDUCED to normal form. ------ 194758/23084652. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194759/23084661. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.z)) REDUCED to normal form. ------ 194760/23084688. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))((a a)(^z.z)))) 3. ==[ beta ]==> ((a b)((^y.(y y))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a b)((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)(((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> ((a b)(((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 194761/23085102. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(a ((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(a ((^z.z) b))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(a ((^z.z) b))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a b)) REDUCED to normal form. ------ 194762/23085138. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.(^y1.y1))) b)) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.(^x1.x1))) b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194763/23085183. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (b (((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (b (((a a)(^x.x)) a)) REDUCED to normal form. ------ 194764/23085192. ------ 1. ==[ start ]==> (((a b)(^c.a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 194765/23085291. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^y1.y1)(^z1.z1))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194766/23085363. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(c (^d.a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(c (^y.a))) 3. ==[ beta ]==> (((a a) b)(c (^y.a))) 4. ==[ alpha ]==> (((a a) b)(c (^x.a))) REDUCED to normal form. ------ 194767/23085390. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(b (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 194768/23085417. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(a (^y.y))) 3. ==[ beta ]==> ((a (b a))(a (^y.y))) 4. ==[ alpha ]==> ((a (b a))(a (^x.x))) REDUCED to normal form. ------ 194769/23085444. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 194770/23085498. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.x)) REDUCED to normal form. ------ 194771/23085525. ------ 1. ==[ start ]==> (((a b)((a a) a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(a a))(a (a a)))) 3. ==[ beta ]==> (((a b)((a a) a))(a a)) REDUCED to normal form. ------ 194772/23085552. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.b)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 194773/23085633. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^y1.y1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)((^y1.y1)(a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)((^x1.x1)(a a)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(a a))) REDUCED to normal form. ------ 194774/23085660. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((b (a a))((^y.a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (a a))((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 194775/23085687. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(b a))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 194776/23085966. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(c ((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(c ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(c ((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194777/23086029. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.(^z.z))) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 194778/23086047. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((b a)(a a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((b a)(a a))) 3. ==[ beta ]==> (((a a)(a a))((b a)(a a))) REDUCED to normal form. ------ 194779/23086074. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(((a a)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^y.y))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 194780/23086083. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 194781/23086128. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((a b)(a (a a)))) 3. ==[ beta ]==> (((b a)(b a))((a b)(a (a a)))) REDUCED to normal form. ------ 194782/23086209. ------ 1. ==[ start ]==> (((^a.b)(a b))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a b))((a (a a))(a b))) 3. ==[ beta ]==> (b ((a (a a))(a b))) REDUCED to normal form. ------ 194783/23086326. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((b a)(^x1.x1))) REDUCED to normal form. ------ 194784/23086353. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 194785/23086380. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((a a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 194786/23086416. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.b)(a (a a)))) 3. ==[ beta ]==> (((a a)((a a)(a a))) b) REDUCED to normal form. ------ 194787/23086443. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b) a) REDUCED to normal form. ------ 194788/23086470. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 194789/23086497. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(x x))(a b))) 3. ==[ beta ]==> (((a (a a))(b a))((a b)(a b))) REDUCED to normal form. ------ 194790/23086524. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.a)((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 194791/23086551. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 194792/23086578. ------ 1. ==[ start ]==> (((a b)(a b))((^a.a)(b a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.x)(b a))) 3. ==[ beta ]==> (((a b)(a b))(b a)) REDUCED to normal form. ------ 194793/23086686. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 194794/23086713. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 194795/23086740. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 194796/23086767. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))(^z.b))) 3. ==[ beta ]==> ((a (b (^x.x)))((^z.b)(^z.b))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.b)(^z.b))) 5. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 194797/23086857. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(a (b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(a (b a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(a (b a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(a (b a))) 5. ==[ beta ]==> ((^y.(^z.z))(a (b a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194798/23086938. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((a b)((^z.z) a))) 3. ==[ beta ]==> (b ((a b)((^z.z) a))) 4. ==[ alpha ]==> (b ((a b)((^x.x) a))) 5. ==[ beta ]==> (b ((a b) a)) REDUCED to normal form. ------ 194799/23087046. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194800/23087217. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 194801/23087244. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 194802/23087325. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 194803/23087352. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 194804/23087433. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a b) c)) REDUCED to normal form. ------ 194805/23087550. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 194806/23087577. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 194807/23087604. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 194808/23087820. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(b (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(b (^z.(a a)))) REDUCED to normal form. ------ 194809/23087847. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(a (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(a (^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 194810/23087874. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.(a a))(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a a)) REDUCED to normal form. ------ 194811/23088324. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.b) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.b) b)) 3. ==[ beta ]==> (((^y.y) a)((^z.b) b)) 4. ==[ alpha ]==> (((^x.x) a)((^y.b) b)) 5. ==[ beta ]==> (a ((^y.b) b)) 6. ==[ alpha ]==> (a ((^x.b) b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 194812/23088342. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(((a a) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(((a a) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(((a a) a)(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.y)))) 7. ==[ beta ]==> (((a a) a)(a (^y.y))) 8. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 194813/23088369. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) a)) 7. ==[ beta ]==> ((^y.y)((^z.z) a)) 8. ==[ alpha ]==> ((^x.x)((^y.y) a)) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 194814/23088423. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y) a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b b)(((^y.y) a)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> ((b b)(((^x.x) a)((^y.y)(^z.z)))) 9. ==[ beta ]==> ((b b)(a ((^y.y)(^z.z)))) 10. ==[ alpha ]==> ((b b)(a ((^x.x)(^y.y)))) 11. ==[ beta ]==> ((b b)(a (^y.y))) 12. ==[ alpha ]==> ((b b)(a (^x.x))) REDUCED to normal form. ------ 194815/23088513. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.z))) REDUCED to normal form. ------ 194816/23088540. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 194817/23088567. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(^x1.a)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.a)) REDUCED to normal form. ------ 194818/23088621. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) REDUCED to normal form. ------ 194819/23088648. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 194820/23088675. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)(^y.b))) REDUCED to normal form. ------ 194821/23088729. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((a a) a) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a) b)) 5. ==[ beta ]==> ((^y.y)(((a a) a) b)) 6. ==[ alpha ]==> ((^x.x)(((a a) a) b)) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 194822/23088765. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 194823/23088792. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.(x1 x1))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 194824/23088819. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 194825/23088846. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 194826/23088873. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.y1)(^z1.b))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(^y1.b))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.b))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.b)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 194827/23089035. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b (^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b (^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b (^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b (^x1.a))) REDUCED to normal form. ------ 194828/23089062. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a (^y.b))) 3. ==[ beta ]==> ((b (a (a a)))(a (^y.b))) 4. ==[ alpha ]==> ((b (a (a a)))(a (^x.b))) REDUCED to normal form. ------ 194829/23089143. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((a a)((^y.(y y))((^z.z) a))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((^y.y) a))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((^y.y) a))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((^y.y) a))) 9. ==[ beta ]==> ((a a)(a ((^y.y) a))) 10. ==[ alpha ]==> ((a a)(a ((^x.x) a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 194830/23089161. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.(z z)))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 194831/23089170. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.a)(a (a a)))) 3. ==[ beta ]==> ((a (a (a (^x.x)))) a) REDUCED to normal form. ------ 194832/23089566. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194833/23089593. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 194834/23089620. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a (^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a (^z.a))) REDUCED to normal form. ------ 194835/23089728. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a a)) b)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a)) b)) 5. ==[ beta ]==> ((^y.y)((a (a a)) b)) 6. ==[ alpha ]==> ((^x.x)((a (a a)) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 194836/23089773. ------ 1. ==[ start ]==> (((^a.b)(b a))(c ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))(c ((^y.y) a))) 3. ==[ beta ]==> (b (c ((^y.y) a))) 4. ==[ alpha ]==> (b (c ((^x.x) a))) 5. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 194837/23089836. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 194838/23089881. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194839/23089998. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194840/23090025. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 194841/23090061. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a (a a))) REDUCED to normal form. ------ 194842/23090088. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.x1))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 194843/23090115. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 194844/23090142. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 194845/23090169. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(z z)))) 7. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 8. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 9. ==[ beta ]==> (b (^y.(y y))) 10. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 194846/23090223. ------ 1. ==[ start ]==> (((a b)(b a))(c (^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(c (^x.(^y.y)))) REDUCED to normal form. ------ 194847/23090250. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b (^z.a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b (^z.a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (^y.a))) REDUCED to normal form. ------ 194848/23090277. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a (^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(a (^y.(y y)))) REDUCED to normal form. ------ 194849/23090331. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 194850/23090358. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((b (^x.x))((^z.z) a)) 8. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 194851/23090385. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.a)(^y.y))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a))) a) REDUCED to normal form. ------ 194852/23090439. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.a))) 7. ==[ beta ]==> ((a (^x.x))(^z.a)) 8. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 194853/23090457. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^b.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.a) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.a) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.a) a)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 194854/23090493. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 194855/23090502. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194856/23090664. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a a)(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a a)(a a))) 3. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 194857/23090772. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(a a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(a a)) 3. ==[ beta ]==> ((^y.(^z.z))(a a)) 4. ==[ alpha ]==> ((^x.(^y.y))(a a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194858/23102541. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b)) b) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b)) b) 3. ==[ beta ]==> ((^y.(^z.z)) b) 4. ==[ alpha ]==> ((^x.(^y.y)) b) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194859/23102565. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194860/23102808. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194861/23102847. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194862/23102880. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(z (^x1.x1))) b)) 3. ==[ eta ]==> ((^y.y)((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((^y.(y (^z.z))) b) 6. ==[ alpha ]==> ((^x.(x (^y.y))) b) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194863/23103297. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194864/23103501. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194865/23103729. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 194866/23104170. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(y y)))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 194867/23104833. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> (^y.(((^z.b)((a a)(^x1.x1)))((^z.b)((a a)(^x1.x1))))) 4. ==[ alpha ]==> (^x.(((^y.b)((a a)(^z.z)))((^x1.b)((a a)(^y1.y1))))) 5. ==[ beta ]==> (^x.(b ((^x1.b)((a a)(^y1.y1))))) 6. ==[ alpha ]==> (^x.(b ((^y.b)((a a)(^z.z))))) 7. ==[ beta ]==> (^x.(b b)) REDUCED to normal form. ------ 194868/23105040. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((b (^z.z)) b)) 3. ==[ beta ]==> ((^y.y)(((b (^z.z)) b)((b (^z.z)) b))) 4. ==[ alpha ]==> ((^x.x)(((b (^y.y)) b)((b (^z.z)) b))) 5. ==[ beta ]==> (((b (^y.y)) b)((b (^z.z)) b)) 6. ==[ alpha ]==> (((b (^x.x)) b)((b (^y.y)) b)) REDUCED to normal form. ------ 194869/23105412. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((((a a) a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 194870/23106924. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(^y.((a a)(a a)))) REDUCED to normal form. ------ 194871/23107020. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2)))((^y2.y2) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194872/23107308. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((a a)(a a)) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.y))) REDUCED to normal form. ------ 194873/23107644. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(a a)))) 5. ==[ beta ]==> (^y.(^z.(a a))) 6. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 194874/23108226. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 194875/23108643. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(^z.(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 194876/23109264. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(a (^y.(^z.z)))) REDUCED to normal form. ------ 194877/23109570. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 194878/23109858. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194879/23110119. ------ 1. ==[ start ]==> (((a b)(a b))(^c.(^d.a))) 2. ==[ alpha ]==> (((a b)(a b))(^x.(^y.a))) REDUCED to normal form. ------ 194880/23110650. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(^x.((a a)(^y.y)))) REDUCED to normal form. ------ 194881/23111466. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((a a) a)(^x1.a))) 3. ==[ eta ]==> ((^y.(^z.z))(((a a) a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194882/23112045. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (b (^z.(^x1.(z z)))) 4. ==[ alpha ]==> (b (^x.(^y.(x x)))) REDUCED to normal form. ------ 194883/23112708. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((^z.z) a)(^x1.(x1 x1)))((((^z.z) a)(^x1.(x1 x1)))(^y.y))) 4. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((((^z.z) a)(^x1.(x1 x1)))(^y1.y1))) 5. ==[ beta ]==> ((a (^y.(y y)))((((^z.z) a)(^x1.(x1 x1)))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(x x)))((((^y.y) a)(^z.(z z)))(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(x x)))((a (^z.(z z)))(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(y y)))(^z.z))) REDUCED to normal form. ------ 194884/23113233. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^x.(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.(^y.y))) REDUCED to normal form. ------ 194885/23113377. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 194886/23113581. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 194887/23113710. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.d)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.d)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.d)) 5. ==[ beta ]==> (((^y.y) b)(^z.d)) 6. ==[ alpha ]==> (((^x.x) b)(^y.d)) 7. ==[ beta ]==> (b (^y.d)) 8. ==[ alpha ]==> (b (^x.d)) REDUCED to normal form. ------ 194888/23113899. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.a))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 194889/23113998. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.(x (^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.z)) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 194890/23114031. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194891/23114070. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(^z1.y1))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.y1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 5. ==[ beta ]==> (^y.(^z.y)) 6. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 194892/23114313. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194893/23114343. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 194894/23114505. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194895/23114586. ------ 1. ==[ start ]==> ((a (^b.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 194896/23114622. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 194897/23114631. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 194898/23114658. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z))) b)) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y))) b)) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 194899/23114703. ------ 1. ==[ start ]==> (((a (^a.a)) b)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((b (^y.y)) a)) REDUCED to normal form. ------ 194900/23114730. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 194901/23114757. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.a))(b (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 194902/23114784. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (^x1.(^y1.y1)))((a a) a))) REDUCED to normal form. ------ 194903/23114811. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b a)(a b))) 3. ==[ beta ]==> ((a (^y.y))((b a)(a b))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(a b))) REDUCED to normal form. ------ 194904/23114919. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a a)(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a a)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 194905/23115000. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a b)(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> ((a b)(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> ((a b)(a (b (^y.y)))) 6. ==[ alpha ]==> ((a b)(a (b (^x.x)))) REDUCED to normal form. ------ 194906/23115027. ------ 1. ==[ start ]==> (((a (a a)) a)((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a)) a)((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a)) a)((a (^x.x))(^z.z))) 4. ==[ alpha ]==> (((a (a a)) a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 194907/23115045. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a (a a))(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a (a a))(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 194908/23115054. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 194909/23115072. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 194910/23115171. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 194911/23115198. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) a)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.(^z.z)))) REDUCED to normal form. ------ 194912/23115252. ------ 1. ==[ start ]==> (((a (a a))(a a))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a a))((b a)(^x.b))) REDUCED to normal form. ------ 194913/23115279. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 194914/23115288. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194915/23115315. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194916/23115423. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 7. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 8. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 9. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 194917/23115450. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((^y.a)(b (^z.z))) 6. ==[ alpha ]==> ((^x.a)(b (^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 194918/23115504. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (a (^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (a (^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 194919/23115576. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b (^z.z)) c)) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z)) c)) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y)) c)) REDUCED to normal form. ------ 194920/23115747. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194921/23115801. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (a ((^z.a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (a ((^x.a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194922/23115918. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.x1))) REDUCED to normal form. ------ 194923/23115945. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((a (^y.(y y)))(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a (a (a (^y.y))))) REDUCED to normal form. ------ 194924/23115972. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.z)(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(a a))) 5. ==[ beta ]==> (((a (a a))(^x.a))(a a)) REDUCED to normal form. ------ 194925/23115999. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b (^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b (^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194926/23116026. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(((a a)(a a)) a)) REDUCED to normal form. ------ 194927/23116215. ------ 1. ==[ start ]==> (((^a.b) a)(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.b) a)(((a a) a)(b a))) 3. ==[ beta ]==> (b (((a a) a)(b a))) REDUCED to normal form. ------ 194928/23116503. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 194929/23116584. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (b ((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 194930/23116611. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^x.(a a))) b) REDUCED to normal form. ------ 194931/23116656. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 194932/23116683. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (a a))(^x1.x1))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a a))(^z.z))) 5. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 194933/23116791. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a b)(a a))(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> (((a b)(a a))((^y.y) a)) 4. ==[ alpha ]==> (((a b)(a a))((^x.x) a)) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 194934/23116818. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((b (^y.y)) b)) 3. ==[ beta ]==> ((a (a a))((b (^y.y)) b)) 4. ==[ alpha ]==> ((a (a a))((b (^x.x)) b)) REDUCED to normal form. ------ 194935/23116854. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((^y.(a a))(^z.a)) 6. ==[ alpha ]==> ((^x.(a a))(^y.a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194936/23116908. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(^y2.(^z2.z2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 194937/23116989. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 194938/23117070. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194939/23117124. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)(^z1.(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)(^z1.(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)(^y1.(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(^y1.(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(^x1.(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(a a)))) 11. ==[ beta ]==> ((^y.a)(^z.(a a))) 12. ==[ alpha ]==> ((^x.a)(^y.(a a))) 13. ==[ beta ]==> a REDUCED to normal form. ------ 194940/23117133. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(c ((a a)(a a)))) REDUCED to normal form. ------ 194941/23117160. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))(b (b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))(b (b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))(b (b (^z.z)))) 5. ==[ beta ]==> ((^y.(y y))(b (b (^z.z)))) 6. ==[ alpha ]==> ((^x.(x x))(b (b (^y.y)))) 7. ==[ beta ]==> ((b (b (^y.y)))(b (b (^y.y)))) 8. ==[ alpha ]==> ((b (b (^x.x)))(b (b (^y.y)))) REDUCED to normal form. ------ 194942/23117187. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 194943/23117214. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b (^z.z))(a a))) REDUCED to normal form. ------ 194944/23117241. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 194945/23117430. ------ 1. ==[ start ]==> (((^a.b) c)(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> (b (((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> (b (((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 194946/23117529. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(c (^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(c (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(c (^y.(a a)))) 5. ==[ beta ]==> (c (^y.(a a))) 6. ==[ alpha ]==> (c (^x.(a a))) REDUCED to normal form. ------ 194947/23117664. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 194948/23117772. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(a a))(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a b))) 5. ==[ beta ]==> ((^y.(a a))(a b)) 6. ==[ alpha ]==> ((^x.(a a))(a b)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194949/23117907. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (b ((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 194950/23118006. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a)(a a)) b)) REDUCED to normal form. ------ 194951/23118033. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z) b) c)) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) b) c)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) b) c)) 5. ==[ beta ]==> (((a (^x.x))(a a))(b c)) REDUCED to normal form. ------ 194952/23118483. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 194953/23118591. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)((a a)(^z.z)))) 7. ==[ beta ]==> ((a (^x.(a a)))((a a)(^z.z))) 8. ==[ alpha ]==> ((a (^x.(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 194954/23118618. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (a a))(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (a a))(b a))) REDUCED to normal form. ------ 194955/23118672. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 194956/23118690. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(b (^y.(a a)))) 3. ==[ beta ]==> (b (b (^y.(a a)))) 4. ==[ alpha ]==> (b (b (^x.(a a)))) REDUCED to normal form. ------ 194957/23118699. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 194958/23118798. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.(^z1.z1)))((^x2.x2) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 194959/23118816. ------ 1. ==[ start ]==> (((a a)(b a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 194960/23118843. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 194961/23118897. ------ 1. ==[ start ]==> (((a (a a))(a b))((a b)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a b))((a b)(^x.b))) REDUCED to normal form. ------ 194962/23118924. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a) a)(^y.(a a)))) 5. ==[ beta ]==> (((a a) a)(((a a) a)(^y.(a a)))) 6. ==[ alpha ]==> (((a a) a)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 194963/23119005. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a) a)(((^y.y) a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(a (^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> (((a a) a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 194964/23119032. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 194965/23119086. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((a a)(a a)) a)) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(a a)) a)) REDUCED to normal form. ------ 194966/23119257. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(^y1.b))) 3. ==[ beta ]==> (b ((^x1.b)(^y1.b))) 4. ==[ alpha ]==> (b ((^x.b)(^y.b))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 194967/23119365. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 194968/23119392. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 194969/23119401. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(b ((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 194970/23119419. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(a a))) 6. ==[ alpha ]==> ((^x.x)(^y.(a a))) 7. ==[ beta ]==> (^y.(a a)) 8. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 194971/23119482. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 194972/23119509. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((b a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^z.b))((b a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((b a)((^z.z) a))) 5. ==[ beta ]==> ((^y.b)((b a)((^z.z) a))) 6. ==[ alpha ]==> ((^x.b)((b a)((^y.y) a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 194973/23119563. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 194974/23119590. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a b)((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a b)((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)((a a) a))) REDUCED to normal form. ------ 194975/23119617. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((a a) a)(a b))) REDUCED to normal form. ------ 194976/23119671. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a))((a a)(^x1.x1)))) REDUCED to normal form. ------ 194977/23119788. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y) b)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x) b)(^y.y))) 5. ==[ beta ]==> (((a (a a))(a a))(b (^y.y))) 6. ==[ alpha ]==> (((a (a a))(a a))(b (^x.x))) REDUCED to normal form. ------ 194978/23119815. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 194979/23119842. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((b a)(^x.a))) REDUCED to normal form. ------ 194980/23119869. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a b)(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 194981/23119896. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a (a a)))((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (((a a)(a (a a)))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 194982/23119923. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a b)(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a b)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a b)(^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a b)(^y.a))) REDUCED to normal form. ------ 194983/23119977. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.(a a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(a a))) REDUCED to normal form. ------ 194984/23120004. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 194985/23120013. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(^y.y))) 7. ==[ beta ]==> (((a a)(^y.y))((a a)(^y.y))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 194986/23120040. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.a)(b a))) 3. ==[ beta ]==> ((^y.y)((^z1.a)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(b a))) 5. ==[ beta ]==> ((^y.a)(b a)) 6. ==[ alpha ]==> ((^x.a)(b a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 194987/23120175. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^d.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b ((^z.a)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 194988/23120337. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> (b ((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 194989/23120418. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 194990/23120454. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> ((^y.(a a))((a (^z.(^x1.x1)))(a a))) 6. ==[ alpha ]==> ((^x.(a a))((a (^y.(^z.z)))(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 194991/23120481. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((b a)(a (^y.y)))) REDUCED to normal form. ------ 194992/23120508. ------ 1. ==[ start ]==> (((a b)(^c.a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.a))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 194993/23120535. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(a (a a)))) REDUCED to normal form. ------ 194994/23120562. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a b)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a b)(^z.z))) REDUCED to normal form. ------ 194995/23120616. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a b)) REDUCED to normal form. ------ 194996/23120643. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a (a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((b (^x.x))((a (a a))(a a))) REDUCED to normal form. ------ 194997/23120760. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 194998/23120787. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))((b a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)((b a)(^y.(^z.z)))) 8. ==[ alpha ]==> ((a a)((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 194999/23120814. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 195000/23120841. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x)(a a))(^y.(y y)))) 3. ==[ beta ]==> (((a b)((a a) a))((a a)(^y.(y y)))) 4. ==[ alpha ]==> (((a b)((a a) a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 195001/23120868. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 195002/23120949. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a (a a))(^x1.(a a)))) REDUCED to normal form. ------ 195003/23120976. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b (a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((b (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 195004/23121039. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 195005/23121174. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 195006/23121282. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195007/23121318. ------ 1. ==[ start ]==> ((((^a.a) b) b)(b (b a))) 2. ==[ alpha ]==> ((((^x.x) b) b)(b (b a))) 3. ==[ beta ]==> ((b b)(b (b a))) REDUCED to normal form. ------ 195008/23121345. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 195009/23121399. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 195010/23121426. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((^y1.y1)(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((^y1.y1)(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(a a))((^y1.y1) a))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)((^y1.y1) a))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)((^x1.x1) a))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a) a)) REDUCED to normal form. ------ 195011/23121507. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((^z.z)((a a) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)((a a) a))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a) a)) REDUCED to normal form. ------ 195012/23121534. ------ 1. ==[ start ]==> (((a b)(^a.b))((a (a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.b))((a (a a))(a b))) REDUCED to normal form. ------ 195013/23121588. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 195014/23121633. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(a (^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195015/23121732. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a b)(^x.(x x)))) REDUCED to normal form. ------ 195016/23121759. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 195017/23121813. ------ 1. ==[ start ]==> (((a (a a))(b a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(b a))((a (a a))(^x.b))) REDUCED to normal form. ------ 195018/23121840. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(a (^z.(a a)))) 8. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 195019/23121921. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((b a) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((b a) a)) 3. ==[ beta ]==> (((a a)((a a) a))((b a) a)) REDUCED to normal form. ------ 195020/23121948. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a)(^x1.x1)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a)(^z.z)) b)) REDUCED to normal form. ------ 195021/23122398. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((b c)((a (^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((b c)((a (^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((b c)((a (^x.x))(a a))) REDUCED to normal form. ------ 195022/23122425. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 195023/23122470. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 195024/23122497. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(a a))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(a a))(a (^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195025/23122632. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)(a b))) 3. ==[ beta ]==> (b ((^z.a)(a b))) 4. ==[ alpha ]==> (b ((^x.a)(a b))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 195026/23122740. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195027/23122974. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(a a)) b)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(a a)) b)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a)) b)) 5. ==[ beta ]==> ((b a)((^y.(a a)) b)) 6. ==[ alpha ]==> ((b a)((^x.(a a)) b)) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 195028/23123001. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.b) c)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) b) REDUCED to normal form. ------ 195029/23123028. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.a) d)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a) d)) 3. ==[ beta ]==> (((a b)(a a))((^y.a) d)) 4. ==[ alpha ]==> (((a b)(a a))((^x.a) d)) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 195030/23123190. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y)(a a))(^z.z))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 195031/23123244. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((a a) a)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((a a) a)(^z.a))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.a))) REDUCED to normal form. ------ 195032/23123334. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((a a) a))) 5. ==[ beta ]==> ((^y.y)((^z.a)((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((a a) a))) 7. ==[ beta ]==> ((^y.a)((a a) a)) 8. ==[ alpha ]==> ((^x.a)((a a) a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 195033/23123415. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 195034/23123523. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(z1 z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195035/23123640. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a b)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a b)(a a))) 3. ==[ beta ]==> (((^y.y) a)((a b)(a a))) 4. ==[ alpha ]==> (((^x.x) a)((a b)(a a))) 5. ==[ beta ]==> (a ((a b)(a a))) REDUCED to normal form. ------ 195036/23123748. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.y))) REDUCED to normal form. ------ 195037/23123775. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a (^z1.z1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (^z1.z1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))((a a) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195038/23123820. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(a (^z.(a a)))) 3. ==[ beta ]==> (b (a (^z.(a a)))) 4. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 195039/23123928. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(z1 z1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(z1 z1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195040/23124216. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.b) a)) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.b) a)) 3. ==[ beta ]==> ((((a a) a)(b a)) b) REDUCED to normal form. ------ 195041/23124243. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^c.a) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a) b)) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 195042/23124270. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z)) c)) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z)) c)) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y)) c)) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 195043/23124405. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((a a) a)(^y.y))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((a a) a)(^y.y))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((a a) a)(^x.x))) REDUCED to normal form. ------ 195044/23124459. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (a a))(^z.a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))(^y.a))) 5. ==[ beta ]==> ((a a)((a (a a))(^y.a))) 6. ==[ alpha ]==> ((a a)((a (a a))(^x.a))) REDUCED to normal form. ------ 195045/23124486. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y) a)(^z.(z z)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a (^z.(z z)))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.(y y)))) REDUCED to normal form. ------ 195046/23124495. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.a)(a (a a)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.a)(a (a a)))) 5. ==[ beta ]==> (((^z.a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> (((^x.a)(a (a a)))(^y.y)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 195047/23124900. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 7. ==[ beta ]==> ((^y.(^z.z))(a a)) 8. ==[ alpha ]==> ((^x.(^y.y))(a a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195048/23124927. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x)))((a (^z.z))(a (^z.z)))) 6. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 195049/23124954. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.a)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^y1.a)((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) a))) 5. ==[ beta ]==> ((^y.a)((^z.z) a)) 6. ==[ alpha ]==> ((^x.a)((^y.y) a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 195050/23125008. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 195051/23125089. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a)(^z.a))) 3. ==[ beta ]==> (b ((^y.a)(^z.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 195052/23125152. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.z))) REDUCED to normal form. ------ 195053/23125233. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((a (^z.z)) a)) REDUCED to normal form. ------ 195054/23125260. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a a)(a (a a)))) REDUCED to normal form. ------ 195055/23125332. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 195056/23125359. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 195057/23125377. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(^y.(y y)))) REDUCED to normal form. ------ 195058/23125404. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (a a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (a a)) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a)) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a)) a)) REDUCED to normal form. ------ 195059/23125431. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(((^z.z) a) b)) 3. ==[ beta ]==> ((a (b (^y.y)))(((^z.z) a) b)) 4. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a) b)) 5. ==[ beta ]==> ((a (b (^x.x)))(a b)) REDUCED to normal form. ------ 195060/23125512. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(z z)) a)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 195061/23125539. ------ 1. ==[ start ]==> (((a b)(b a))((^b.a) b)) 2. ==[ alpha ]==> (((a b)(b a))((^x.a) b)) 3. ==[ beta ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 195062/23125647. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 195063/23125674. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a)(^x1.a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a)(^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a)(^z.a))) 5. ==[ beta ]==> ((b (^y.y))((a a)(^z.a))) 6. ==[ alpha ]==> ((b (^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 195064/23125701. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(((^x.x) a) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(a a)) REDUCED to normal form. ------ 195065/23125773. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a ((^z.z) a))) 3. ==[ beta ]==> ((b (^y.y))(a ((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.x))(a ((^y.y) a))) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 195066/23125782. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^b.a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.a) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(a a)) a) REDUCED to normal form. ------ 195067/23125809. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195068/23125818. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195069/23125845. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(a (^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(a (^y1.a))) 3. ==[ beta ]==> ((^y.y)(a (^y1.a))) 4. ==[ alpha ]==> ((^x.x)(a (^y.a))) 5. ==[ beta ]==> (a (^y.a)) 6. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 195070/23125980. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(b (^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(b (^y1.y1))) 3. ==[ beta ]==> (b (b (^y1.y1))) 4. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 195071/23126088. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(a (^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(a (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195072/23137866. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b)) c) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b)) c) 3. ==[ beta ]==> ((^y.(^z.z)) c) 4. ==[ alpha ]==> ((^x.(^y.y)) c) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195073/23138181. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 195074/23138190. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 195075/23138214. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((a (a (^z.z)))(a a))) 3. ==[ eta ]==> ((^y.y)((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a (^y.y)))(a a)) 6. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 195076/23138484. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((((a a) a)(a (^y.(^z.z))))((((a a) a)(a (^y.(^z.z))))(((a a) a)(a (^y.(^z.z)))))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((((a a) a)(a (^z.(^x1.x1))))(((a a) a)(a (^y1.(^z1.z1)))))) REDUCED to normal form. ------ 195077/23138640. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 195078/23138709. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195079/23139072. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 195080/23139504. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(y y)))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 195081/23139600. ------ 1. ==[ start ]==> ((^a.(^a.b))((^c.(a a)) d)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(a a)) d)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 195082/23139780. ------ 1. ==[ start ]==> ((^a.(a b))(((a a) a)(b a))) 2. ==[ alpha ]==> ((^x.(x b))(((a a) a)(b a))) 3. ==[ beta ]==> ((((a a) a)(b a)) b) REDUCED to normal form. ------ 195083/23139936. ------ 1. ==[ start ]==> ((((a a) a) b)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 195084/23140167. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (^y.(((a b)(^z.(^x1.x1)))((a b)(^z.(^x1.x1))))) 4. ==[ alpha ]==> (^x.(((a b)(^y.(^z.z)))((a b)(^x1.(^y1.y1))))) REDUCED to normal form. ------ 195085/23140341. ------ 1. ==[ start ]==> (((^a.b) b)(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) b)(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b (^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b (^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 195086/23141049. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a (a a))(a (^z.(^x1.x1))))((a (a a))(a (^z.(^x1.x1)))))(^y.y)) 4. ==[ alpha ]==> ((((a (a a))(a (^x.(^y.y))))((a (a a))(a (^z.(^x1.x1)))))(^y1.y1)) REDUCED to normal form. ------ 195087/23141529. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 195088/23142354. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195089/23142636. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(^x1.((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195090/23144292. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(^y.(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))(^y.(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 195091/23144598. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 195092/23144904. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 195093/23145201. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 195094/23146506. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.((z z)(^x1.x1)))) REDUCED to normal form. ------ 195095/23146722. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(^y.((^z.z)(a a)))) 5. ==[ beta ]==> ((b a)(^y.((^z.z)(a a)))) 6. ==[ alpha ]==> ((b a)(^x.((^y.y)(a a)))) 7. ==[ beta ]==> ((b a)(^x.(a a))) REDUCED to normal form. ------ 195096/23147388. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 195097/23147619. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((a a) a) b)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((a a) a) b)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 195098/23147775. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^a.(a b))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(x b))) REDUCED to normal form. ------ 195099/23147937. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^c.((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.((a a) a))) 3. ==[ beta ]==> ((b (a (a a)))(^y.((a a) a))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.((a a) a))) REDUCED to normal form. ------ 195100/23148441. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.(^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.z))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.z))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.y))) 5. ==[ beta ]==> (b (^y.(^z.y))) 6. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 195101/23148711. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 195102/23148915. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195103/23149071. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(z (z z)))) REDUCED to normal form. ------ 195104/23149332. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 195105/23149341. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.((^z.z) y))) 3. ==[ eta ]==> (((a (a (^x.x)))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 195106/23149365. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a (^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195107/23149404. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.c)) 3. ==[ beta ]==> ((^y.y)(^y1.c)) 4. ==[ alpha ]==> ((^x.x)(^y.c)) 5. ==[ beta ]==> (^y.c) 6. ==[ alpha ]==> (^x.c) REDUCED to normal form. ------ 195108/23149647. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^b.a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.a)) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.a)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195109/23149695. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))(^y1.b))) 4. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.b))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 195110/23149803. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 195111/23149830. ------ 1. ==[ start ]==> (((a a) b)((^c.a)(^b.b))) 2. ==[ alpha ]==> (((a a) b)((^x.a)(^y.y))) 3. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 195112/23149857. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.y)) REDUCED to normal form. ------ 195113/23149947. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))(b (a (a (^y.y))))) REDUCED to normal form. ------ 195114/23149965. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195115/23149974. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 195116/23150001. ------ 1. ==[ start ]==> ((a ((^a.a) a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a ((^x.x) a))((a (a (^y.y)))(a a))) 3. ==[ beta ]==> ((a a)((a (a (^y.y)))(a a))) 4. ==[ alpha ]==> ((a a)((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 195117/23150010. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> ((^y.a)((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> ((^x.a)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 195118/23150190. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a a) a)(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> (((a a) a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 195119/23150217. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)((a a)(^z.z)))) REDUCED to normal form. ------ 195120/23150244. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a b)(b a))) 3. ==[ beta ]==> ((a (a a))((a b)(b a))) REDUCED to normal form. ------ 195121/23150271. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (a a)))(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 195122/23150397. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 195123/23150424. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 195124/23150451. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z (^x1.x1)))(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 195125/23150469. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 195126/23150496. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(^x1.a))) REDUCED to normal form. ------ 195127/23150586. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((b b)((^y.(^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((b b)((^x.(^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((b b)(^y.(^z.z))) 6. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 195128/23150631. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195129/23150712. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a) a)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 195130/23150721. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 195131/23150748. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (a ((^y.(^z.z))((^x1.x1) b))) 6. ==[ alpha ]==> (a ((^x.(^y.y))((^z.z) b))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 195132/23150775. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 195133/23150802. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 195134/23150829. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 195135/23150847. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 195136/23150856. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 195137/23150883. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 (^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 (^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 9. ==[ beta ]==> ((^z.z)(^y.y)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195138/23151180. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195139/23151288. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 195140/23151306. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(z (^x1.x1))) a)) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z (^x1.x1))) a)) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(z (^x1.x1))) a)) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y (^z.z))) a)) 7. ==[ beta ]==> ((a a)((^y.(y (^z.z))) a)) 8. ==[ alpha ]==> ((a a)((^x.(x (^y.y))) a)) 9. ==[ beta ]==> ((a a)(a (^y.y))) 10. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 195141/23151387. ------ 1. ==[ start ]==> ((a (^a.b))((^c.(a a)) d)) 2. ==[ alpha ]==> ((a (^x.b))((^y.(a a)) d)) 3. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 195142/23151405. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(b (a (a a)))) REDUCED to normal form. ------ 195143/23151432. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) REDUCED to normal form. ------ 195144/23151459. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((b a)((a a) a))) 3. ==[ beta ]==> ((a (a (a a)))((b a)((a a) a))) REDUCED to normal form. ------ 195145/23151486. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((a a)(^y.y))(a b))) 3. ==[ beta ]==> (((a (a a)) a)(((a a)(^y.y))(a b))) 4. ==[ alpha ]==> (((a (a a)) a)(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 195146/23151513. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1)(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z)(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a a)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(a a)))) 9. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 195147/23151540. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 195148/23151567. ------ 1. ==[ start ]==> ((a (a b))(((a a) a)(b a))) REDUCED to normal form. ------ 195149/23151720. ------ 1. ==[ start ]==> ((((a a) a) b)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 195150/23151738. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> (b (((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a)(^z.z))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195151/23151765. ------ 1. ==[ start ]==> (((^a.a)(a b))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 195152/23151792. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^z.a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.a))) 5. ==[ beta ]==> (((a a)(a a))(^y.a)) 6. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 195153/23151828. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 195154/23151846. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 195155/23151855. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 195156/23151927. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> (b ((a a)(^y.(a a)))) 6. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 195157/23151936. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 195158/23151954. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 195159/23152125. ------ 1. ==[ start ]==> (((^a.b) b)((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b ((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b ((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> (b ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195160/23152170. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((b (^z.z)) b)) 3. ==[ beta ]==> ((^y.(a a))((b (^z.z)) b)) 4. ==[ alpha ]==> ((^x.(a a))((b (^y.y)) b)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195161/23152197. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((a a)(a a)) c)) 3. ==[ beta ]==> ((^y.y)(((a a)(a a)) c)) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a)) c)) 5. ==[ beta ]==> (((a a)(a a)) c) REDUCED to normal form. ------ 195162/23152341. ------ 1. ==[ start ]==> (((a b) b)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 195163/23152368. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 195164/23152395. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 195165/23152422. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 195166/23152476. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 195167/23152620. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))(b ((^y.y) a))) 6. ==[ alpha ]==> (((a a)(a a))(b ((^x.x) a))) 7. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 195168/23152647. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 195169/23152674. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a ((a a) a))((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a ((a a) a))((b a)(^y.y))) 6. ==[ alpha ]==> ((a ((a a) a))((b a)(^x.x))) REDUCED to normal form. ------ 195170/23152701. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 195171/23152728. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z)(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(a a))(a b))) 5. ==[ beta ]==> ((a (a a))(((^y.y)(a a))(a b))) 6. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))(a b))) 7. ==[ beta ]==> ((a (a a))((a a)(a b))) REDUCED to normal form. ------ 195172/23152755. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a) a)((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((a b)((^x.x)(a a)))) 5. ==[ beta ]==> ((((a a) a) a)((a b)(a a))) REDUCED to normal form. ------ 195173/23152782. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 195174/23152809. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(b a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(b a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(b a))) 7. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 195175/23152836. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (a a))(a (^y.(^z.z))))) REDUCED to normal form. ------ 195176/23153007. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (b (((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.a))) 5. ==[ beta ]==> (b (b (^y.a))) 6. ==[ alpha ]==> (b (b (^x.a))) REDUCED to normal form. ------ 195177/23153016. ------ 1. ==[ start ]==> (((a b) c)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b) c)((^x.x)((^y.y) a))) 3. ==[ beta ]==> (((a b) c)((^y.y) a)) 4. ==[ alpha ]==> (((a b) c)((^x.x) a)) 5. ==[ beta ]==> (((a b) c) a) REDUCED to normal form. ------ 195178/23153043. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a a) b)((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 195179/23153115. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.b)) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.b)) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 195180/23153124. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))(a b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 195181/23153151. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.b)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.b)) b) REDUCED to normal form. ------ 195182/23153205. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(b a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(b a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(b a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195183/23153232. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 195184/23153250. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.y))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 195185/23153259. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 195186/23153286. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195187/23153313. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(b (^z.z))) REDUCED to normal form. ------ 195188/23153763. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.z) c)) 3. ==[ beta ]==> (b ((^z.z) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 195189/23154015. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(c (^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(c (^z.z))) REDUCED to normal form. ------ 195190/23154042. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(b (^y.(a a)))) REDUCED to normal form. ------ 195191/23154141. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.(^y1.y1)))(^z1.a))) REDUCED to normal form. ------ 195192/23154420. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.x1)((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((a a)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195193/23154438. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a)(a a)) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a)(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a)(a a)) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195194/23154717. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 195195/23154744. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 195196/23154816. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.z) b)) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.z) b)) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z) b)) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z) b)) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y) b)) 7. ==[ beta ]==> (((a a)(a a))((^y.y) b)) 8. ==[ alpha ]==> (((a a)(a a))((^x.x) b)) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 195197/23155050. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a (b a))) REDUCED to normal form. ------ 195198/23155077. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 195199/23155104. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a a)((^z.z) b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a a)((^z.z) b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)((^y.y) b))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a) b)) REDUCED to normal form. ------ 195200/23155311. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195201/23155356. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 195202/23155518. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((b a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b a) c)) 3. ==[ beta ]==> (b ((b a) c)) REDUCED to normal form. ------ 195203/23155635. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) a) REDUCED to normal form. ------ 195204/23155662. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 195205/23155689. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 195206/23156022. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) b)(a ((a a)(^y.y)))) 6. ==[ alpha ]==> (((a a) b)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 195207/23156049. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (^x1.x1))(b a))) REDUCED to normal form. ------ 195208/23156076. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (b a))((a a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (b a))((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 195209/23156382. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((a a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 195210/23156688. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 195211/23156706. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 195212/23156931. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(c (^x1.(^y1.y1)))) REDUCED to normal form. ------ 195213/23156985. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a (^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 195214/23157597. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(a a)) c)) 3. ==[ beta ]==> (b ((^z.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 195215/23157741. ------ 1. ==[ start ]==> ((((^a.a) b) c)(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(c (^y.(a a)))) 3. ==[ beta ]==> ((b c)(c (^y.(a a)))) 4. ==[ alpha ]==> ((b c)(c (^x.(a a)))) REDUCED to normal form. ------ 195216/23157768. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 195217/23157813. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 195218/23157840. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 195219/23157876. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 195220/23157894. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a) a)(^y1.(y1 y1)))) REDUCED to normal form. ------ 195221/23157975. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.b))) 5. ==[ beta ]==> (b (a (^y.b))) 6. ==[ alpha ]==> (b (a (^x.b))) REDUCED to normal form. ------ 195222/23157984. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(a b))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 195223/23158011. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 195224/23158083. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195225/23158092. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a a)) REDUCED to normal form. ------ 195226/23158119. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((b (^y.a))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.b)(^z.a))) 5. ==[ beta ]==> ((b (^x.a)) b) REDUCED to normal form. ------ 195227/23158263. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(b ((^z.z)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))(b ((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)(b ((^y.y)(a a)))) 6. ==[ alpha ]==> ((a b)(b ((^x.x)(a a)))) 7. ==[ beta ]==> ((a b)(b (a a))) REDUCED to normal form. ------ 195228/23158290. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 195229/23158317. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (((^y.y)(b a))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((b a)(((^y.y)(a a))(a a))) 6. ==[ alpha ]==> ((b a)(((^x.x)(a a))(a a))) 7. ==[ beta ]==> ((b a)((a a)(a a))) REDUCED to normal form. ------ 195230/23158344. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 195231/23158371. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (((a b)(a a))(((a a) a)((^y.y) a))) 4. ==[ alpha ]==> (((a b)(a a))(((a a) a)((^x.x) a))) 5. ==[ beta ]==> (((a b)(a a))(((a a) a) a)) REDUCED to normal form. ------ 195232/23158398. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x)(^y.y))(a (a a)))) 5. ==[ beta ]==> (((a a)(a b))((^y.y)(a (a a)))) 6. ==[ alpha ]==> (((a a)(a b))((^x.x)(a (a a)))) 7. ==[ beta ]==> (((a a)(a b))(a (a a))) REDUCED to normal form. ------ 195233/23158425. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a (a a))(^y.y))) REDUCED to normal form. ------ 195234/23158479. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (^z.z))(a b))) REDUCED to normal form. ------ 195235/23158506. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> ((b a)((a a)((^x.x)(a a)))) 7. ==[ beta ]==> ((b a)((a a)(a a))) REDUCED to normal form. ------ 195236/23158677. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.a))) 7. ==[ beta ]==> (((^y.y) a)(^z.a)) 8. ==[ alpha ]==> (((^x.x) a)(^y.a)) 9. ==[ beta ]==> (a (^y.a)) 10. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 195237/23158758. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(a a)) a)) 3. ==[ beta ]==> (b (((^x1.x1)(a a)) a)) 4. ==[ alpha ]==> (b (((^x.x)(a a)) a)) 5. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 195238/23159001. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.b) b)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.b) b)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.b) b)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.b) b)) 5. ==[ beta ]==> ((^y.y)((^z.b) b)) 6. ==[ alpha ]==> ((^x.x)((^y.b) b)) 7. ==[ beta ]==> ((^y.b) b) 8. ==[ alpha ]==> ((^x.b) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 195239/23159028. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^c.a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a) c)) 3. ==[ beta ]==> ((^y.y)((^x1.a) c)) 4. ==[ alpha ]==> ((^x.x)((^y.a) c)) 5. ==[ beta ]==> ((^y.a) c) 6. ==[ alpha ]==> ((^x.a) c) 7. ==[ beta ]==> a REDUCED to normal form. ------ 195240/23159172. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.(a a)))) REDUCED to normal form. ------ 195241/23159199. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.b)(a a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b)(a a))) 5. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 195242/23159226. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 195243/23159271. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195244/23159280. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(y1 y1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 195245/23159307. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 195246/23159334. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 195247/23159388. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.b)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(^z.z))) 7. ==[ beta ]==> ((^y.b)(^z.z)) 8. ==[ alpha ]==> ((^x.b)(^y.y)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 195248/23159406. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((a a) a) b)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((a a) a) b)) REDUCED to normal form. ------ 195249/23159505. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)(c ((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)(c ((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a (a a)) b)(c (^y.y))) 6. ==[ alpha ]==> (((a (a a)) b)(c (^x.x))) REDUCED to normal form. ------ 195250/23159532. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(b ((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(b ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(b ((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(b ((a a) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b ((a a) a))) REDUCED to normal form. ------ 195251/23159559. ------ 1. ==[ start ]==> ((((a a) a)(b a))(a (a b))) REDUCED to normal form. ------ 195252/23159586. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((a a) a)(a a))) REDUCED to normal form. ------ 195253/23159613. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> (((a a)(a a))((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.x)(a (^y.y)))) 9. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 10. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 195254/23159640. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((a (a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((a (a a)) a)) REDUCED to normal form. ------ 195255/23159694. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 195256/23159721. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a a)((a a) a))) 3. ==[ beta ]==> ((b (a (a a)))((a a)((a a) a))) REDUCED to normal form. ------ 195257/23159820. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y y))((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x))(((^z.z) a)((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> ((a (^x.x))(a ((^z.z) a))) 8. ==[ alpha ]==> ((a (^x.x))(a ((^y.y) a))) 9. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 195258/23159838. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1) a)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1) a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((((^z.z) a)(^x1.(x1 x1)))(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(^z.z)) 7. ==[ beta ]==> ((a (^y.(y y)))(^z.z)) 8. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 195259/23160225. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a (^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(a (^z.a))) 3. ==[ beta ]==> (((^y.y) b)(a (^z.a))) 4. ==[ alpha ]==> (((^x.x) b)(a (^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 195260/23160243. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195261/23160252. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 195262/23160270. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))(^y.(^z.z)))) REDUCED to normal form. ------ 195263/23160279. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(z z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((a (^x1.x1))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 195264/23160297. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1) a)(^z1.a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.a))) 5. ==[ beta ]==> (((^y.y) a)(^z.a)) 6. ==[ alpha ]==> (((^x.x) a)(^y.a)) 7. ==[ beta ]==> (a (^y.a)) 8. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 195265/23160351. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 195266/23160387. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195267/23160414. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((^y1.(^z1.z1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 195268/23160432. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a) a) c)) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y) a) c)) 3. ==[ beta ]==> (b (((^y.y) a) c)) 4. ==[ alpha ]==> (b (((^x.x) a) c)) 5. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 195269/23160495. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 195270/23160540. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195271/23160576. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c (^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (^x1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (^x1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (^z.a))) REDUCED to normal form. ------ 195272/23160603. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b (^y.(y y)))) REDUCED to normal form. ------ 195273/23160657. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(y1 y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195274/23160675. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 195275/23160684. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 195276/23160702. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))(^y1.a))) REDUCED to normal form. ------ 195277/23160828. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(b ((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(b ((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(b ((^z.z) a))) 5. ==[ beta ]==> (((^y.y) b)(b ((^z.z) a))) 6. ==[ alpha ]==> (((^x.x) b)(b ((^y.y) a))) 7. ==[ beta ]==> (b (b ((^y.y) a))) 8. ==[ alpha ]==> (b (b ((^x.x) a))) 9. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 195278/23160855. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(a (a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (a (a a)))) REDUCED to normal form. ------ 195279/23160882. ------ 1. ==[ start ]==> (((a b)(b a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a b)(b a))(((^x.x) a)(a a))) 3. ==[ beta ]==> (((a b)(b a))(a (a a))) REDUCED to normal form. ------ 195280/23160909. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 195281/23160936. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a a)((^y.y) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))((a a) a)) REDUCED to normal form. ------ 195282/23161017. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b c)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b c)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b c)) 5. ==[ beta ]==> ((b (^y.y))(b c)) 6. ==[ alpha ]==> ((b (^x.x))(b c)) REDUCED to normal form. ------ 195283/23161098. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(b (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(b (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (a (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(b (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.x))(b (a (^y.y)))) REDUCED to normal form. ------ 195284/23161116. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z)(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.a))) 5. ==[ beta ]==> ((b (^x.x))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 195285/23161125. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a ((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a ((^y.y) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(a a)) REDUCED to normal form. ------ 195286/23161152. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a (^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(a a))) REDUCED to normal form. ------ 195287/23161161. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1)) b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195288/23161323. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> (b ((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) a)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195289/23161431. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((^a.a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.y1) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195290/23161457. ------ 1. ==[ start ]==> (^a.((^b.b)(^c.a))) 2. ==[ alpha ]==> (^x.((^y.y)(^z.x))) 3. ==[ beta ]==> (^x.(^z.x)) 4. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 195291/23161458. ------ 1. ==[ start ]==> (a ((^b.b)(^c.a))) 2. ==[ alpha ]==> (a ((^x.x)(^y.a))) 3. ==[ beta ]==> (a (^y.a)) 4. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 195292/23166213. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(^x1.((a a)(a a)))) 3. ==[ beta ]==> ((^x1.((a a)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((^x.((a a)(a a)))(^y.(^z.z))) 5. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 195293/23173251. ------ 1. ==[ start ]==> ((^a.a)((^b.b)(^c.a))) 2. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 3. ==[ beta ]==> ((^y.y)(^z.a)) 4. ==[ alpha ]==> ((^x.x)(^y.a)) 5. ==[ beta ]==> (^y.a) 6. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 195294/23173278. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.b))((^y.(^z.(^x1.x1)))(^y1.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.(^z1.(^x2.x2)))(^y2.b))) 5. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195295/23173386. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^z.b)(^x1.(^y1.(^z1.z1))))(^y.y)) 4. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (b (^y1.y1)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195296/23173503. ------ 1. ==[ start ]==> ((^a.(^b.a))(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.x))(c ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.(c ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (^x.(c ((^y.(^z.z)) a))) 5. ==[ beta ]==> (^x.(c (^z.z))) 6. ==[ alpha ]==> (^x.(c (^y.y))) REDUCED to normal form. ------ 195297/23173551. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 195298/23173746. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b a)(a b))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 195299/23174883. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.(z (z (^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(z (z (^x1.x1))))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.(z (z (^x1.x1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.(y (y (^z.z))))) 7. ==[ beta ]==> ((a a)(^y.(y (y (^z.z))))) 8. ==[ alpha ]==> ((a a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 195300/23174961. ------ 1. ==[ start ]==> ((^a.(^a.b))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 195301/23175711. ------ 1. ==[ start ]==> (((a b)(a a))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(a a))(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a b)(a a))(^x.(^z.z))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 195302/23176125. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((^x.b)(a (^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.b)(a (^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> (b (^z.(^x1.x1))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 195303/23178003. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.x1)((a a)(a a)))) 3. ==[ beta ]==> (((^x1.x1)((a a)(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.x)((a a)(a a)))(^y.(^z.z))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 195304/23178006. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(^b.((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.((a a)(a a)))) REDUCED to normal form. ------ 195305/23178606. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195306/23178921. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 195307/23179680. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 195308/23179920. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> ((((^y.a)((a a)(^z.z)))((^y.a)((a a)(^z.z))))(((^y.a)((a a)(^z.z)))((^y.a)((a a)(^z.z))))) 4. ==[ alpha ]==> ((((^x.a)((a a)(^y.y)))((^z.a)((a a)(^x1.x1))))(((^y1.a)((a a)(^z1.z1)))((^x2.a)((a a)(^y2.y2))))) 5. ==[ beta ]==> ((a ((^z.a)((a a)(^x1.x1))))(((^y1.a)((a a)(^z1.z1)))((^x2.a)((a a)(^y2.y2))))) 6. ==[ alpha ]==> ((a ((^x.a)((a a)(^y.y))))(((^z.a)((a a)(^x1.x1)))((^y1.a)((a a)(^z1.z1))))) 7. ==[ beta ]==> ((a a)(((^z.a)((a a)(^x1.x1)))((^y1.a)((a a)(^z1.z1))))) 8. ==[ alpha ]==> ((a a)(((^x.a)((a a)(^y.y)))((^z.a)((a a)(^x1.x1))))) 9. ==[ beta ]==> ((a a)(a ((^z.a)((a a)(^x1.x1))))) 10. ==[ alpha ]==> ((a a)(a ((^x.a)((a a)(^y.y))))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 195309/23180283. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 195310/23180841. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(^y.(y a))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.(y a))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(x a))) REDUCED to normal form. ------ 195311/23181000. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195312/23181867. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 195313/23182161. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.b)(a (^y1.y1)))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195314/23182740. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^c.(a b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(a b))) 3. ==[ beta ]==> (b (^z.(a b))) 4. ==[ alpha ]==> (b (^x.(a b))) REDUCED to normal form. ------ 195315/23183136. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.x))) REDUCED to normal form. ------ 195316/23183325. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.(^z.b))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.b))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.b))) REDUCED to normal form. ------ 195317/23183403. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(z z))((^x1.x1) a))) 3. ==[ beta ]==> (((^z.(z z))((^x1.x1) a))(((^z.(z z))((^x1.x1) a))(^y.y))) 4. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(((^z.(z z))((^x1.x1) a))(^y1.y1))) 5. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(((^z.(z z))((^x1.x1) a))(^y1.y1))) 6. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(z z))((^x1.x1) a))(^y1.y1))) 7. ==[ beta ]==> ((a ((^y.y) a))(((^z.(z z))((^x1.x1) a))(^y1.y1))) 8. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(y y))((^z.z) a))(^x1.x1))) 9. ==[ beta ]==> ((a a)(((^y.(y y))((^z.z) a))(^x1.x1))) 10. ==[ alpha ]==> ((a a)(((^x.(x x))((^y.y) a))(^z.z))) 11. ==[ beta ]==> ((a a)((((^y.y) a)((^y.y) a))(^z.z))) 12. ==[ alpha ]==> ((a a)((((^x.x) a)((^y.y) a))(^z.z))) 13. ==[ beta ]==> ((a a)((a ((^y.y) a))(^z.z))) 14. ==[ alpha ]==> ((a a)((a ((^x.x) a))(^y.y))) 15. ==[ beta ]==> ((a a)((a a)(^y.y))) 16. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 195318/23184276. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(c c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(c c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195319/23184324. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(a (a a)))) REDUCED to normal form. ------ 195320/23184432. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 195321/23184621. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^x.a)) REDUCED to normal form. ------ 195322/23184693. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.z)) 3. ==[ beta ]==> ((b (^y.y))(^z.z)) 4. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 195323/23184702. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(^z.a))) REDUCED to normal form. ------ 195324/23184900. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> (b (^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 195325/23185008. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^a.(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(y1 y1))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(y1 y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195326/23185047. ------ 1. ==[ start ]==> ((a a)((^b.b)(^c.a))) 2. ==[ alpha ]==> ((a a)((^x.x)(^y.a))) 3. ==[ beta ]==> ((a a)(^y.a)) 4. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 195327/23185074. ------ 1. ==[ start ]==> ((a (a a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.b))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 195328/23185182. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 195329/23185299. ------ 1. ==[ start ]==> ((a (^b.a))(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.a))(c ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (^x.a))(c (^z.z))) 4. ==[ alpha ]==> ((a (^x.a))(c (^y.y))) REDUCED to normal form. ------ 195330/23185317. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 195331/23185344. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 195332/23185380. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> ((^y.a)((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> ((^x.a)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 195333/23185407. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a)(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 195334/23185461. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (a (((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 195335/23185488. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195336/23185542. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b a)(a b))) 2. ==[ alpha ]==> ((a (^x.(x x)))((b a)(a b))) REDUCED to normal form. ------ 195337/23185650. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.(y y))(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.(x x))(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a)(a (^y.(^z.z))))(((a a) a)(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(((a a) a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 195338/23185677. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 195339/23185731. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 7. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 8. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 9. ==[ beta ]==> (a (b (^y.y))) 10. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 195340/23185758. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a a))((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (a a))((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a a))((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((a (a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 195341/23185785. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a a)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)((a a)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (a (^y.y))))) 5. ==[ beta ]==> ((a a)(a (a (^y.y)))) 6. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 195342/23185821. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 195343/23185848. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a (a a))(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 195344/23185938. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 195345/23185956. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (^y.(^z.z)))(^x1.a))) 3. ==[ beta ]==> ((b b)((a (^y.(^z.z)))(^x1.a))) 4. ==[ alpha ]==> ((b b)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 195346/23185965. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 195347/23186091. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a)) b)(((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 195348/23186118. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (a (((^y.y)(^z.z))(^x1.x1))) 6. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.z))) 7. ==[ beta ]==> (a ((^y.y)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 195349/23186145. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))(^z.(a a)))) REDUCED to normal form. ------ 195350/23186226. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((a a)(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 195351/23186253. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a (^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a (^x1.x1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a (^z.z))) a)) 5. ==[ beta ]==> ((^y.y)((a (a (^z.z))) a)) 6. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) a)) 7. ==[ beta ]==> ((a (a (^y.y))) a) 8. ==[ alpha ]==> ((a (a (^x.x))) a) REDUCED to normal form. ------ 195352/23186370. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 195353/23186676. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(a (a (a (^z.z))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(a (a (a (^z.z))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(a (a (a (^z.z))))) 5. ==[ beta ]==> ((a ((^y.y) a))(a (a (a (^z.z))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(a (a (a (^y.y))))) 7. ==[ beta ]==> ((a a)(a (a (a (^y.y))))) 8. ==[ alpha ]==> ((a a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 195354/23186685. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a (a a))(^x.a))(a (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(a (^y.y))) REDUCED to normal form. ------ 195355/23186757. ------ 1. ==[ start ]==> ((a (^a.b))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.b))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> ((a (^x.b))(((a a)(a a)) a)) REDUCED to normal form. ------ 195356/23186946. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a) a)(b a))) 3. ==[ beta ]==> ((^y.b)(((a a) a)(b a))) 4. ==[ alpha ]==> ((^x.b)(((a a) a)(b a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 195357/23187027. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z) a)((a a)(a a)))) IRREDUCIBLE: cycle. ------ 195358/23187117. ------ 1. ==[ start ]==> (((a b) a)(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a b) a)(((^x.(^y.y)) a)(^z.z))) 3. ==[ beta ]==> (((a b) a)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 195359/23187144. ------ 1. ==[ start ]==> (((a a)(^a.b))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 195360/23187198. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(b (^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 195361/23187225. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 195362/23187252. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b a)(^z.a))) 5. ==[ beta ]==> ((^y.a)((b a)(^z.a))) 6. ==[ alpha ]==> ((^x.a)((b a)(^y.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 195363/23187279. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))(^x1.b))) REDUCED to normal form. ------ 195364/23187306. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a b)(^x.x))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 195365/23187342. ------ 1. ==[ start ]==> (((a a)(a b))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 195366/23187396. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 195367/23187423. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(x x))((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(b ((^y.y) b))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(b ((^x.x) b))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(b b)) REDUCED to normal form. ------ 195368/23187450. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.a)((a a)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.a)((a a)(a a)))) 7. ==[ beta ]==> (a ((^y.a)((a a)(a a)))) 8. ==[ alpha ]==> (a ((^x.a)((a a)(a a)))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195369/23187477. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 195370/23187504. ------ 1. ==[ start ]==> (((a b)(a a))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.x)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 195371/23187918. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b (a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b (a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 195372/23188242. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1) a)((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) b))) 5. ==[ beta ]==> (((^y.y) a)((^z.z) b)) 6. ==[ alpha ]==> (((^x.x) a)((^y.y) b)) 7. ==[ beta ]==> (a ((^y.y) b)) 8. ==[ alpha ]==> (a ((^x.x) b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 195373/23188386. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) b)(^y.a))) 3. ==[ beta ]==> (((a b) c)(b (^y.a))) 4. ==[ alpha ]==> (((a b) c)(b (^x.a))) REDUCED to normal form. ------ 195374/23188413. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a) b)((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a) b)((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 195375/23188440. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 195376/23188494. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((a a)(^x1.b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a a)(^z.b))) REDUCED to normal form. ------ 195377/23188521. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a b)(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.b))((a b)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((a b)(^y.(a a)))) REDUCED to normal form. ------ 195378/23188602. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 195379/23188629. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.a))(a (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 195380/23188773. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a (a b))((^y.y)(^z.a))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(^y.a))) 5. ==[ beta ]==> ((a (a b))(^y.a)) 6. ==[ alpha ]==> ((a (a b))(^x.a)) REDUCED to normal form. ------ 195381/23188800. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 195382/23188881. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))(^z.b))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.b))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 195383/23188908. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(^z.(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 195384/23189052. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(b ((a a)(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))(b ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(b ((a a)(a a)))) 5. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 195385/23189133. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> (b (((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (b (b (a (^y.y)))) 6. ==[ alpha ]==> (b (b (a (^x.x)))) REDUCED to normal form. ------ 195386/23189241. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> ((b a)(((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> ((b a)(((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> ((b a)((a a)((a a) a))) REDUCED to normal form. ------ 195387/23189268. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a b)(a b))) 3. ==[ beta ]==> ((^y.y)((a b)(a b))) 4. ==[ alpha ]==> ((^x.x)((a b)(a b))) 5. ==[ beta ]==> ((a b)(a b)) REDUCED to normal form. ------ 195388/23189322. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (((a b)(a b))((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> (((a b)(a b))((a a)(^y.y))) 8. ==[ alpha ]==> (((a b)(a b))((a a)(^x.x))) REDUCED to normal form. ------ 195389/23189403. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (b ((a (^y.y))((^z.z) b))) 4. ==[ alpha ]==> (b ((a (^x.x))((^y.y) b))) 5. ==[ beta ]==> (b ((a (^x.x)) b)) REDUCED to normal form. ------ 195390/23189466. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(a a))(^x1.x1))) REDUCED to normal form. ------ 195391/23189529. ------ 1. ==[ start ]==> (((a a)(b a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 195392/23189610. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(a a))((a a) a))) 3. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 195393/23189637. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.b)(a b))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.b)(a b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.b)(a b))) 5. ==[ beta ]==> (((a a) a)((^y.b)(a b))) 6. ==[ alpha ]==> (((a a) a)((^x.b)(a b))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 195394/23189691. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 195395/23189718. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(z z))(b a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y y))(b a))) 5. ==[ beta ]==> (((a a) a)((^y.(y y))(b a))) 6. ==[ alpha ]==> (((a a) a)((^x.(x x))(b a))) 7. ==[ beta ]==> (((a a) a)((b a)(b a))) REDUCED to normal form. ------ 195396/23189745. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 195397/23189799. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 195398/23190132. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(b ((^z.z) b))) 3. ==[ beta ]==> ((^y.y)(b ((^z.z) b))) 4. ==[ alpha ]==> ((^x.x)(b ((^y.y) b))) 5. ==[ beta ]==> (b ((^y.y) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 195399/23190186. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(((^z.z) b)(a a))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((^z.z) b)(a a))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(((^z.z) b)(a a))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((^y.y) b)(a a))) 7. ==[ beta ]==> (((a a)(a a))(((^y.y) b)(a a))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)(a a))) 9. ==[ beta ]==> (((a a)(a a))(b (a a))) REDUCED to normal form. ------ 195400/23190195. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.b) b)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y) b)) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) b) REDUCED to normal form. ------ 195401/23190222. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.(^z1.z1))) c)) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.(^z1.z1))) c)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.(^y1.y1))) c)) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.(^y1.y1))) c)) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1))) c)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 195402/23190267. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (b (((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a (a a)))) REDUCED to normal form. ------ 195403/23190375. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195404/23190402. ------ 1. ==[ start ]==> ((a (^b.b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 195405/23190447. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 195406/23190474. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(b (^z.z))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(b (^z.z))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 195407/23190528. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((^z.z)(a a))) 3. ==[ beta ]==> (((^y.y)(a b))((^z.z)(a a))) 4. ==[ alpha ]==> (((^x.x)(a b))((^y.y)(a a))) 5. ==[ beta ]==> ((a b)((^y.y)(a a))) 6. ==[ alpha ]==> ((a b)((^x.x)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 195408/23190555. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.(^z.z)))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 195409/23190636. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 195410/23190681. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((a a) a)(^x1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195411/23190717. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 195412/23191131. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))(b (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))(b (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 195413/23191167. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.x1) a)) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.x1) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z) a)) 5. ==[ beta ]==> ((^y.(a a))((^z.z) a)) 6. ==[ alpha ]==> ((^x.(a a))((^y.y) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195414/23191194. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 195415/23191212. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((b a)(a (^y.y)))) 3. ==[ beta ]==> (b ((b a)(a (^y.y)))) 4. ==[ alpha ]==> (b ((b a)(a (^x.x)))) REDUCED to normal form. ------ 195416/23191221. ------ 1. ==[ start ]==> (((a b)(^c.a))((^d.a) c)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a) c)) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 195417/23191248. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1)) d)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1)) d)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1)) d)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195418/23191320. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195419/23191446. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(b (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (b a))(b (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (b a))(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 195420/23191473. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 195421/23191500. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))(a a))) 6. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))(a a))) 7. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(a a))) 8. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(a a))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 195422/23191554. ------ 1. ==[ start ]==> (((a b)((a a) a))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.x)) REDUCED to normal form. ------ 195423/23191581. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))(a (a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(a (a a)))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 195424/23191608. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a))) b) REDUCED to normal form. ------ 195425/23191662. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.x1)) REDUCED to normal form. ------ 195426/23191689. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((b (a a))((^y.(y y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.(x x))((^y.y)(a a)))) 5. ==[ beta ]==> ((b (a a))(((^y.y)(a a))((^y.y)(a a)))) 6. ==[ alpha ]==> ((b (a a))(((^x.x)(a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((b (a a))((a a)((^y.y)(a a)))) 8. ==[ alpha ]==> ((b (a a))((a a)((^x.x)(a a)))) 9. ==[ beta ]==> ((b (a a))((a a)(a a))) REDUCED to normal form. ------ 195427/23191716. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)((a a)(^y.y)))) 3. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 195428/23192076. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(a a))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 195429/23192103. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((b a)(a a))) 3. ==[ beta ]==> ((^y.y)((b a)(a a))) 4. ==[ alpha ]==> ((^x.x)((b a)(a a))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 195430/23192157. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (((b a)(b a))(((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> (((b a)(b a))(((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> (((b a)(b a))((a a)((^y.y) a))) 6. ==[ alpha ]==> (((b a)(b a))((a a)((^x.x) a))) 7. ==[ beta ]==> (((b a)(b a))((a a) a)) REDUCED to normal form. ------ 195431/23192238. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))((a a) a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a) a))) 5. ==[ beta ]==> (b ((^y.y)((a a) a))) 6. ==[ alpha ]==> (b ((^x.x)((a a) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 195432/23192346. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a a)(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a a)(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195433/23192382. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((b a)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((b a)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((b a)(^z.z))) REDUCED to normal form. ------ 195434/23192409. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 195435/23192445. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a a)) REDUCED to normal form. ------ 195436/23192472. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.b)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.b)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x)) b) b) REDUCED to normal form. ------ 195437/23192526. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 195438/23192553. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(z z))(a b))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(a b))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(a b))) 7. ==[ beta ]==> (((a a)(^x.x))((a b)(a b))) REDUCED to normal form. ------ 195439/23192580. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)(a a)) a) REDUCED to normal form. ------ 195440/23192607. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 195441/23192634. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.y)(b a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)(b a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(b a))) 5. ==[ beta ]==> (((a a)((a a) a))(b a)) REDUCED to normal form. ------ 195442/23192715. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 195443/23192742. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.b)(^z.(z z)))) 5. ==[ beta ]==> ((b (a (^x.x))) b) REDUCED to normal form. ------ 195444/23192796. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 195445/23192886. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))(b ((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))(b ((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))(b ((a a)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.z))(b ((a a)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b ((a a)(^z.z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195446/23192967. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((^z.z)(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (b (((^z.z)(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> (b ((a a)(a (^y.y)))) 6. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 195447/23193075. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a (a a))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195448/23193246. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a b)(^z.a))) 3. ==[ beta ]==> ((a (^y.y))((a b)(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(^y.a))) REDUCED to normal form. ------ 195449/23193273. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((a a) a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 195450/23193354. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y) a)(^z.b))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a (^z.b))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(a (^y.b))) REDUCED to normal form. ------ 195451/23193381. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 195452/23193462. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a) b)) REDUCED to normal form. ------ 195453/23193489. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a b) c)) 3. ==[ beta ]==> ((b (^y.a))((a b) c)) 4. ==[ alpha ]==> ((b (^x.a))((a b) c)) REDUCED to normal form. ------ 195454/23193579. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((^z.a)(^z.a))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(^z.a))) 5. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 195455/23193606. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) a) REDUCED to normal form. ------ 195456/23193633. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 195457/23193876. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(b (^z.(a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))(b (^z.(a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(b (^y.(a a)))) 5. ==[ beta ]==> ((b a)(b (^y.(a a)))) 6. ==[ alpha ]==> ((b a)(b (^x.(a a)))) REDUCED to normal form. ------ 195458/23193957. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 195459/23194353. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(a a)) a)) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a)) a)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a)) a)) 5. ==[ beta ]==> (a ((^y.(a a)) a)) 6. ==[ alpha ]==> (a ((^x.(a a)) a)) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 195460/23194371. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((a b)(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((a b)(a a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a b)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a b)(a a))) 5. ==[ beta ]==> ((^y.y)((a b)(a a))) 6. ==[ alpha ]==> ((^x.x)((a b)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 195461/23194398. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(((a a) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.y)))) 5. ==[ beta ]==> (((a a) a)(a (^y.y))) 6. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 195462/23194452. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))((a (a a))(a (a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a (a a))(a (a a)))) 7. ==[ beta ]==> ((b b)((a (a a))(a (a a)))) REDUCED to normal form. ------ 195463/23194533. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a a)(a b))) 3. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 195464/23194569. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a b)(^z.z))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a b)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a b)(^y.y))) REDUCED to normal form. ------ 195465/23194596. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 195466/23194650. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (a a))(^y1.(y1 y1)))) REDUCED to normal form. ------ 195467/23194677. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(x x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 195468/23194704. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 195469/23194758. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a b) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a b) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b) a)) 5. ==[ beta ]==> ((^y.y)((a b) a)) 6. ==[ alpha ]==> ((^x.x)((a b) a)) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 195470/23194821. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 195471/23194848. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))(^z.(z z)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 195472/23194875. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 195473/23194929. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(^y.b))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.b)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.b)) REDUCED to normal form. ------ 195474/23195091. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b (^y.a))) 3. ==[ beta ]==> ((b (a (a a)))(b (^y.a))) 4. ==[ alpha ]==> ((b (a (a a)))(b (^x.a))) REDUCED to normal form. ------ 195475/23195118. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(a (^y.b))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a (^y.b))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.b))) REDUCED to normal form. ------ 195476/23195172. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 195477/23195190. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (a a))(^z.a))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.a))) REDUCED to normal form. ------ 195478/23195199. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(y y))((^z.z) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(((^z.z) a)((^z.z) a))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((a (a (a (^x.x))))(a ((^z.z) a))) 6. ==[ alpha ]==> ((a (a (a (^x.x))))(a ((^y.y) a))) 7. ==[ beta ]==> ((a (a (a (^x.x))))(a a)) REDUCED to normal form. ------ 195479/23195622. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 6. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 195480/23195649. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 195481/23195757. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z)) a)) 7. ==[ beta ]==> (((^y.y)(^z.z)) a) 8. ==[ alpha ]==> (((^x.x)(^y.y)) a) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 195482/23195784. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (a a)) b)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (a a)) b)) REDUCED to normal form. ------ 195483/23195910. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (a a))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195484/23195946. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a) c)) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 195485/23196027. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (a a))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195486/23196054. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 195487/23196072. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(c c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(c c)) REDUCED to normal form. ------ 195488/23196090. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 195489/23196117. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (a a))) REDUCED to normal form. ------ 195490/23196144. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((a (b (^x.x)))((^z.z)(^z.z))) 6. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 195491/23196171. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 195492/23196198. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> (b ((^y.(^z.z))(^x1.a))) 8. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195493/23196225. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.(x1 x1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(z z))) REDUCED to normal form. ------ 195494/23196306. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b (^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b (^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b (^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b (^y.a))) REDUCED to normal form. ------ 195495/23196360. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^b.a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.a)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a)) a) REDUCED to normal form. ------ 195496/23196387. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 195497/23196414. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))((^y.y) a)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x) a)) 5. ==[ beta ]==> ((((a a)(a a))(a (a a))) a) REDUCED to normal form. ------ 195498/23196468. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 195499/23196486. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a) c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a) c)) 3. ==[ beta ]==> ((b (^y.y))((a a) c)) 4. ==[ alpha ]==> ((b (^x.x))((a a) c)) REDUCED to normal form. ------ 195500/23196495. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.a)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.a)) REDUCED to normal form. ------ 195501/23196531. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195502/23196558. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(a (^y.y)))) 5. ==[ beta ]==> ((a a)(a (^y.y))) 6. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 195503/23196693. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a (a (^y1.y1)))) 3. ==[ beta ]==> (b (a (a (^y1.y1)))) 4. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 195504/23196801. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(a (a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(a (a a))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195505/23208648. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.b)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195506/23208963. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.(^y1.y1))) a)) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195507/23209389. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 195508/23209584. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195509/23210271. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((a ((^y.y) a))(^z.(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(z (^x1.x1))))) 7. ==[ beta ]==> ((a a)(^y.(^z.(z (^x1.x1))))) 8. ==[ alpha ]==> ((a a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 195510/23210280. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 195511/23210685. ------ 1. ==[ start ]==> ((((a a) a) b)(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) b)(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a) b)(^x.(^z.z))) 4. ==[ alpha ]==> ((((a a) a) b)(^x.(^y.y))) REDUCED to normal form. ------ 195512/23210703. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (b (^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 195513/23210916. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (^y.(((^z.(a a))((^x1.x1)(a a)))((^z.(a a))((^x1.x1)(a a))))) 4. ==[ alpha ]==> (^x.(((^y.(a a))((^z.z)(a a)))((^x1.(a a))((^y1.y1)(a a))))) 5. ==[ beta ]==> (^x.((a a)((^x1.(a a))((^y1.y1)(a a))))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a))((^z.z)(a a))))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 195514/23211123. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((^y.y)((((^z.(^x1.x1)) a) a)(((^z.(^x1.x1)) a) a))) 4. ==[ alpha ]==> ((^x.x)((((^y.(^z.z)) a) a)(((^x1.(^y1.y1)) a) a))) 5. ==[ beta ]==> ((((^y.(^z.z)) a) a)(((^x1.(^y1.y1)) a) a)) 6. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(((^z.(^x1.x1)) a) a)) 7. ==[ beta ]==> (((^y.y) a)(((^z.(^x1.x1)) a) a)) 8. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a) a)) 9. ==[ beta ]==> (a (((^y.(^z.z)) a) a)) 10. ==[ alpha ]==> (a (((^x.(^y.y)) a) a)) 11. ==[ beta ]==> (a ((^y.y) a)) 12. ==[ alpha ]==> (a ((^x.x) a)) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195515/23211522. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 195516/23213034. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.((a a)(a a)))) REDUCED to normal form. ------ 195517/23213103. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195518/23213403. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((a a)(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195519/23214309. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 195520/23214762. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(a a))(^z.((^x1.x1) b))) 6. ==[ alpha ]==> ((^x.(a a))(^y.((^z.z) b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195521/23215671. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 195522/23215950. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(^c.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(^x1.(b a))) REDUCED to normal form. ------ 195523/23217549. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a b)(^x1.(^y1.y1)))) 3. ==[ eta ]==> ((^y.(^z.z))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195524/23217723. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((^y1.y1)(a a)))) 3. ==[ beta ]==> (b (^x1.((^y1.y1)(a a)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(a a)))) 5. ==[ beta ]==> (b (^x.(a a))) REDUCED to normal form. ------ 195525/23217948. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((^y.y) a)(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> (((^x.x) a)(^y.((^z.z)(y y)))) 5. ==[ beta ]==> (a (^y.((^z.z)(y y)))) 6. ==[ alpha ]==> (a (^x.((^y.y)(x x)))) 7. ==[ beta ]==> (a (^x.(x x))) REDUCED to normal form. ------ 195526/23218137. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^c.(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a b))) REDUCED to normal form. ------ 195527/23218368. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.b)(^y1.y1))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 195528/23218791. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a))(^z.a))) 3. ==[ beta ]==> (((a (a a))(^z.a))(((a (a a))(^z.a))(^y.y))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(((a (a a))(^y.a))(^z.z))) REDUCED to normal form. ------ 195529/23219190. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 7. ==[ beta ]==> (b (^x.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 195530/23219664. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a)(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195531/23220114. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.a) a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195532/23220288. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b (^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 195533/23220396. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195534/23220453. ------ 1. ==[ start ]==> ((a (^a.a))((^b.b)(^c.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a (^x.x))(^z.a)) 4. ==[ alpha ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 195535/23220480. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195536/23220588. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195537/23220642. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 195538/23220732. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(b (a (a (^z.z))))) 3. ==[ beta ]==> ((^y.y)(b (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 195539/23220768. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 195540/23220813. ------ 1. ==[ start ]==> (((a (^a.a)) b)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) b)(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.y))) REDUCED to normal form. ------ 195541/23220840. ------ 1. ==[ start ]==> ((((^a.a) a) a)((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a a)((b (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((a a)((b (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((a a)((b (^x.x)) a)) REDUCED to normal form. ------ 195542/23220867. ------ 1. ==[ start ]==> (((a a)(^b.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 195543/23220894. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.x1))) REDUCED to normal form. ------ 195544/23220921. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 195545/23221029. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a b)(b a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a b)(b a))) 3. ==[ beta ]==> ((a a)((a b)(b a))) REDUCED to normal form. ------ 195546/23221110. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a b)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 195547/23221137. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> (((a (a a)) a)(a (b (^y.y)))) 4. ==[ alpha ]==> (((a (a a)) a)(a (b (^x.x)))) REDUCED to normal form. ------ 195548/23221164. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 195549/23221182. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(b (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(b (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(y (^z.z))))) 5. ==[ beta ]==> (b (^y.(y (^z.z)))) 6. ==[ alpha ]==> (b (^x.(x (^y.y)))) REDUCED to normal form. ------ 195550/23221191. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a a)(a (a (^z.z))))) REDUCED to normal form. ------ 195551/23221236. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> (((a a)(a a))((a a)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))((a a)(^x.x))) REDUCED to normal form. ------ 195552/23221281. ------ 1. ==[ start ]==> (((a a)(a (a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 195553/23221308. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 195554/23221335. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (^x.x)))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 195555/23221389. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b a)(^z.b))) 3. ==[ beta ]==> ((a (^y.y))((b a)(^z.b))) 4. ==[ alpha ]==> ((a (^x.x))((b a)(^y.b))) REDUCED to normal form. ------ 195556/23221479. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.b)(b a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.b)(b a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.b)(b a))) 5. ==[ beta ]==> ((^y.y)((^y1.b)(b a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 7. ==[ beta ]==> ((^y.b)(b a)) 8. ==[ alpha ]==> ((^x.b)(b a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 195557/23221533. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195558/23221560. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 7. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 195559/23221614. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 195560/23221686. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 195561/23221713. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((b (^y.y)) c)) REDUCED to normal form. ------ 195562/23221857. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195563/23222028. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))(c (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(c (b (^x1.x1)))) REDUCED to normal form. ------ 195564/23222055. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (^y.(y y)))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (^x.(x x)))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 195565/23222073. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.z)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.z)(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(^z.(z (^x1.x1))))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(z (^x1.x1))))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(y (^z.z))))) 9. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 10. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 195566/23222082. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(a (a (a (^y.y))))) REDUCED to normal form. ------ 195567/23222109. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.(^z1.z1)) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195568/23222136. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 195569/23222325. ------ 1. ==[ start ]==> (((^a.b) a)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((a b)((a a)(^y.y)))) 3. ==[ beta ]==> (b ((a b)((a a)(^y.y)))) 4. ==[ alpha ]==> (b ((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 195570/23222487. ------ 1. ==[ start ]==> ((((a a) a) b)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a) b)((a a)((^x.(^y.y)) a))) 3. ==[ beta ]==> ((((a a) a) b)((a a)(^y.y))) 4. ==[ alpha ]==> ((((a a) a) b)((a a)(^x.x))) REDUCED to normal form. ------ 195571/23222505. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (b (a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (b (a (^x.(x (^y.y))))) REDUCED to normal form. ------ 195572/23222613. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(a (a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a (a a))) REDUCED to normal form. ------ 195573/23222694. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195574/23222721. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 195575/23222739. ------ 1. ==[ start ]==> (((a a)(a b))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 195576/23222793. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> ((a (^x.x))(^z.(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 195577/23222820. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a (a a))(^x.x))) REDUCED to normal form. ------ 195578/23222928. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.(^z.z)) a) a)) 3. ==[ beta ]==> ((a (a a))(((^y.(^z.z)) a) a)) 4. ==[ alpha ]==> ((a (a a))(((^x.(^y.y)) a) a)) 5. ==[ beta ]==> ((a (a a))((^y.y) a)) 6. ==[ alpha ]==> ((a (a a))((^x.x) a)) 7. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 195579/23223018. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((^y.y)(^z.(z z))) 8. ==[ alpha ]==> ((^x.x)(^y.(y y))) 9. ==[ beta ]==> (^y.(y y)) 10. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 195580/23223099. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195581/23223153. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 195582/23223180. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 195583/23223234. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(y1 y1))(^z1.z1))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(x1 x1))(^y1.y1))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(^y1.y1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.x1))) 9. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 11. ==[ beta ]==> ((^y.(y y))(^z.z)) 12. ==[ alpha ]==> ((^x.(x x))(^y.y)) 13. ==[ beta ]==> ((^y.y)(^y.y)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195584/23223297. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(b (b (^y.y)))) REDUCED to normal form. ------ 195585/23223324. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 195586/23223351. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((b (^z.z))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))(a a))) REDUCED to normal form. ------ 195587/23223540. ------ 1. ==[ start ]==> (((^a.b) c)((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) c)((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (b ((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (b ((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 195588/23223774. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 195589/23223936. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.b)((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a)) b) REDUCED to normal form. ------ 195590/23224017. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 195591/23224116. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((b (^y.y)) a)) REDUCED to normal form. ------ 195592/23224143. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))(a a))(((a a)(a a)) b)) REDUCED to normal form. ------ 195593/23224170. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) b) c)) 3. ==[ beta ]==> ((a (a b))(((^y.y) b) c)) 4. ==[ alpha ]==> ((a (a b))(((^x.x) b) c)) 5. ==[ beta ]==> ((a (a b))(b c)) REDUCED to normal form. ------ 195594/23224449. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195595/23224593. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((b a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((b a)(a (a a)))) REDUCED to normal form. ------ 195596/23224701. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.(a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 195597/23224728. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(^x.b))((a a)(^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 195598/23224782. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 195599/23224800. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(c (^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(c (^y.y))) 3. ==[ beta ]==> (b (c (^y.y))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 195600/23224809. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((a (^y.y)) b)) REDUCED to normal form. ------ 195601/23224836. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))((a a)((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 195602/23224908. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 195603/23224926. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 195604/23224953. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((b a)(^z.(z z)))) REDUCED to normal form. ------ 195605/23224980. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))(((a a)(^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 195606/23225007. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> (((a (a a))(a b))((a a)(^y.a))) 4. ==[ alpha ]==> (((a (a a))(a b))((a a)(^x.a))) REDUCED to normal form. ------ 195607/23225034. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a b)(^z.b))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a b)(^z.b))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a b)(^y.b))) 5. ==[ beta ]==> (((a a) a)((a b)(^y.b))) 6. ==[ alpha ]==> (((a a) a)((a b)(^x.b))) REDUCED to normal form. ------ 195608/23225061. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a) a)(^y.(a a)))) REDUCED to normal form. ------ 195609/23225088. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a)(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (a a)))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 195610/23225142. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 195611/23225205. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)((a a)(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((a a)(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195612/23225286. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> ((a a)((^z.(^x1.(^y1.y1)))(^z1.a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 195613/23225367. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 195614/23225502. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 195615/23225529. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195616/23225592. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(((^y.y) b)(a a))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(b (a a))) REDUCED to normal form. ------ 195617/23225619. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1)))(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))(a (^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 195618/23225673. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 195619/23225700. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(^x.(x x)))((a a)(^z.z))) 8. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 195620/23225727. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a b)((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a b)((a a) a))) REDUCED to normal form. ------ 195621/23225781. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)((^y1.y1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(a a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(a a))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a a)) REDUCED to normal form. ------ 195622/23225925. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> ((a b)(((^y.y) b)(^z.z))) 6. ==[ alpha ]==> ((a b)(((^x.x) b)(^y.y))) 7. ==[ beta ]==> ((a b)(b (^y.y))) 8. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 195623/23225952. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 195624/23225979. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((b a)(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((b a)(^z.a))) 3. ==[ beta ]==> (((a b)(^y.y))((b a)(^z.a))) 4. ==[ alpha ]==> (((a b)(^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 195625/23226006. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((a a)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(a (a a)))(((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 195626/23226033. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 195627/23226087. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((a a) a)(^z.b))) REDUCED to normal form. ------ 195628/23226114. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.(a a)))) 7. ==[ beta ]==> ((a b)(^y.(a a))) 8. ==[ alpha ]==> ((a b)(^x.(a a))) REDUCED to normal form. ------ 195629/23226123. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195630/23226150. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(z1 z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z1.(z1 z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(y y))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(x x))((a a)(^y.y))) 7. ==[ beta ]==> (((a a)(^y.y))((a a)(^y.y))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 195631/23226285. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 195632/23226393. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b)(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b)(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195633/23226447. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195634/23226528. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 195635/23226564. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(a ((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(a ((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(a ((^z.z) b))) 5. ==[ beta ]==> ((^y.(a a))(a ((^z.z) b))) 6. ==[ alpha ]==> ((^x.(a a))(a ((^y.y) b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195636/23226591. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 195637/23226618. ------ 1. ==[ start ]==> (((a b)(^c.a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)(a (^y.y)))) REDUCED to normal form. ------ 195638/23226645. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((a a)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 195639/23226672. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))((a a)(a (a a)))) REDUCED to normal form. ------ 195640/23226726. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 195641/23226753. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z)(^x1.x1))(a b))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(^x1.x1))(a b))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))(a b))) 5. ==[ beta ]==> ((b (^x.x))((^z.z)(a b))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(a b))) 7. ==[ beta ]==> ((b (^x.x))(a b)) REDUCED to normal form. ------ 195642/23226897. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (((^y.y)(a a))((a (^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (^y.(^z.z)))(^x1.x1))) 7. ==[ beta ]==> ((a a)((a (^y.(^z.z)))(^x1.x1))) 8. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 195643/23226924. ------ 1. ==[ start ]==> ((((a a) a)(a b))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 195644/23226951. ------ 1. ==[ start ]==> (((a b)((a a) a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)((a a) a))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 195645/23226978. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.(z z)))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.(z z)))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(y y)))) REDUCED to normal form. ------ 195646/23227005. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 195647/23227059. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((^y1.y1)(^z1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.x1)(^y1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.b)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.b)) REDUCED to normal form. ------ 195648/23227086. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a (a a))(^y.(a a)))) 3. ==[ beta ]==> ((b (a a))((a (a a))(^y.(a a)))) 4. ==[ alpha ]==> ((b (a a))((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 195649/23227149. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b a))) 5. ==[ beta ]==> ((^y.(^z.z))(b a)) 6. ==[ alpha ]==> ((^x.(^y.y))(b a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195650/23227284. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (b ((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 195651/23227392. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(y1 y1))(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(y1 y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195652/23227428. ------ 1. ==[ start ]==> ((((^a.a) b) b)(c ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)(c ((a a)(^y.y)))) 3. ==[ beta ]==> ((b b)(c ((a a)(^y.y)))) 4. ==[ alpha ]==> ((b b)(c ((a a)(^x.x)))) REDUCED to normal form. ------ 195653/23227455. ------ 1. ==[ start ]==> ((((a a)(a a)) a)(b (b a))) REDUCED to normal form. ------ 195654/23227473. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 195655/23227509. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((b a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((b a)(a a))) REDUCED to normal form. ------ 195656/23227536. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(((a a)(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 195657/23227617. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a) a)(^y.y))) REDUCED to normal form. ------ 195658/23227644. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.b))((^z.z)((a a) a))) 4. ==[ alpha ]==> (((a b)(^x.b))((^y.y)((a a) a))) 5. ==[ beta ]==> (((a b)(^x.b))((a a) a)) REDUCED to normal form. ------ 195659/23227698. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a ((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a ((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (a a))) REDUCED to normal form. ------ 195660/23227752. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a a)(b a))) REDUCED to normal form. ------ 195661/23227842. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> (((a a)((a a)(a a)))((a a)(^y.a))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))((a a)(^x.a))) REDUCED to normal form. ------ 195662/23227869. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a b)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a b)(^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a b)(^y.(y y)))) REDUCED to normal form. ------ 195663/23227896. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 195664/23227923. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a (a a))(b a))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a (a a))(b a))((^x.x)(^y.a))) 5. ==[ beta ]==> (((a (a a))(b a))(^y.a)) 6. ==[ alpha ]==> (((a (a a))(b a))(^x.a)) REDUCED to normal form. ------ 195665/23227950. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a (a a))(^x1.b))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a (a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (a a))(^z.b))) 5. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.b))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.b))) REDUCED to normal form. ------ 195666/23227977. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> ((((a a) a)(a a))(a (^y.(a a)))) 6. ==[ alpha ]==> ((((a a) a)(a a))(a (^x.(a a)))) REDUCED to normal form. ------ 195667/23228004. ------ 1. ==[ start ]==> (((a b)(a b))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 195668/23228058. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((b a) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((b a) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((b a) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((b a) a)) REDUCED to normal form. ------ 195669/23228508. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y) a)(a b))) 3. ==[ beta ]==> ((b c)(((^y.y) a)(a b))) 4. ==[ alpha ]==> ((b c)(((^x.x) a)(a b))) 5. ==[ beta ]==> ((b c)(a (a b))) REDUCED to normal form. ------ 195670/23228535. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a (^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a (^x.x))(a a))) REDUCED to normal form. ------ 195671/23228661. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.b)((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.b)((^z1.z1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1)))) b) REDUCED to normal form. ------ 195672/23228742. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (b ((^z.(z z))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(x x))((a a) a))) 5. ==[ beta ]==> (b (((a a) a)((a a) a))) REDUCED to normal form. ------ 195673/23229084. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((b a)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((b a)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 195674/23229111. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(a a)) b)) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 195675/23229138. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.b) c)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.b) c)) 3. ==[ beta ]==> (((a b)(a a))((^y.b) c)) 4. ==[ alpha ]==> (((a b)(a a))((^x.b) c)) 5. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 195676/23229165. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a) d)) 3. ==[ beta ]==> (((a a)(a b))((^y.a) d)) 4. ==[ alpha ]==> (((a a)(a b))((^x.a) d)) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 195677/23229354. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 195678/23229444. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.(y y))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.z))) 9. ==[ beta ]==> (((^y.y)(^z.z))((^y.y)(^z.z))) 10. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1))) 11. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 12. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 13. ==[ beta ]==> ((^y.y)(^z.z)) 14. ==[ alpha ]==> ((^x.x)(^y.y)) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195679/23229525. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)((^y1.y1)(a a)))) 3. ==[ beta ]==> (b ((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> (b ((^y.y)(a a))) 6. ==[ alpha ]==> (b ((^x.x)(a a))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 195680/23229633. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(^y2.(y2 y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(^y2.(y2 y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195681/23229750. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(a ((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y) a)(a ((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(a ((^y.y)(a a)))) 5. ==[ beta ]==> (a (a ((^y.y)(a a)))) 6. ==[ alpha ]==> (a (a ((^x.x)(a a)))) 7. ==[ beta ]==> (a (a (a a))) REDUCED to normal form. ------ 195682/23229858. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(a (a a)))) REDUCED to normal form. ------ 195683/23229885. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1) a)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1) a)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195684/23229930. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(b (^z.b))) 3. ==[ beta ]==> (b (b (^z.b))) 4. ==[ alpha ]==> (b (b (^x.b))) REDUCED to normal form. ------ 195685/23229939. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a a)(a b))) REDUCED to normal form. ------ 195686/23230038. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.(^x2.x2))((^y2.y2) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))((^y2.y2) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195687/23230173. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.b)(^x1.x1))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) b) REDUCED to normal form. ------ 195688/23230191. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((a a) a) b)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((a a) a) b)) 3. ==[ beta ]==> (((a a)(^y.y))(((a a) a) b)) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a) a) b)) REDUCED to normal form. ------ 195689/23230218. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z)(^x1.x1)) c)) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((^x1.x1) c)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z) c)) 5. ==[ beta ]==> (((a (^x.x))(b (^y.y))) c) REDUCED to normal form. ------ 195690/23230353. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.b) a)) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) b) REDUCED to normal form. ------ 195691/23230407. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 195692/23230569. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 9. ==[ beta ]==> ((a a)(^y.(^z.z))) 10. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 195693/23230596. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (a a))(^b.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (a a))(^y.a))) REDUCED to normal form. ------ 195694/23230605. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^a.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(x1 x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(x1 x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(z z))((^x1.x1) a))) 5. ==[ beta ]==> (((^z.(z z))((^x1.x1) a))(^y.y)) 6. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(^z.z)) 7. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(^z.z)) 8. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.z)) 9. ==[ beta ]==> ((a ((^y.y) a))(^z.z)) 10. ==[ alpha ]==> ((a ((^x.x) a))(^y.y)) 11. ==[ beta ]==> ((a a)(^y.y)) 12. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 195695/23230992. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((a a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b ((a a)((^x.x)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 195696/23231037. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 195697/23231064. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(y1 y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.z)))) 5. ==[ beta ]==> ((^y.(y y))(a (^z.z))) 6. ==[ alpha ]==> ((^x.(x x))(a (^y.y))) 7. ==[ beta ]==> ((a (^y.y))(a (^y.y))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 195698/23231118. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 195699/23231199. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195700/23231262. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(b (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(b (a (a a)))) REDUCED to normal form. ------ 195701/23231343. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (a (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a (a (^z.z)))) REDUCED to normal form. ------ 195702/23231370. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))((a (^y.y)) a)) REDUCED to normal form. ------ 195703/23231442. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(z z))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(a a))) 5. ==[ beta ]==> (((a a)(^x.x))((a a)(a a))) REDUCED to normal form. ------ 195704/23231469. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 195705/23231487. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 195706/23231514. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(^z.(z z)))) REDUCED to normal form. ------ 195707/23231541. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (a a)) a)) 3. ==[ beta ]==> ((a (b (^y.y)))((a (a a)) a)) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (a a)) a)) REDUCED to normal form. ------ 195708/23231568. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(((^x.x) a) b)) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a b)) REDUCED to normal form. ------ 195709/23231595. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z)) c)) 5. ==[ beta ]==> (((^y.y) b)((a (^z.z)) c)) 6. ==[ alpha ]==> (((^x.x) b)((a (^y.y)) c)) 7. ==[ beta ]==> (b ((a (^y.y)) c)) 8. ==[ alpha ]==> (b ((a (^x.x)) c)) REDUCED to normal form. ------ 195710/23231649. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a b)(b a))((^x.(x x)) a)) 3. ==[ beta ]==> (((a b)(b a))(a a)) REDUCED to normal form. ------ 195711/23231676. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.a) b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.a) b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a) b)) 5. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 195712/23231757. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (^z.z))) REDUCED to normal form. ------ 195713/23231784. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^y.y))((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 195714/23231811. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a a)(^x.a))) REDUCED to normal form. ------ 195715/23231865. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a (^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z)) b)) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z)) b)) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y)) b)) REDUCED to normal form. ------ 195716/23231883. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(b (a (^z.z)))) 3. ==[ beta ]==> ((b (^y.y))(b (a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))(b (a (^y.y)))) REDUCED to normal form. ------ 195717/23231919. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.a) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a) a)) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 195718/23231928. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(c (^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(c (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(c (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(c (^x1.x1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195719/23231955. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 195720/23232090. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b ((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 195721/23232198. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195722/23232570. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ eta ]==> ((^y.y)(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195723/23243721. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195724/23244378. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ eta ]==> ((^y.y)(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 195725/23244381. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(^x.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 195726/23244648. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a b)(b a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a b)(b a))) 3. ==[ beta ]==> (((a b)(b a))(((a b)(b a))((a b)(b a)))) REDUCED to normal form. ------ 195727/23244831. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 195728/23244873. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195729/23245263. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a (a (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a (a (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(^z.(a (a (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)(^y.(a (a (^z.z))))) 7. ==[ beta ]==> (^y.(a (a (^z.z)))) 8. ==[ alpha ]==> (^x.(a (a (^y.y)))) REDUCED to normal form. ------ 195730/23245695. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 195731/23245944. ------ 1. ==[ start ]==> ((^a.(a b))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a b)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)((a a)(^y.y))) b) 4. ==[ alpha ]==> (((a b)((a a)(^x.x))) b) REDUCED to normal form. ------ 195732/23246127. ------ 1. ==[ start ]==> (((a b) a)(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a b) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 195733/23246331. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z)(a a))(^x1.(a a)))) 3. ==[ beta ]==> (^y.((((^z.z)(a a))(^x1.(a a)))(((^z.z)(a a))(^x1.(a a))))) 4. ==[ alpha ]==> (^x.((((^y.y)(a a))(^z.(a a)))(((^x1.x1)(a a))(^y1.(a a))))) 5. ==[ beta ]==> (^x.(((a a)(^z.(a a)))(((^x1.x1)(a a))(^y1.(a a))))) 6. ==[ alpha ]==> (^x.(((a a)(^y.(a a)))(((^z.z)(a a))(^x1.(a a))))) 7. ==[ beta ]==> (^x.(((a a)(^y.(a a)))((a a)(^x1.(a a))))) 8. ==[ alpha ]==> (^x.(((a a)(^y.(a a)))((a a)(^z.(a a))))) REDUCED to normal form. ------ 195734/23247213. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (((((^z.z)(^x1.x1))(b a))(((^z.z)(^x1.x1))(b a)))(^y.y)) 4. ==[ alpha ]==> (((((^x.x)(^y.y))(b a))(((^z.z)(^x1.x1))(b a)))(^y1.y1)) 5. ==[ beta ]==> ((((^y.y)(b a))(((^z.z)(^x1.x1))(b a)))(^y1.y1)) 6. ==[ alpha ]==> ((((^x.x)(b a))(((^y.y)(^z.z))(b a)))(^x1.x1)) 7. ==[ beta ]==> (((b a)(((^y.y)(^z.z))(b a)))(^x1.x1)) 8. ==[ alpha ]==> (((b a)(((^x.x)(^y.y))(b a)))(^z.z)) 9. ==[ beta ]==> (((b a)((^y.y)(b a)))(^z.z)) 10. ==[ alpha ]==> (((b a)((^x.x)(b a)))(^y.y)) 11. ==[ beta ]==> (((b a)(b a))(^y.y)) 12. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 195735/23248518. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195736/23250177. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195737/23251392. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 195738/23252697. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.((z z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.((z z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.((y y)(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.((y y)(^z.z)))) 6. ==[ alpha ]==> ((b a)(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 195739/23253138. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (b (^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 195740/23253363. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(a a)))) 5. ==[ beta ]==> (a (^y.(^z.(a a)))) 6. ==[ alpha ]==> (a (^x.(^y.(a a)))) REDUCED to normal form. ------ 195741/23253552. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^d.(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 195742/23253579. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 195743/23253768. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(^x1.(a x1))) 3. ==[ eta ]==> ((((^x.(^y.y)) a)(^z.z)) a) 4. ==[ beta ]==> (((^y.y)(^z.z)) a) 5. ==[ alpha ]==> (((^x.x)(^y.y)) a) 6. ==[ beta ]==> ((^y.y) a) 7. ==[ alpha ]==> ((^x.x) a) 8. ==[ beta ]==> a REDUCED to normal form. ------ 195744/23253783. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a b) a)) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a b) a)) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 195745/23253966. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(y b))) REDUCED to normal form. ------ 195746/23254767. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195747/23255037. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195748/23255079. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195749/23255262. ------ 1. ==[ start ]==> (((a b)(b a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(x (x x)))) REDUCED to normal form. ------ 195750/23255529. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a ((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195751/23255532. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.((^y1.y1) x1))) 3. ==[ eta ]==> ((a ((^x.x)(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.x1)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195752/23255703. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^c.b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.b)) 3. ==[ beta ]==> (b (^y1.b)) 4. ==[ alpha ]==> (b (^x.b)) REDUCED to normal form. ------ 195753/23255811. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^c.a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.a)) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.a)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195754/23255886. ------ 1. ==[ start ]==> (((^a.a) a)((^b.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.a))) 3. ==[ beta ]==> (a ((^y.y)(^z.a))) 4. ==[ alpha ]==> (a ((^x.x)(^y.a))) 5. ==[ beta ]==> (a (^y.a)) 6. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 195755/23255913. ------ 1. ==[ start ]==> (((a a) a)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.b))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 195756/23255967. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195757/23256021. ------ 1. ==[ start ]==> (((a a) b)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a) b)((^x.b)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a) b) b) REDUCED to normal form. ------ 195758/23256075. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195759/23256156. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195760/23256165. ------ 1. ==[ start ]==> (((a (^a.a))(a a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))(b (a (a (^y.y))))) REDUCED to normal form. ------ 195761/23256192. ------ 1. ==[ start ]==> ((a ((^a.a) a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(a ((^y.y)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(a ((^x.x)(^y.(^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 195762/23256201. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> a REDUCED to normal form. ------ 195763/23256228. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(y1 (^z1.z1))) b)) 3. ==[ beta ]==> ((^y.y)((^y1.(y1 (^z1.z1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((^y.(y (^z.z))) b) 6. ==[ alpha ]==> ((^x.(x (^y.y))) b) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195764/23256381. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b a)(a b))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((b a)(a b))) 3. ==[ beta ]==> (((a a) a)((b a)(a b))) REDUCED to normal form. ------ 195765/23256408. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a a)(^z.z))(a a))) REDUCED to normal form. ------ 195766/23256435. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a))((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a (a a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 195767/23256462. ------ 1. ==[ start ]==> ((a (a (a a)))((a b)(b a))) REDUCED to normal form. ------ 195768/23256615. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 195769/23256642. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 195770/23256660. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> (((a a)(a a))((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 195771/23256669. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 195772/23256687. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 195773/23256777. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b b)(^y.y)) 8. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 195774/23256822. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195775/23256849. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 195776/23256912. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.b)(b a))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.b)(b a))) 3. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 195777/23256957. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195778/23256966. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195779/23256993. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 195780/23257020. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 195781/23257047. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195782/23257074. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)(a (a (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(a (a (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a (a (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)((^z.z)(a (a (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a (a (^z.z))))) 7. ==[ beta ]==> ((^y.y)(a (a (^z.z)))) 8. ==[ alpha ]==> ((^x.x)(a (a (^y.y)))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 195783/23257371. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b ((^y.a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 195784/23257398. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(^y.y))(^z.z))) 3. ==[ beta ]==> ((((a a) a) a)(^y.y)) 4. ==[ alpha ]==> ((((a a) a) a)(^x.x)) REDUCED to normal form. ------ 195785/23257506. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 195786/23257596. ------ 1. ==[ start ]==> (((a a)((a a) a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> (((a a)((a a) a))(((a a)(a a)) a)) REDUCED to normal form. ------ 195787/23257623. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(b (a (a a)))) REDUCED to normal form. ------ 195788/23257650. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (a a)))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (a a)))((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (a (a a)))((a (^x.(^y.y)))(^x1.x1))) 6. ==[ alpha ]==> ((a (a (a a)))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 195789/23257677. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((b a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((b a)((a a) a))) 3. ==[ beta ]==> (((a (a a)) a)((b a)((a a) a))) REDUCED to normal form. ------ 195790/23257704. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((a a)(^x1.x1))(a b))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a)(^x1.x1))(a b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(^z.z))(a b))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(a b))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(a b))) REDUCED to normal form. ------ 195791/23257731. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(a a))) REDUCED to normal form. ------ 195792/23257758. ------ 1. ==[ start ]==> ((a (a b))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 195793/23257938. ------ 1. ==[ start ]==> (((a b) a)(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a b) a)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 195794/23257956. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> ((a b)(((^y.(^z.z)) a)(^x1.x1))) 4. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a)(^z.z))) 5. ==[ beta ]==> ((a b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 195795/23257983. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((b (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 195796/23258019. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 195797/23258037. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(b (^y.(y y)))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(b (^x.(x x)))) REDUCED to normal form. ------ 195798/23258046. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(a (a a))) REDUCED to normal form. ------ 195799/23258073. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.a)((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.a)((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 195800/23258118. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(a a))(((a a)(^y.y))(^z.b))) 3. ==[ beta ]==> (b (((a a)(^y.y))(^z.b))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 195801/23258127. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.z))(a b))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 195802/23258145. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 195803/23258316. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195804/23258361. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.(^x1.x1)) a) a)) 3. ==[ beta ]==> ((^y.(a a))(((^z.(^x1.x1)) a) a)) 4. ==[ alpha ]==> ((^x.(a a))(((^y.(^z.z)) a) a)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195805/23258388. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((b (^x1.x1)) b)) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1)) b)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) b)) 5. ==[ beta ]==> ((b (^y.y)) b) 6. ==[ alpha ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 195806/23258532. ------ 1. ==[ start ]==> (((a b) b)((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> (((a b) b)(^y.y)) 4. ==[ alpha ]==> (((a b) b)(^x.x)) REDUCED to normal form. ------ 195807/23258559. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 195808/23258586. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 195809/23258613. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) a) REDUCED to normal form. ------ 195810/23258667. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195811/23258694. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.a)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.a)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.a)(^z.(a a)))) 7. ==[ beta ]==> (((^y.a)(^z.(a a)))((^y.a)(^z.(a a)))) 8. ==[ alpha ]==> (((^x.a)(^y.(a a)))((^z.a)(^x1.(a a)))) 9. ==[ beta ]==> (a ((^z.a)(^x1.(a a)))) 10. ==[ alpha ]==> (a ((^x.a)(^y.(a a)))) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195812/23258811. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 195813/23258838. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(b ((^y.y) a))) 5. ==[ beta ]==> (((a (^x.x))(a b))(b a)) REDUCED to normal form. ------ 195814/23258865. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> ((a ((a a) a))((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 195815/23258892. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a))(^x.x))((b a)(^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 195816/23258919. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((a a)(^z.z))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(^y.y))((a a) a))) 5. ==[ beta ]==> ((a (a a))(((a a)(^y.y))((a a) a))) 6. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 195817/23258946. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x)(a a))(a b))) 5. ==[ beta ]==> ((((a a) a) a)((a a)(a b))) REDUCED to normal form. ------ 195818/23258973. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a b)(a a))) REDUCED to normal form. ------ 195819/23259000. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((a a) a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(((a a) a)((a a)(^x.x)))) REDUCED to normal form. ------ 195820/23259027. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(^z.z))(b a))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)(b a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(b a))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(b a)) REDUCED to normal form. ------ 195821/23259198. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 195822/23259207. ------ 1. ==[ start ]==> (((a b) c)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b) c)((^x.(a a))(a (^y.y)))) 3. ==[ beta ]==> (((a b) c)(a a)) REDUCED to normal form. ------ 195823/23259234. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a a) b)((^y.y)((^z.z) a))) 4. ==[ alpha ]==> (((a a) b)((^x.x)((^y.y) a))) 5. ==[ beta ]==> (((a a) b)((^y.y) a)) 6. ==[ alpha ]==> (((a a) b)((^x.x) a)) 7. ==[ beta ]==> (((a a) b) a) REDUCED to normal form. ------ 195824/23259261. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 195825/23259279. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 195826/23259315. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 195827/23259342. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))(a b))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))(a b))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(a b))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 195828/23259360. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a b)(^y.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a b)(^y.(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a b)(^x.(a a)))) REDUCED to normal form. ------ 195829/23259396. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.a)((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a)((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a)((a a)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a)((a a)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195830/23259423. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 195831/23259441. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 195832/23259450. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^x.a))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 195833/23259477. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.a)((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.a)((^y1.y1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)((^x1.x1) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 195834/23259504. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 195835/23259954. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(a a)) b)) 3. ==[ beta ]==> (b ((^z.(a a)) b)) 4. ==[ alpha ]==> (b ((^x.(a a)) b)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 195836/23260233. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(c (^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(c (^y.y))) REDUCED to normal form. ------ 195837/23260260. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(b (^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(b (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(b (^y.(a a)))) REDUCED to normal form. ------ 195838/23260332. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 195839/23260611. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195840/23260710. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.(^x1.x1))) c)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.(^x1.x1))) c)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.(^x1.x1))) c)) 5. ==[ beta ]==> ((a a)((a (^z.(^x1.x1))) c)) 6. ==[ alpha ]==> ((a a)((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 195841/23260935. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 195842/23261241. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a (a a))((a a)(^z.z)))) REDUCED to normal form. ------ 195843/23261268. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a (^x.x))(b a))(a (b a))) REDUCED to normal form. ------ 195844/23261295. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 195845/23261322. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(a a))((a a)((^y.y) b))) 4. ==[ alpha ]==> (((a (a a))(a a))((a a)((^x.x) b))) 5. ==[ beta ]==> (((a (a a))(a a))((a a) b)) REDUCED to normal form. ------ 195846/23261502. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.b)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195847/23261547. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a a))) 7. ==[ beta ]==> ((^y.y)(^z.(a a))) 8. ==[ alpha ]==> ((^x.x)(^y.(a a))) 9. ==[ beta ]==> (^y.(a a)) 10. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 195848/23261709. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 195849/23261826. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b) b) REDUCED to normal form. ------ 195850/23261853. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.a)(^z.b))) 3. ==[ beta ]==> ((b a)((^y.a)(^z.b))) 4. ==[ alpha ]==> ((b a)((^x.a)(^y.b))) 5. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 195851/23261880. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 195852/23261988. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195853/23262033. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) b)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 195854/23262213. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a) b)((a (a a))((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a) b)((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> (((a a) b)((a (a a))(a a))) REDUCED to normal form. ------ 195855/23262240. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a ((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(a ((a a)(^x1.x1)))) REDUCED to normal form. ------ 195856/23262267. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (^y.y))(b a))) 3. ==[ beta ]==> ((a (b a))((a (^y.y))(b a))) 4. ==[ alpha ]==> ((a (b a))((a (^x.x))(b a))) REDUCED to normal form. ------ 195857/23262294. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 195858/23262852. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 195859/23262924. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195860/23262978. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.z)) c)) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.y)) c)) 5. ==[ beta ]==> (((b a)(b a))(^y.y)) 6. ==[ alpha ]==> (((b a)(b a))(^x.x)) REDUCED to normal form. ------ 195861/23263203. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 195862/23263788. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^c.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (b ((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195863/23263932. ------ 1. ==[ start ]==> ((((^a.a) b) c)(d (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) c)(d (^y.b))) 3. ==[ beta ]==> ((b c)(d (^y.b))) 4. ==[ alpha ]==> ((b c)(d (^x.b))) REDUCED to normal form. ------ 195864/23263959. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(c (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(c (^x.(a a)))) REDUCED to normal form. ------ 195865/23264031. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 195866/23264067. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 195867/23264085. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a b)(^x1.a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a b)(^x1.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a b)(^y1.a))) REDUCED to normal form. ------ 195868/23264094. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.b)((^y1.y1) a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 195869/23264166. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a (a a))(^z.a))) 3. ==[ beta ]==> (b ((a (a a))(^z.a))) 4. ==[ alpha ]==> (b ((a (a a))(^x.a))) REDUCED to normal form. ------ 195870/23264175. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(y y))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 195871/23264202. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(a b))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(a b))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(a b))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 195872/23264274. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((a a)(^x1.x1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195873/23264310. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.a))(a a)) REDUCED to normal form. ------ 195874/23264337. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 195875/23264454. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(c (a b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(c (a b))) 3. ==[ beta ]==> ((a ((^y.y) b))(c (a b))) 4. ==[ alpha ]==> ((a ((^x.x) b))(c (a b))) 5. ==[ beta ]==> ((a b)(c (a b))) REDUCED to normal form. ------ 195876/23264481. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(b (a a))) REDUCED to normal form. ------ 195877/23264508. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(a ((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(b a))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)(b a))(a ((a a)(^y.y)))) 5. ==[ beta ]==> ((b a)(a ((a a)(^y.y)))) 6. ==[ alpha ]==> ((b a)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 195878/23264535. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))((a a)(a a))) REDUCED to normal form. ------ 195879/23264562. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((a b)(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a a))((a b)(a (^y.y)))) 4. ==[ alpha ]==> (((a b)(a a))((a b)(a (^x.x)))) REDUCED to normal form. ------ 195880/23264589. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> (((a a)(a b))(((a a) a)((^y.y) a))) 4. ==[ alpha ]==> (((a a)(a b))(((a a) a)((^x.x) a))) 5. ==[ beta ]==> (((a a)(a b))(((a a) a) a)) REDUCED to normal form. ------ 195881/23264616. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a (a a))) REDUCED to normal form. ------ 195882/23264670. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a ((a a) a))) REDUCED to normal form. ------ 195883/23264697. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (^z.z))(a b))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (^z.z))(a b))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (^y.y))(a b))) 5. ==[ beta ]==> ((b a)((a (^y.y))(a b))) 6. ==[ alpha ]==> ((b a)((a (^x.x))(a b))) REDUCED to normal form. ------ 195884/23264724. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 195885/23264868. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 195886/23264949. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.(a a)))) 3. ==[ beta ]==> (b ((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 195887/23265174. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(a a)))) 5. ==[ beta ]==> (a ((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (a (^y.(a a))) 8. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 195888/23265192. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(a a)) a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(a a)) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(a a)) a)) 5. ==[ beta ]==> ((^y.y)((^z.(a a)) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(a a)) a)) 7. ==[ beta ]==> ((^y.(a a)) a) 8. ==[ alpha ]==> ((^x.(a a)) a) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 195889/23265219. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.b) b)) 3. ==[ beta ]==> ((^y.y)((^x1.b) b)) 4. ==[ alpha ]==> ((^x.x)((^y.b) b)) 5. ==[ beta ]==> ((^y.b) b) 6. ==[ alpha ]==> ((^x.b) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 195890/23265363. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (^z.b))) REDUCED to normal form. ------ 195891/23265390. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(a (^z.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.(a a)))) REDUCED to normal form. ------ 195892/23265417. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) b) REDUCED to normal form. ------ 195893/23265462. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1)(^x2.x2))(^y2.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(^x2.x2))(^y2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195894/23265471. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 195895/23265498. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> ((b (^x.(x x)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 195896/23265525. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 195897/23265579. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.x1)(a b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(a b))) 5. ==[ beta ]==> ((^y.y)((^z.z)(a b))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a b))) 7. ==[ beta ]==> ((^y.y)(a b)) 8. ==[ alpha ]==> ((^x.x)(a b)) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 195898/23265597. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a b) a)) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a b) a)) REDUCED to normal form. ------ 195899/23265750. ------ 1. ==[ start ]==> ((((a a) a)(b a))(b ((a a) a))) REDUCED to normal form. ------ 195900/23265777. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(a (a b))) REDUCED to normal form. ------ 195901/23265804. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(((a a) a)(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(((a a) a)(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(((a a) a)(a a))) 5. ==[ beta ]==> (((a a)(a a))(((a a) a)(a a))) REDUCED to normal form. ------ 195902/23265831. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a b))(a (^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (^y.y))) REDUCED to normal form. ------ 195903/23265885. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1) a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1) a)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1) a)(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (a (a a)))) REDUCED to normal form. ------ 195904/23265912. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))((a (^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))((a (^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((b (a (a a)))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 195905/23265939. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a a)((a a) a))) REDUCED to normal form. ------ 195906/23266011. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 195907/23266029. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (a a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (a a))(^x1.a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))(^z.a))) 5. ==[ beta ]==> (((a (a a))(^z.a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 195908/23266416. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (b (^y.(^z.z)))) 6. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 195909/23266461. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 195910/23266470. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 195911/23266488. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 195912/23266542. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 195913/23266578. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195914/23266605. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 195915/23266623. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.b)(b a))((a (a a)) b)) 3. ==[ beta ]==> (b ((a (a a)) b)) REDUCED to normal form. ------ 195916/23266686. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 195917/23266731. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195918/23266848. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195919/23266866. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (a a))(^z.z))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 195920/23266875. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(z z))(a a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 195921/23266893. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 195922/23267019. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(c (a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(c (a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(c (a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(c (a (^z.z)))) 5. ==[ beta ]==> (((^y.y) b)(c (a (^z.z)))) 6. ==[ alpha ]==> (((^x.x) b)(c (a (^y.y)))) 7. ==[ beta ]==> (b (c (a (^y.y)))) 8. ==[ alpha ]==> (b (c (a (^x.x)))) REDUCED to normal form. ------ 195923/23267046. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(b ((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(b a)) REDUCED to normal form. ------ 195924/23267073. ------ 1. ==[ start ]==> (((a b)(b a))(a (a (a a)))) REDUCED to normal form. ------ 195925/23267100. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(((^z.z) a)(a a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(((^z.z) a)(a a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) a)(a a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 195926/23267127. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 195927/23267208. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(c b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(c b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(c b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(c b)) 5. ==[ beta ]==> ((b (^y.y))(c b)) 6. ==[ alpha ]==> ((b (^x.x))(c b)) REDUCED to normal form. ------ 195928/23267235. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(b c)) REDUCED to normal form. ------ 195929/23267307. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 195930/23267316. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(b (a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(b (a (^y.y)))) REDUCED to normal form. ------ 195931/23267343. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a ((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a ((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a ((^z.z) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 195932/23267352. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195933/23267379. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b)) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195934/23267514. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a a) b)) 3. ==[ beta ]==> (b ((a a) b)) REDUCED to normal form. ------ 195935/23267622. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((a a) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((a a) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195936/23268003. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ eta ]==> ((^y.y)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 195937/23270163. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)((^z.((^x1.(^y1.y1)) a))(^z.((^x1.(^y1.y1)) a)))) 4. ==[ alpha ]==> ((^x.x)((^y.((^z.(^x1.x1)) a))(^y1.((^z1.(^x2.x2)) a)))) 5. ==[ beta ]==> ((^y.((^z.(^x1.x1)) a))(^y1.((^z1.(^x2.x2)) a))) 6. ==[ alpha ]==> ((^x.((^y.(^z.z)) a))(^x1.((^y1.(^z1.z1)) a))) 7. ==[ beta ]==> ((^y.(^z.z)) a) 8. ==[ alpha ]==> ((^x.(^y.y)) a) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195938/23279154. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195939/23279523. ------ 1. ==[ start ]==> ((^a.(a a))((^b.b)(^c.a))) 2. ==[ alpha ]==> ((^x.(x x))((^y.y)(^z.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((^y.a)((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(^z.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 195940/23279550. ------ 1. ==[ start ]==> ((^a.b)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 195941/23279820. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ eta ]==> ((^y.y)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195942/23279823. ------ 1. ==[ start ]==> ((a ((^a.a) a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 195943/23279832. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.a)(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.a)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 195944/23279991. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 195945/23280441. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195946/23281206. ------ 1. ==[ start ]==> ((^a.(^a.b))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((b (^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 195947/23281560. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (b (^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (b (^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 195948/23281980. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.y)(((^z.z)((^x1.(^y1.y1)) a))((^z.z)((^x1.(^y1.y1)) a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)((^z.(^x1.x1)) a))((^y1.y1)((^z1.(^x2.x2)) a)))) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1)) a))((^y1.y1)((^z1.(^x2.x2)) a))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)((^y1.(^z1.z1)) a))) 7. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)((^y1.(^z1.z1)) a))) 8. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)((^x1.(^y1.y1)) a))) 9. ==[ beta ]==> ((^y.y)((^z.z)((^x1.(^y1.y1)) a))) 10. ==[ alpha ]==> ((^x.x)((^y.y)((^z.(^x1.x1)) a))) 11. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 12. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 13. ==[ beta ]==> ((^y.(^z.z)) a) 14. ==[ alpha ]==> ((^x.(^y.y)) a) 15. ==[ beta ]==> (^y.y) 16. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195949/23281983. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a a))(^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (a a))(^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a a))(^x.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 195950/23283171. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(y (^z.z)))) REDUCED to normal form. ------ 195951/23283411. ------ 1. ==[ start ]==> ((^a.(b a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.a)(^z.(^x1.x1)))) 3. ==[ eta ]==> (b ((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 195952/23284248. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^x1.(^y1.y1))((^z1.z1) b))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195953/23284638. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.((z z)(z z)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.((z z)(z z)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.((z z)(z z)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.((z z)(z z)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.((y y)(y y)))) 7. ==[ beta ]==> (((a a)(a a))(^y.((y y)(y y)))) 8. ==[ alpha ]==> (((a a)(a a))(^x.((x x)(x x)))) REDUCED to normal form. ------ 195954/23284851. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195955/23284980. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^a.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(y y)))) 5. ==[ beta ]==> ((a b)(^y.(^z.(y y)))) 6. ==[ alpha ]==> ((a b)(^x.(^y.(x x)))) REDUCED to normal form. ------ 195956/23285166. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.a)(a b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.a)(a b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 195957/23285952. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(^a.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 195958/23286165. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(y y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((^y.(y y))((^z.z)(a a)))((^y.(y y))((^z.z)(a a))))(((^y.(y y))((^z.z)(a a)))((^y.(y y))((^z.z)(a a))))) 4. ==[ alpha ]==> ((((^x.(x x))((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a))))(((^y1.(y1 y1))((^z1.z1)(a a)))((^x2.(x2 x2))((^y2.y2)(a a))))) 5. ==[ beta ]==> (((((^y.y)(a a))((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a))))(((^y1.(y1 y1))((^z1.z1)(a a)))((^x2.(x2 x2))((^y2.y2)(a a))))) 6. ==[ alpha ]==> (((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a))))(((^y1.(y1 y1))((^z1.z1)(a a)))((^x2.(x2 x2))((^y2.y2)(a a))))) 7. ==[ beta ]==> ((((a a)((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a))))(((^y1.(y1 y1))((^z1.z1)(a a)))((^x2.(x2 x2))((^y2.y2)(a a))))) 8. ==[ alpha ]==> ((((a a)((^x.x)(a a)))((^y.(y y))((^z.z)(a a))))(((^x1.(x1 x1))((^y1.y1)(a a)))((^z1.(z1 z1))((^x2.x2)(a a))))) 9. ==[ beta ]==> ((((a a)(a a))((^y.(y y))((^z.z)(a a))))(((^x1.(x1 x1))((^y1.y1)(a a)))((^z1.(z1 z1))((^x2.x2)(a a))))) 10. ==[ alpha ]==> ((((a a)(a a))((^x.(x x))((^y.y)(a a))))(((^z.(z z))((^x1.x1)(a a)))((^y1.(y1 y1))((^z1.z1)(a a))))) 11. ==[ beta ]==> ((((a a)(a a))(((^y.y)(a a))((^y.y)(a a))))(((^z.(z z))((^x1.x1)(a a)))((^y1.(y1 y1))((^z1.z1)(a a))))) 12. ==[ alpha ]==> ((((a a)(a a))(((^x.x)(a a))((^y.y)(a a))))(((^z.(z z))((^x1.x1)(a a)))((^y1.(y1 y1))((^z1.z1)(a a))))) 13. ==[ beta ]==> ((((a a)(a a))((a a)((^y.y)(a a))))(((^z.(z z))((^x1.x1)(a a)))((^y1.(y1 y1))((^z1.z1)(a a))))) 14. ==[ alpha ]==> ((((a a)(a a))((a a)((^x.x)(a a))))(((^y.(y y))((^z.z)(a a)))((^x1.(x1 x1))((^y1.y1)(a a))))) 15. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.(y y))((^z.z)(a a)))((^x1.(x1 x1))((^y1.y1)(a a))))) 16. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.(x x))((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a))))) 17. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((((^y.y)(a a))((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a))))) 18. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a))))) 19. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((a a)((^y.y)(a a)))((^z.(z z))((^x1.x1)(a a))))) 20. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((a a)((^x.x)(a a)))((^y.(y y))((^z.z)(a a))))) 21. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))((^y.(y y))((^z.z)(a a))))) 22. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))((^x.(x x))((^y.y)(a a))))) 23. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))(((^y.y)(a a))((^y.y)(a a))))) 24. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))(((^x.x)(a a))((^y.y)(a a))))) 25. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))((a a)((^y.y)(a a))))) 26. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))((a a)((^x.x)(a a))))) 27. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 195959/23286555. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(x1 (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^x1.(x1 (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(y (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.(y (^z.(^x1.x1)))) 6. ==[ alpha ]==> (^x.(x (^y.(^z.z)))) REDUCED to normal form. ------ 195960/23287113. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(^b.(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(^x1.(x1 a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(^x1.(x1 a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.(z a))) REDUCED to normal form. ------ 195961/23287245. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 195962/23287635. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 195963/23288139. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))(^y.(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 195964/23288406. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((^x1.(a a))(a a))) 3. ==[ eta ]==> ((^y.(^z.z))((^x1.(a a))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195965/23288823. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(z z)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(y y)))) 7. ==[ beta ]==> (^y.((^z.z)(y y))) 8. ==[ alpha ]==> (^x.((^y.y)(x x))) 9. ==[ beta ]==> (^x.(x x)) REDUCED to normal form. ------ 195966/23289408. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.(^z.y))) REDUCED to normal form. ------ 195967/23289648. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^z.(^x1.x1))(a (^y1.y1)))(((^z.(^x1.x1))(a (^y1.y1)))(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.(^y1.y1))(a (^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1))(a (^z1.z1)))(^x2.x2))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(a (^x1.x1)))(^y1.y1))) 7. ==[ beta ]==> (((^y.(^z.z))(a (^x1.x1)))(^y1.y1)) 8. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.x1)) 9. ==[ beta ]==> ((^y.y)(^x1.x1)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195968/23290209. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 195969/23290362. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195970/23290596. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(a (a a)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(a (a a)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a (a a)))) REDUCED to normal form. ------ 195971/23290704. ------ 1. ==[ start ]==> (((a b)(b a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 195972/23290812. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 195973/23290971. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195974/23290974. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.a))) REDUCED to normal form. ------ 195975/23290983. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 195976/23291253. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^a.b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.b)) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.b)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 195977/23291346. ------ 1. ==[ start ]==> ((a (a a))((^b.b)(^c.a))) 2. ==[ alpha ]==> ((a (a a))((^x.x)(^y.a))) 3. ==[ beta ]==> ((a (a a))(^y.a)) 4. ==[ alpha ]==> ((a (a a))(^x.a)) REDUCED to normal form. ------ 195978/23291373. ------ 1. ==[ start ]==> ((a b)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.b))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 195979/23291616. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 195980/23291643. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 195981/23291652. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.a)(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.a)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 195982/23291679. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((a (a (^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (a (^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a (^y.y)))(a a)) 6. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 195983/23291688. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (((a (^x.x)) b)(b (^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) b)(b (^y.y))) REDUCED to normal form. ------ 195984/23291733. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) a)((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) a)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> (a ((b (^y.y))((^z.z) a))) 6. ==[ alpha ]==> (a ((b (^x.x))((^y.y) a))) 7. ==[ beta ]==> (a ((b (^x.x)) a)) REDUCED to normal form. ------ 195985/23291760. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a)(a a))(a (a a))) REDUCED to normal form. ------ 195986/23291814. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (^y.(^z.z)))((a a) a))) REDUCED to normal form. ------ 195987/23291922. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a b)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a b)(b a))) 3. ==[ beta ]==> ((^y.(y y))((a b)(b a))) 4. ==[ alpha ]==> ((^x.(x x))((a b)(b a))) 5. ==[ beta ]==> (((a b)(b a))((a b)(b a))) REDUCED to normal form. ------ 195988/23291949. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((a a) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 195989/23292003. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 7. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 195990/23292030. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> ((a (a a))(a (b (^y.y)))) 6. ==[ alpha ]==> ((a (a a))(a (b (^x.x)))) REDUCED to normal form. ------ 195991/23292057. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 195992/23292120. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 195993/23292228. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.y) b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)(((^y.y) b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)(((^x.x) b)(^y.(^z.z)))) 5. ==[ beta ]==> ((b b)(b (^y.(^z.z)))) 6. ==[ alpha ]==> ((b b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 195994/23292237. ------ 1. ==[ start ]==> (((a (a a))(a a))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.x)) REDUCED to normal form. ------ 195995/23292264. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 195996/23292390. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) a)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) a)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (((a a) a)(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (a (((a a) a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 195997/23292417. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 195998/23292525. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(y (^z.z))))) 7. ==[ beta ]==> ((a a)(^y.(y (^z.z)))) 8. ==[ alpha ]==> ((a a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 195999/23292561. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))((^x1.x1)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 196000/23292669. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 196001/23292948. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))(b ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a ((^y.y) a))(b ((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((a ((^x.x) a))(b ((^y.(^z.z)) a))) 7. ==[ beta ]==> ((a a)(b ((^y.(^z.z)) a))) 8. ==[ alpha ]==> ((a a)(b ((^x.(^y.y)) a))) 9. ==[ beta ]==> ((a a)(b (^y.y))) 10. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 196002/23292984. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(y1 (^z1.z1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 (^z1.z1))) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 (^y1.y1))) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 (^y1.y1))) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1))) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196003/23293029. ------ 1. ==[ start ]==> ((a (^a.b))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 196004/23293218. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.b)((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.b)((a b)((a a)(^y.y)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 196005/23293299. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a (a a))((^z.z) b))) IRREDUCIBLE: cycle. ------ 196006/23293380. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (b ((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (b ((a a)((^x.(^y.y)) a))) 5. ==[ beta ]==> (b ((a a)(^y.y))) 6. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 196007/23293416. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 196008/23293470. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a)(a a))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 196009/23293497. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))(b (^y.(y y)))) REDUCED to normal form. ------ 196010/23293524. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.a)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 196011/23293551. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b a)(^z.a))) REDUCED to normal form. ------ 196012/23293578. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 196013/23293614. ------ 1. ==[ start ]==> (((a a)(a b))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 196014/23293641. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a)) b) REDUCED to normal form. ------ 196015/23293695. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 196016/23293722. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y) a)((^z.(z z))((^x1.x1) b))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(y y))((^z.z) b))) 7. ==[ beta ]==> (a ((^y.(y y))((^z.z) b))) 8. ==[ alpha ]==> (a ((^x.(x x))((^y.y) b))) 9. ==[ beta ]==> (a (((^y.y) b)((^y.y) b))) 10. ==[ alpha ]==> (a (((^x.x) b)((^y.y) b))) 11. ==[ beta ]==> (a (b ((^y.y) b))) 12. ==[ alpha ]==> (a (b ((^x.x) b))) 13. ==[ beta ]==> (a (b b)) REDUCED to normal form. ------ 196017/23293749. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x))) a) REDUCED to normal form. ------ 196018/23293776. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 196019/23293803. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a (a a))((^y.y)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a (a a))((^x.x)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a (a a))(^y.y)) 8. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 196020/23294190. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(b (b (^z.z)))) 3. ==[ beta ]==> (b (b (b (^z.z)))) 4. ==[ alpha ]==> (b (b (b (^x.x)))) REDUCED to normal form. ------ 196021/23294514. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a (a a))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a a))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(a (^x.(^y.y)))) REDUCED to normal form. ------ 196022/23294658. ------ 1. ==[ start ]==> (((a b) c)(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 196023/23294685. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) b)(^z.a))) 3. ==[ beta ]==> (((a a) b)(((^y.y) b)(^z.a))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) b)(^y.a))) 5. ==[ beta ]==> (((a a) b)(b (^y.a))) 6. ==[ alpha ]==> (((a a) b)(b (^x.a))) REDUCED to normal form. ------ 196024/23294712. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 196025/23294766. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(^z.z))(^x1.a))) REDUCED to normal form. ------ 196026/23294793. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y)(a a))(^z.b))) 5. ==[ beta ]==> ((a (^x.b))((a a)(^z.b))) 6. ==[ alpha ]==> ((a (^x.b))((a a)(^y.b))) REDUCED to normal form. ------ 196027/23294847. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196028/23294901. ------ 1. ==[ start ]==> (((a b)(^b.a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 196029/23294928. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 196030/23294991. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(b (^z.z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b (^y.y))) REDUCED to normal form. ------ 196031/23295045. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 196032/23295072. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.x)(^y.a))) 3. ==[ beta ]==> (((a (a a))((a a) a))(^y.a)) 4. ==[ alpha ]==> (((a (a a))((a a) a))(^x.a)) REDUCED to normal form. ------ 196033/23295099. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.(y2 y2)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.(x2 x2)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(y1 y1))) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(x1 x1))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196034/23295153. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a b) a)(^y.y)) 6. ==[ alpha ]==> (((a b) a)(^x.x)) REDUCED to normal form. ------ 196035/23295180. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(a a))(^z.b))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 196036/23295207. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.b)(^z.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a)) b) REDUCED to normal form. ------ 196037/23295234. ------ 1. ==[ start ]==> ((a (b a))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (b a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((a (b a)) a) REDUCED to normal form. ------ 196038/23295324. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))(c ((^z.z) b))) 3. ==[ beta ]==> (((^y.b)(^y.b))(c ((^z.z) b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))(c ((^z.z) b))) 5. ==[ beta ]==> (b (c ((^z.z) b))) 6. ==[ alpha ]==> (b (c ((^x.x) b))) 7. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 196039/23295405. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(((a a)(a a))(a a))) 3. ==[ beta ]==> (b (((a a)(a a))(a a))) REDUCED to normal form. ------ 196040/23295513. ------ 1. ==[ start ]==> (((^a.a)(b a))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b a)(((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b a)(((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)(((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> ((b a)(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 196041/23295540. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1)(a a))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> (((^y.y)(a a))((a a) a)) 6. ==[ alpha ]==> (((^x.x)(a a))((a a) a)) 7. ==[ beta ]==> ((a a)((a a) a)) REDUCED to normal form. ------ 196042/23295594. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a b))(((a a) a)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> (((a b)(a b))(((a a) a)(a a))) REDUCED to normal form. ------ 196043/23295675. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (((^y.y) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (((^x.x) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (a (^y.(^z.z))))) 6. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 196044/23295801. ------ 1. ==[ start ]==> (((a a)(b a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(b a))(a (^y.y))) 4. ==[ alpha ]==> (((a a)(b a))(a (^x.x))) REDUCED to normal form. ------ 196045/23295828. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 196046/23295882. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.x)) REDUCED to normal form. ------ 196047/23295909. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a))((a a) a))) 5. ==[ beta ]==> (((a a) a)((^y.(a a))((a a) a))) 6. ==[ alpha ]==> (((a a) a)((^x.(a a))((a a) a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 196048/23295936. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.b)(a b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.b)(a b))) 5. ==[ beta ]==> ((((a a) a)(^x.x)) b) REDUCED to normal form. ------ 196049/23295963. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a (a a))) a) REDUCED to normal form. ------ 196050/23295990. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.z))((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.y))((a a)(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.y)) 8. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 196051/23296017. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(z z))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))((b a)(b a))) REDUCED to normal form. ------ 196052/23296062. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196053/23296071. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 196054/23296404. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))(c (a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(c (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(c (a (^y.(^z.z))))) 5. ==[ beta ]==> (c (a (^y.(^z.z)))) 6. ==[ alpha ]==> (c (a (^x.(^y.y)))) REDUCED to normal form. ------ 196055/23296458. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(a ((a a)(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(a ((a a)(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(a ((a a)(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(a ((a a)(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a ((a a)(a a)))) 7. ==[ beta ]==> (((a a)(a a))(a ((a a)(a a)))) REDUCED to normal form. ------ 196056/23296467. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(a a)) REDUCED to normal form. ------ 196057/23296494. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.x1) b)) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.x1) b)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z) b)) 5. ==[ beta ]==> ((^y.b)((^z.z) b)) 6. ==[ alpha ]==> ((^x.b)((^y.y) b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 196058/23296539. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((b a)((^x1.x1) a))) 3. ==[ beta ]==> (b ((b a)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((b a)((^x.x) a))) 5. ==[ beta ]==> (b ((b a) a)) REDUCED to normal form. ------ 196059/23296647. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((a a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((a a) a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196060/23296674. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 196061/23296773. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(b (^b.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(b (^y.y))) 3. ==[ beta ]==> (((a (a a))(a a))(b (^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))(b (^x.x))) REDUCED to normal form. ------ 196062/23296800. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(a (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(a (^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))(a (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))(a (^y.(a a)))) 5. ==[ beta ]==> ((a b)(a (^y.(a a)))) 6. ==[ alpha ]==> ((a b)(a (^x.(a a)))) REDUCED to normal form. ------ 196063/23296827. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(a a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 196064/23296854. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 196065/23296953. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a b)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196066/23296962. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.b)((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a)) b) REDUCED to normal form. ------ 196067/23296989. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.a)(a b))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(a b))) 3. ==[ beta ]==> ((a b)((^y.a)(a b))) 4. ==[ alpha ]==> ((a b)((^x.a)(a b))) 5. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 196068/23297466. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.b) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y) a)) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 196069/23297484. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((a (^y.(^z.z)))(a a))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(a a))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a a))) REDUCED to normal form. ------ 196070/23297493. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((a b)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 196071/23297592. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196072/23297718. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(c (^d.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(c (^y.a))) 3. ==[ beta ]==> ((a (b a))(c (^y.a))) 4. ==[ alpha ]==> ((a (b a))(c (^x.a))) REDUCED to normal form. ------ 196073/23297745. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 196074/23297772. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(a (^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(a (^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(a (^z.z))) 5. ==[ beta ]==> (((^y.y)(a a))(a (^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))(a (^y.y))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 196075/23297799. ------ 1. ==[ start ]==> ((((a a) a)(a b))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((^x.(^y.(^z.z)))(a a))) 3. ==[ beta ]==> ((((a a) a)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 196076/23297880. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(a a)) REDUCED to normal form. ------ 196077/23297961. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))(a b))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))(a b))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 196078/23297988. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))((^y.y)(a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y)(a a))((^y.y)(a a)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> ((a ((a a)(a a)))((a a)((^x.x)(a a)))) 7. ==[ beta ]==> ((a ((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 196079/23298348. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))(b (b a))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))(b (b a))) 3. ==[ beta ]==> (((a a)(a a))(b (b a))) REDUCED to normal form. ------ 196080/23298375. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(a (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(a (a (^y.(^z.z))))) 5. ==[ beta ]==> (a (a (^y.(^z.z)))) 6. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 196081/23298384. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 196082/23298429. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((b a)(b a))(((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((b a)(b a))(((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 196083/23298510. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (b (((a a) a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b (((a a) a)(^y.y))) 6. ==[ alpha ]==> (b (((a a) a)(^x.x))) REDUCED to normal form. ------ 196084/23298618. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a (^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196085/23298681. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((b a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 196086/23298744. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(a a))((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x)) b)(a a)) REDUCED to normal form. ------ 196087/23298771. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.b)(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.b)(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(a (a a)))) 5. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 196088/23298798. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a)) a) REDUCED to normal form. ------ 196089/23298825. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((a a) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((a a) a))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 196090/23298852. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(y y))(a b))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(y y))(a b))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(x x))(a b))) 5. ==[ beta ]==> ((((a a) a)(a a))((a b)(a b))) REDUCED to normal form. ------ 196091/23298879. ------ 1. ==[ start ]==> (((a b)(a b))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 196092/23298906. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 196093/23298933. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.x1)(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.x1)(b a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.z)(b a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(b a)) REDUCED to normal form. ------ 196094/23299014. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((b (a (^x.x)))(a a)) REDUCED to normal form. ------ 196095/23299041. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.b)(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) b) REDUCED to normal form. ------ 196096/23299068. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 196097/23299239. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(((a a)(^z.z))(a a))) 3. ==[ beta ]==> (b (((a a)(^z.z))(a a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a a))) REDUCED to normal form. ------ 196098/23299347. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196099/23299455. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> ((b (^y.y))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 196100/23299518. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 196101/23299545. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a b)(^x1.a))) REDUCED to normal form. ------ 196102/23299626. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a (a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a (a a))(^y.a))) REDUCED to normal form. ------ 196103/23299653. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> (((a a)(^x.b))(a (^z.b))) 6. ==[ alpha ]==> (((a a)(^x.b))(a (^y.b))) REDUCED to normal form. ------ 196104/23299734. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 196105/23299761. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((b (^x.a))((a a) b)) REDUCED to normal form. ------ 196106/23299788. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a b) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a b) c)) REDUCED to normal form. ------ 196107/23299851. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 196108/23299905. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)(^x1.b))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)(^x1.b))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(^z.b))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.b))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.b))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 196109/23299932. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 196110/23299959. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((b a)(^y.(^z.z))) 8. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 196111/23300148. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(c (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(c (^z.b))) 3. ==[ beta ]==> ((b ((^y.y) a))(c (^z.b))) 4. ==[ alpha ]==> ((b ((^x.x) a))(c (^y.b))) 5. ==[ beta ]==> ((b a)(c (^y.b))) 6. ==[ alpha ]==> ((b a)(c (^x.b))) REDUCED to normal form. ------ 196112/23300175. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(b (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(b (^y.(a a)))) REDUCED to normal form. ------ 196113/23300229. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((^b.(a a))(a a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((^z.(a a))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(a a))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(a a))(a a))) 5. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 196114/23300643. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a ((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.y)(a ((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.x)(a ((^y.y)(a a)))) 7. ==[ beta ]==> (a ((^y.y)(a a))) 8. ==[ alpha ]==> (a ((^x.x)(a a))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 196115/23300670. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((a b)(a a))) 3. ==[ beta ]==> ((^y.y)((a b)(a a))) 4. ==[ alpha ]==> ((^x.x)((a b)(a a))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 196116/23300724. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(((^z.z)(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((^y.y)(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((b b)(((^y.y)(^z.z))((^x1.x1) a))) 8. ==[ alpha ]==> ((b b)(((^x.x)(^y.y))((^z.z) a))) 9. ==[ beta ]==> ((b b)((^y.y)((^z.z) a))) 10. ==[ alpha ]==> ((b b)((^x.x)((^y.y) a))) 11. ==[ beta ]==> ((b b)((^y.y) a)) 12. ==[ alpha ]==> ((b b)((^x.x) a)) 13. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 196117/23300805. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (^z.z))((a a) a))) 3. ==[ beta ]==> (b ((a (^z.z))((a a) a))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a) a))) REDUCED to normal form. ------ 196118/23300868. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a b)(^z.z))) REDUCED to normal form. ------ 196119/23300922. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^z1.z1)(^x2.a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.a)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.a)) REDUCED to normal form. ------ 196120/23300949. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 196121/23300976. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 196122/23301030. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a a)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.b))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.b))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.b))) 7. ==[ beta ]==> ((a a)(^y.b)) 8. ==[ alpha ]==> ((a a)(^x.b)) REDUCED to normal form. ------ 196123/23301066. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.b)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 196124/23301093. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 196125/23301120. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 196126/23301147. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(y y))(^z.(z z)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(^y.(y y)))) 5. ==[ beta ]==> (((a (a a)) b)((^y.(y y))(^y.(y y)))) 6. ==[ alpha ]==> (((a (a a)) b)((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 196127/23301174. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 196128/23301201. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 196129/23301228. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y)(^z.b))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.b)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.b)) REDUCED to normal form. ------ 196130/23301363. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(c (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(c (^y.(^z.z)))) 3. ==[ beta ]==> ((b (a (a a)))(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a (a a)))(c (^x.(^y.y)))) REDUCED to normal form. ------ 196131/23301390. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(b (^c.a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(b (^y.a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(b (^y.a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(b (^x.a))) REDUCED to normal form. ------ 196132/23301462. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 196133/23301471. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(^z.z)) 4. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.y)) REDUCED to normal form. ------ 196134/23301885. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 196135/23301921. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 196136/23302029. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 196137/23302056. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1)) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((^y1.y1) a)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1) a)) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 196138/23302182. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196139/23302218. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1)) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z)) b)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(b b)) REDUCED to normal form. ------ 196140/23302245. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.a) c)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.a) c)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 196141/23302326. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (a a))(^z.z))) REDUCED to normal form. ------ 196142/23302362. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 196143/23302389. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 196144/23302416. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((a (b (^x.x)))(a (a a))) REDUCED to normal form. ------ 196145/23302443. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))((^y.y)(^y.y))) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 196146/23302470. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (b ((^y.a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196147/23302497. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 196148/23302524. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(b a))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a b)(b a))(^y.(y y))) 4. ==[ alpha ]==> (((a b)(b a))(^x.(x x))) REDUCED to normal form. ------ 196149/23302632. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (^z.(z z)))) REDUCED to normal form. ------ 196150/23302659. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.a)(a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.a)(a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.a)(a a))) 5. ==[ beta ]==> ((b (^y.y))((^z.a)(a a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.a)(a a))) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 196151/23302686. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 196152/23302740. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)(^z.z))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 196153/23302758. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a (^z.z)) b)) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z)) b)) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y)) b)) REDUCED to normal form. ------ 196154/23302767. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 196155/23302794. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 196156/23302803. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a ((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a ((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a ((^x1.x1) a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196157/23302830. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a (^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a a))) 5. ==[ beta ]==> ((a (^y.y))(a a)) 6. ==[ alpha ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 196158/23302965. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(b (a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(b (a a))) 3. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 196159/23303073. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(a b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(a b)) 3. ==[ beta ]==> ((^y.(^z.z))(a b)) 4. ==[ alpha ]==> ((^x.(^y.y))(a b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196160/23312868. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(^b.(a b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(^x1.(a x1))) 3. ==[ eta ]==> ((^x.(^y.(y (^z.z)))) a) 4. ==[ beta ]==> (^y.(y (^z.z))) 5. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 196161/23315301. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.a)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 196162/23315760. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 196163/23315784. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196164/23316633. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(y1 (y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(y1 (y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (x1 (^y1.y1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (z (^x1.x1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196165/23317038. ------ 1. ==[ start ]==> (((a b) a)(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) a)(^x.((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a b) a)(^x.(^z.z))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 196166/23317056. ------ 1. ==[ start ]==> (((^a.a)(a b))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a b)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a b)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 196167/23317242. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.x1))(a b))) 3. ==[ beta ]==> (^y.(((^z.(^x1.x1))(a b))((^z.(^x1.x1))(a b)))) 4. ==[ alpha ]==> (^x.(((^y.(^z.z))(a b))((^x1.(^y1.y1))(a b)))) 5. ==[ beta ]==> (^x.((^z.z)((^x1.(^y1.y1))(a b)))) 6. ==[ alpha ]==> (^x.((^y.y)((^z.(^x1.x1))(a b)))) 7. ==[ beta ]==> (^x.((^z.(^x1.x1))(a b))) 8. ==[ alpha ]==> (^x.((^y.(^z.z))(a b))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196168/23317461. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(^z.((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(a a))(^z.((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(a a))(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196169/23317875. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((((^x.x)(a a))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 196170/23319717. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x1.x1))(^y1.y1))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 196171/23320107. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.(a a)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.(a a)))) 7. ==[ beta ]==> (((a a)(a a))(^y.(^z.(a a)))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(^y.(a a)))) REDUCED to normal form. ------ 196172/23320116. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.((y y)(y y)))) REDUCED to normal form. ------ 196173/23320635. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a) a)(^z.b))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 196174/23321115. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^y.b)) REDUCED to normal form. ------ 196175/23321634. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a (a a))(^y.(a a)))) 3. ==[ beta ]==> ((((a (a a))(^y.(a a)))((a (a a))(^y.(a a))))(((a (a a))(^y.(a a)))((a (a a))(^y.(a a))))) 4. ==[ alpha ]==> ((((a (a a))(^x.(a a)))((a (a a))(^y.(a a))))(((a (a a))(^z.(a a)))((a (a a))(^x1.(a a))))) REDUCED to normal form. ------ 196176/23322024. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 196177/23322033. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z (^x1.(^y1.y1))))) REDUCED to normal form. ------ 196178/23322303. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(^c.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(b a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(b a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(b a))) REDUCED to normal form. ------ 196179/23323374. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(^x1.((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196180/23323875. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(a a))(^y1.y1))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196181/23324292. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(a a)))) 7. ==[ beta ]==> (^y.(^z.(a a))) 8. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 196182/23324490. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(^z.(a b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(^z.(a b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(a b))) REDUCED to normal form. ------ 196183/23324694. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.x1)(a b))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 196184/23324697. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(^b.(a b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.(a z))) 3. ==[ eta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 196185/23325117. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^z.z)(^x1.x1))(^y1.(^z1.z1)))((((^z.z)(^x1.x1))(^y1.(^z1.z1)))(^y.y))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))(^z2.z2))) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((((^y1.y1)(^z1.z1))(^x2.(^y2.y2)))(^z2.z2))) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))(^y2.y2))) 7. ==[ beta ]==> ((^y.(^z.z))((((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))(^y2.y2))) 8. ==[ alpha ]==> ((^x.(^y.y))((((^z.z)(^x1.x1))(^y1.(^z1.z1)))(^x2.x2))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196186/23325831. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196187/23325966. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 196188/23325990. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 196189/23326065. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 196190/23326173. ------ 1. ==[ start ]==> (((a b)(b a))(^c.d)) 2. ==[ alpha ]==> (((a b)(b a))(^x.d)) REDUCED to normal form. ------ 196191/23326452. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196192/23326722. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^b.(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196193/23326833. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 196194/23326860. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(^y1.b))) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.b))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 196195/23326968. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.b)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.b)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 196196/23327022. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196197/23327085. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)(c ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.y)(c ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.x)(c ((^y.(^z.z)) a))) 5. ==[ beta ]==> (c ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (c ((^x.(^y.y)) a)) 7. ==[ beta ]==> (c (^y.y)) 8. ==[ alpha ]==> (c (^x.x)) REDUCED to normal form. ------ 196198/23327130. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.a)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.a)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 196199/23327166. ------ 1. ==[ start ]==> (((a (^a.a)) b)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x)) b)((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 196200/23327193. ------ 1. ==[ start ]==> ((((^a.a) a) a)(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) a)(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.(^z.z)) a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a)(a (^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((a a)(a (^y.y))) 8. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 196201/23327220. ------ 1. ==[ start ]==> (((a a)(^b.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.a))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(^x.a))((b (^y.y)) a)) REDUCED to normal form. ------ 196202/23327247. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 196203/23327274. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(b ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(b ((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 196204/23327382. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a a)(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a a)(((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a a)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 196205/23327463. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a b)((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a b)((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a b)((^y.y) b)) 8. ==[ alpha ]==> ((a b)((^x.x) b)) 9. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 196206/23327490. ------ 1. ==[ start ]==> (((a (a a)) a)((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 196207/23327517. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a (b (^y.y)))) REDUCED to normal form. ------ 196208/23327544. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 196209/23327571. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a a)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a (a (^z.z))))) REDUCED to normal form. ------ 196210/23327589. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a a))(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 196211/23327616. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 196212/23327634. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 196213/23327661. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) a)((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((b (^y.y))(^z.a))) REDUCED to normal form. ------ 196214/23327688. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 196215/23327715. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 196216/23327751. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196217/23327832. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))((a a)(^z1.z1)))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))((a a)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196218/23327913. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196219/23327967. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.a)(b (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) a) REDUCED to normal form. ------ 196220/23328039. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (a (^z.z))) a)) 3. ==[ beta ]==> (((a a)(^y.y))((a (a (^z.z))) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a (^y.y))) a)) REDUCED to normal form. ------ 196221/23328066. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^z.z) b)) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y) b)) 5. ==[ beta ]==> (((a (^x.x))(a (a a))) b) REDUCED to normal form. ------ 196222/23328093. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((b (^z.z)) c)) 3. ==[ beta ]==> ((a ((^y.y) a))((b (^z.z)) c)) 4. ==[ alpha ]==> ((a ((^x.x) a))((b (^y.y)) c)) 5. ==[ beta ]==> ((a a)((b (^y.y)) c)) 6. ==[ alpha ]==> ((a a)((b (^x.x)) c)) REDUCED to normal form. ------ 196223/23328264. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a ((^z.(a a))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a ((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 196224/23328345. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 196225/23328435. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(^x.a))(b (^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.a))(b (^y.y))) REDUCED to normal form. ------ 196226/23328462. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(a (a (a (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (a (a (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a (a (^x1.x1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a (a (^x1.x1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a (a (^z.z))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196227/23328489. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(a a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 196228/23328678. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (b (((^y.y)(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (b ((a a)((^y.y)(a a)))) 6. ==[ alpha ]==> (b ((a a)((^x.x)(a a)))) 7. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 196229/23328840. ------ 1. ==[ start ]==> ((((a a) a) b)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 196230/23328867. ------ 1. ==[ start ]==> (((a b) a)((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a b) a)((a a)((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a b) a)((a a)(^y.y))) 4. ==[ alpha ]==> (((a b) a)((a a)(^x.x))) REDUCED to normal form. ------ 196231/23328885. ------ 1. ==[ start ]==> (((^a.a)(a b))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a b))(a (^y.(y (^z.z))))) 3. ==[ beta ]==> ((a b)(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((a b)(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 196232/23329074. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.y)) REDUCED to normal form. ------ 196233/23329092. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a a)(a b))((a a)(^y.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))((a a)(^x.(a a)))) REDUCED to normal form. ------ 196234/23329119. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 196235/23329173. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 196236/23329200. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a a))(^z.z))) 5. ==[ beta ]==> (((^y.y) a)((a (a a))(^z.z))) 6. ==[ alpha ]==> (((^x.x) a)((a (a a))(^y.y))) 7. ==[ beta ]==> (a ((a (a a))(^y.y))) 8. ==[ alpha ]==> (a ((a (a a))(^x.x))) REDUCED to normal form. ------ 196237/23329290. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.z)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((^y.(a a))((^z.z)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196238/23329371. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.a))) 5. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.a))) 7. ==[ beta ]==> ((^y.(a a))(^z.a)) 8. ==[ alpha ]==> ((^x.(a a))(^y.a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196239/23329506. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a a)((^y.(a a))(^z.(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 196240/23329533. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 196241/23329587. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.(^z2.z2))))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 9. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196242/23329650. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))(c ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))(c ((a a)(a a)))) REDUCED to normal form. ------ 196243/23329677. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b (b (^z.z)))) REDUCED to normal form. ------ 196244/23329704. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^y.y))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 196245/23329767. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(a a)) c)) 3. ==[ beta ]==> (((a (^x.x))(a b))(a a)) REDUCED to normal form. ------ 196246/23329893. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (b (((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(a b))) 5. ==[ beta ]==> (b ((a a)(a b))) REDUCED to normal form. ------ 196247/23330208. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 196248/23330289. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(a a))(a b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(a a))(a b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 196249/23330370. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196250/23330496. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((b (^z.z)) a)) 3. ==[ beta ]==> (((a (^x.x))(a a))((b (^z.z)) a)) 4. ==[ alpha ]==> (((a (^x.x))(a a))((b (^y.y)) a)) REDUCED to normal form. ------ 196251/23330523. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((a a)(a a)) b)) 3. ==[ beta ]==> ((a (a b))(((a a)(a a)) b)) REDUCED to normal form. ------ 196252/23330550. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x) b) c)) 3. ==[ beta ]==> (((a (a a))((a a) a))(b c)) REDUCED to normal form. ------ 196253/23330802. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(^x1.x1))) 5. ==[ beta ]==> (b ((^z.a)(^x1.x1))) 6. ==[ alpha ]==> (b ((^x.a)(^y.y))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196254/23330946. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 196255/23331054. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a b)(a b))) 3. ==[ beta ]==> ((a (^y.(a a)))((a b)(a b))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a b)(a b))) REDUCED to normal form. ------ 196256/23331081. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(((a a) a)(a a))) REDUCED to normal form. ------ 196257/23331135. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (a a))(b a))) REDUCED to normal form. ------ 196258/23331162. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(a (a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 196259/23331189. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.a))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.a))((a (^y.y)) b)) REDUCED to normal form. ------ 196260/23331216. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 196261/23331279. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)(b a))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)(b a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 196262/23331306. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 196263/23331333. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((b a)(^z.(z z)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((b a)(^z.(z z)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((b a)(^y.(y y)))) 5. ==[ beta ]==> ((a (a a))((b a)(^y.(y y)))) 6. ==[ alpha ]==> ((a (a a))((b a)(^x.(x x)))) REDUCED to normal form. ------ 196264/23331360. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 196265/23331414. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a b)(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a b)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a b)(^y.b))) REDUCED to normal form. ------ 196266/23331441. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 196267/23331549. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 196268/23331558. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((^x2.x2) b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))((^x2.x2) b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((^z1.z1) b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196269/23331639. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a a)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 196270/23331720. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196271/23331828. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196272/23331882. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 196273/23331945. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 196274/23331972. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.b))(((^x1.x1) b)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) b)(a a))) 5. ==[ beta ]==> ((^y.b)(((^z.z) b)(a a))) 6. ==[ alpha ]==> ((^x.b)(((^y.y) b)(a a))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 196275/23332026. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((b a) a)) REDUCED to normal form. ------ 196276/23332053. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((a a)(^z.z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 196277/23332080. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a a)(^z.z))) REDUCED to normal form. ------ 196278/23332134. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a) a)(a b))) REDUCED to normal form. ------ 196279/23332305. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) b)(^y.y))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(b (^y.y))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(b (^x.x))) REDUCED to normal form. ------ 196280/23332332. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 196281/23332359. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((b a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((b a)(^y.a))) 3. ==[ beta ]==> (((a a)(a (a a)))((b a)(^y.a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((b a)(^x.a))) REDUCED to normal form. ------ 196282/23332386. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(^y.y))(^z.(z z)))) REDUCED to normal form. ------ 196283/23332440. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a b)(^z.a))) REDUCED to normal form. ------ 196284/23332467. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a) a)(^y.b))) 3. ==[ beta ]==> ((a b)(((a a) a)(^y.b))) 4. ==[ alpha ]==> ((a b)(((a a) a)(^x.b))) REDUCED to normal form. ------ 196285/23332476. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(a b))) 3. ==[ beta ]==> ((^y.y)((^z.a)(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(a b))) 5. ==[ beta ]==> ((^y.a)(a b)) 6. ==[ alpha ]==> ((^x.a)(a b)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 196286/23332503. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))((^y2.y2)(a a)))) 3. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))((^y2.y2)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196287/23332638. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.x)(^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196288/23332746. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(a a))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(a a))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196289/23332800. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((^y.y) b)((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x) b)((^y.a)(^z.b))) 5. ==[ beta ]==> (b ((^y.a)(^z.b))) 6. ==[ alpha ]==> (b ((^x.a)(^y.b))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196290/23332827. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196291/23332917. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(b (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(b (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.(a a))(b (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((^x.(a a))(b (a (^y.(^z.z))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196292/23332944. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(a ((^y.y) b))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(a b)) REDUCED to normal form. ------ 196293/23332971. ------ 1. ==[ start ]==> (((a b)(^c.a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)(^x.a))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 196294/23332998. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((b a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((b a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(a (^z.z)))) REDUCED to normal form. ------ 196295/23333025. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 196296/23333079. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(^y1.y1))) REDUCED to normal form. ------ 196297/23333106. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((b (^y.y))(((a a) a)((a a) a))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)((a a) a))) REDUCED to normal form. ------ 196298/23333277. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 196299/23333304. ------ 1. ==[ start ]==> (((a b)((a a) a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 196300/23333331. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((a a)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 196301/23333358. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))((a a)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 196302/23333439. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(^y.y))(^z.b))) 5. ==[ beta ]==> ((b (a a))((^y.y)(^z.b))) 6. ==[ alpha ]==> ((b (a a))((^x.x)(^y.b))) 7. ==[ beta ]==> ((b (a a))(^y.b)) 8. ==[ alpha ]==> ((b (a a))(^x.b)) REDUCED to normal form. ------ 196303/23333466. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a (a a))(^x.(a a)))) REDUCED to normal form. ------ 196304/23333502. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.a)((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.a)((a a)(^y.y))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 196305/23333637. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196306/23333745. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196307/23333853. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 196308/23333862. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 196309/23333889. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((b a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((b a)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((b a)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((b a)(a a))) REDUCED to normal form. ------ 196310/23333970. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a b)(a (a a)))) REDUCED to normal form. ------ 196311/23333997. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a) a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.b))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.b))(((a a) a)(^y.y))) REDUCED to normal form. ------ 196312/23334051. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (a a))(a b))) REDUCED to normal form. ------ 196313/23334105. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (^x1.x1))((a a)(^y1.y1)))) REDUCED to normal form. ------ 196314/23334132. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a a)(b a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a a)(b a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a a)(b a))) REDUCED to normal form. ------ 196315/23334195. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 196316/23334222. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z)(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z)(a a))(^x1.a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y)(a a))(^z.a))) 5. ==[ beta ]==> (((a (^x.x)) b)((a a)(^z.a))) 6. ==[ alpha ]==> (((a (^x.x)) b)((a a)(^y.a))) REDUCED to normal form. ------ 196317/23334249. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(^z.(z z)))) REDUCED to normal form. ------ 196318/23334276. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 196319/23334330. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a (a a))(^y.b))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (a a))(^y.b))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (a a))(^x.b))) REDUCED to normal form. ------ 196320/23334357. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a b))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a b))(a (^x.(a a)))) REDUCED to normal form. ------ 196321/23334465. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((a a)(^x1.x1)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((a a)(^x1.x1)) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((a a)(^z.z)) b)) REDUCED to normal form. ------ 196322/23334492. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z)(a a)) c)) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z)(a a)) c)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y)(a a)) c)) 5. ==[ beta ]==> ((b (a (^x.x)))((a a) c)) REDUCED to normal form. ------ 196323/23334636. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.a)(^y2.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.a)(^y2.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196324/23334861. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a (a a))((a a) a))) 3. ==[ beta ]==> ((b c)((a (a a))((a a) a))) REDUCED to normal form. ------ 196325/23334888. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x) a)(a b))) 3. ==[ beta ]==> ((((a a)(a a)) b)(a (a b))) REDUCED to normal form. ------ 196326/23334933. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 196327/23335014. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((^y1.(a a))(a (^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 196328/23335095. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196329/23335203. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196330/23335491. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(a a)) b)) 3. ==[ beta ]==> (((a b)(a a))((^y.(a a)) b)) 4. ==[ alpha ]==> (((a b)(a a))((^x.(a a)) b)) 5. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 196331/23335518. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.b) c)) 3. ==[ beta ]==> (((a a)(a b))((^y.b) c)) 4. ==[ alpha ]==> (((a a)(a b))((^x.b) c)) 5. ==[ beta ]==> (((a a)(a b)) b) REDUCED to normal form. ------ 196332/23335707. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.z))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 196333/23335797. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 7. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 8. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196334/23335878. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a b))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196335/23335986. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^c.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196336/23336103. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)(b (a b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)(b (a b))) 3. ==[ beta ]==> (((^y.y) a)(b (a b))) 4. ==[ alpha ]==> (((^x.x) a)(b (a b))) 5. ==[ beta ]==> (a (b (a b))) REDUCED to normal form. ------ 196337/23336121. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(a a)))) 7. ==[ beta ]==> ((^y.y)(^z.(a a))) 8. ==[ alpha ]==> ((^x.x)(^y.(a a))) 9. ==[ beta ]==> (^y.(a a)) 10. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 196338/23336211. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(^x.x))((^z.z) a)) 6. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 196339/23336238. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (a a))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))(a (a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196340/23336283. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(c (^c.a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(c (^z.a))) 3. ==[ beta ]==> (b (c (^z.a))) 4. ==[ alpha ]==> (b (c (^x.a))) REDUCED to normal form. ------ 196341/23336292. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 196342/23336319. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a a)(a b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a a)(a b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a a)(a b))) REDUCED to normal form. ------ 196343/23336526. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.a)(a b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(a b))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a b)) REDUCED to normal form. ------ 196344/23336544. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a b) a)) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a b) a)) 3. ==[ beta ]==> (((a a)(^y.y))((a b) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((a b) a)) REDUCED to normal form. ------ 196345/23336571. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((a a) a) b)) REDUCED to normal form. ------ 196346/23336733. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.b) a)) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.b) a)) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.b) a)) 5. ==[ beta ]==> (((a a)(a a))((^y.b) a)) 6. ==[ alpha ]==> (((a a)(a a))((^x.b) a)) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 196347/23336760. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^c.a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 196348/23336922. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((a a) a)(^z.z))) 3. ==[ beta ]==> (((^y.y)(a a))(((a a) a)(^z.z))) 4. ==[ alpha ]==> (((^x.x)(a a))(((a a) a)(^y.y))) 5. ==[ beta ]==> ((a a)(((a a) a)(^y.y))) 6. ==[ alpha ]==> ((a a)(((a a) a)(^x.x))) REDUCED to normal form. ------ 196349/23336949. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a (a (^x.x))))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.z))) REDUCED to normal form. ------ 196350/23336958. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((^b.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> (((^z.(^x1.x1))(a (^y1.y1)))(^y.y)) 6. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.x1)) 7. ==[ beta ]==> ((^y.y)(^x1.x1)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196351/23337345. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (^z.z))(a (a a)))) 3. ==[ beta ]==> (((^y.y) b)((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(a (a a)))) 5. ==[ beta ]==> (b ((a (^y.y))(a (a a)))) 6. ==[ alpha ]==> (b ((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 196352/23337363. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196353/23337372. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((a a)(^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((a a)(^y.y))) REDUCED to normal form. ------ 196354/23337417. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))(a a)) 6. ==[ alpha ]==> ((^x.(^y.y))(a a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196355/23337471. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.a)((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a))) a) REDUCED to normal form. ------ 196356/23337552. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196357/23337615. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(c a)) REDUCED to normal form. ------ 196358/23337660. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196359/23337696. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a))(a a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a))(a a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a))(a a))) REDUCED to normal form. ------ 196360/23337723. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a (a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (a (^y.y)))) REDUCED to normal form. ------ 196361/23337777. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a a)(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a a)(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a a)(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196362/23337795. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 196363/23337822. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(a a))) REDUCED to normal form. ------ 196364/23337840. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (^y.(^z.z)))) REDUCED to normal form. ------ 196365/23337867. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 196366/23337894. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a)(^z.(z z)))) 3. ==[ beta ]==> ((a (b (^y.y)))((a a)(^z.(z z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 196367/23337921. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (a a)) a)) REDUCED to normal form. ------ 196368/23337948. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(((^x1.x1) a) b)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(((^x1.x1) a) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a) b)) 5. ==[ beta ]==> (((^y.y) b)(((^z.z) a) b)) 6. ==[ alpha ]==> (((^x.x) b)(((^y.y) a) b)) 7. ==[ beta ]==> (b (((^y.y) a) b)) 8. ==[ alpha ]==> (b (((^x.x) a) b)) 9. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 196369/23338029. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(z z)) a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(z z)) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(y y)) a)) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 196370/23338056. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^b.a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.a) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.a) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 196371/23338137. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((b (^y.y))(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)(^z.z))) 7. ==[ beta ]==> ((b (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 196372/23338164. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 196373/23338218. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(((^a.a) a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(((^x1.x1) a) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) a) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a) a)) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a) a)) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a) a)) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 196374/23338236. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(c (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(c (a a))) 3. ==[ beta ]==> ((b (^y.y))(c (a a))) 4. ==[ alpha ]==> ((b (^x.x))(c (a a))) REDUCED to normal form. ------ 196375/23338245. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a (^a.a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a (^y.y)) b)) REDUCED to normal form. ------ 196376/23338281. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196377/23338443. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (b ((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196378/23338551. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.y1)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196379/23350785. ------ 1. ==[ start ]==> ((^a.((^a.a) a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))(b (a (a (^z.z))))) 3. ==[ eta ]==> ((^y.y)(b (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 196380/23351055. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((((^y.y)(a a))((a a)(^z.z)))((((^y.y)(a a))((a a)(^z.z)))(((^y.y)(a a))((a a)(^z.z))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((((^z.z)(a a))((a a)(^x1.x1)))(((^y1.y1)(a a))((a a)(^z1.z1))))) 5. ==[ beta ]==> (((a a)((a a)(^y.y)))((((^z.z)(a a))((a a)(^x1.x1)))(((^y1.y1)(a a))((a a)(^z1.z1))))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))((((^y.y)(a a))((a a)(^z.z)))(((^x1.x1)(a a))((a a)(^y1.y1))))) 7. ==[ beta ]==> (((a a)((a a)(^x.x)))(((a a)((a a)(^z.z)))(((^x1.x1)(a a))((a a)(^y1.y1))))) 8. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a)((a a)(^y.y)))(((^z.z)(a a))((a a)(^x1.x1))))) 9. ==[ beta ]==> (((a a)((a a)(^x.x)))(((a a)((a a)(^y.y)))((a a)((a a)(^x1.x1))))) 10. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((a a)((a a)(^y.y)))((a a)((a a)(^z.z))))) REDUCED to normal form. ------ 196381/23351265. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 196382/23351280. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196383/23352129. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(x1 (^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196384/23352351. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y)(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^z.z)(a a))) b) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a))) b) 5. ==[ beta ]==> (((a a)((^y.y)(a a))) b) 6. ==[ alpha ]==> (((a a)((^x.x)(a a))) b) 7. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 196385/23352561. ------ 1. ==[ start ]==> (((a a)(^a.b))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 196386/23352738. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(^z.z))(^x1.b))) 3. ==[ beta ]==> (^y.((((a a)(^z.z))(^x1.b))(((a a)(^z.z))(^x1.b)))) 4. ==[ alpha ]==> (^x.((((a a)(^y.y))(^z.b))(((a a)(^x1.x1))(^y1.b)))) REDUCED to normal form. ------ 196387/23353620. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((a a) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((((a a) a)((a a)(^z.z)))(((a a) a)((a a)(^z.z))))(^y.y)) 4. ==[ alpha ]==> (((((a a) a)((a a)(^x.x)))(((a a) a)((a a)(^y.y))))(^z.z)) REDUCED to normal form. ------ 196388/23354925. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((a a)(a a))(^y1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 196389/23355612. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 196390/23355945. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(^c.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(a b))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(a b))(^y.((^z.z) b))) 5. ==[ beta ]==> ((a b)(^y.((^z.z) b))) 6. ==[ alpha ]==> ((a b)(^x.((^y.y) b))) 7. ==[ beta ]==> ((a b)(^x.b)) REDUCED to normal form. ------ 196391/23356611. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 196392/23357529. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 196393/23357826. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 196394/23358879. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.((a a)(^y1.y1)))) REDUCED to normal form. ------ 196395/23359131. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 196396/23360013. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(^x1.(z z)))) REDUCED to normal form. ------ 196397/23360190. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a a)(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a a)(^x1.b))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 196398/23360400. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(z b))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(z b))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(y b))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y b))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x b))) REDUCED to normal form. ------ 196399/23361201. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^z1.z1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 196400/23361471. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 196401/23361486. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (a a))(^y1.y1))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 196402/23361696. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(z (z z)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(z (z z)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(y (y y)))) REDUCED to normal form. ------ 196403/23361936. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(b (a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196404/23361948. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^c.c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196405/23362218. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^c.(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196406/23362347. ------ 1. ==[ start ]==> (((a a) a)((^b.b)(^c.a))) 2. ==[ alpha ]==> (((a a) a)((^x.x)(^y.a))) 3. ==[ beta ]==> (((a a) a)(^y.a)) 4. ==[ alpha ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 196407/23362374. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 196408/23362482. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a) b) REDUCED to normal form. ------ 196409/23362536. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 196410/23362626. ------ 1. ==[ start ]==> ((a ((^a.a) a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))(b (a (a (^y.y))))) 3. ==[ beta ]==> ((a a)(b (a (a (^y.y))))) 4. ==[ alpha ]==> ((a a)(b (a (a (^x.x))))) REDUCED to normal form. ------ 196411/23362662. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2))) a)) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196412/23362815. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 196413/23362842. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b a)(a b))) REDUCED to normal form. ------ 196414/23362869. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (a a))(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 196415/23362896. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> ((a (a (a a)))((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> ((a (a (a a)))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 196416/23363076. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(b (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 196417/23363103. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 196418/23363121. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a (^z.z)))(^x1.x1))) REDUCED to normal form. ------ 196419/23363211. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((b b)((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> ((b b)((^x.(a a))(a (a a)))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 196420/23363256. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196421/23363283. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((b a)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 196422/23363346. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 196423/23363373. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.b)(b a))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)(b a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)(b a))) 5. ==[ beta ]==> (a ((^y.b)(b a))) 6. ==[ alpha ]==> (a ((^x.b)(b a))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 196424/23363391. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 196425/23363400. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 196426/23363418. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196427/23363427. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 196428/23363454. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.a))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 196429/23363481. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 196430/23363508. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.(^x2.x2)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.(^y1.y1)) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196431/23363886. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))(^y1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 196432/23363967. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(y1 (^z1.z1))))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(x1 (^y1.y1))))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196433/23364030. ------ 1. ==[ start ]==> (((a a)((a a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((a a) a))((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 196434/23364057. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(((a a)(a a)) a)) REDUCED to normal form. ------ 196435/23364084. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.x) b)(a (a a)))) 5. ==[ beta ]==> ((a (a (a a)))(b (a (a a)))) REDUCED to normal form. ------ 196436/23364111. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a)) a)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (a a)) a)((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (a a)) a)((a (^x.(^y.y)))(^x1.x1))) 6. ==[ alpha ]==> (((a (a a)) a)((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 196437/23364138. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((b a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b a)((a a) a))) 5. ==[ beta ]==> ((a (^y.y))((b a)((a a) a))) 6. ==[ alpha ]==> ((a (^x.x))((b a)((a a) a))) REDUCED to normal form. ------ 196438/23364165. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 196439/23364192. ------ 1. ==[ start ]==> ((a (a b))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a b))(((^x.x)(a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a b))((a a)((^y.y)(a a)))) 4. ==[ alpha ]==> ((a (a b))((a a)((^x.x)(a a)))) 5. ==[ beta ]==> ((a (a b))((a a)(a a))) REDUCED to normal form. ------ 196440/23364345. ------ 1. ==[ start ]==> ((((a a) a) b)(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 196441/23364399. ------ 1. ==[ start ]==> (((a a)(^a.b))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 196442/23364417. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.x1))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.x1)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196443/23364471. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((a a)(a a))(^y.a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 196444/23364507. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((^y.a)((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((^x.a)((^y.y)(a (a a)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 196445/23364534. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 196446/23364552. ------ 1. ==[ start ]==> (((^a.b)(a a))((b a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(a a))((b a)(^y.a))) 3. ==[ beta ]==> (b ((b a)(^y.a))) 4. ==[ alpha ]==> (b ((b a)(^x.a))) REDUCED to normal form. ------ 196447/23364579. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 196448/23364750. ------ 1. ==[ start ]==> (((^a.b) b)((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.a)((a a)(a a)))) 3. ==[ beta ]==> (b ((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196449/23364822. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) a)) 5. ==[ beta ]==> (((^y.(^z.z)) a) a) 6. ==[ alpha ]==> (((^x.(^y.y)) a) a) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 196450/23364876. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a)) c)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a)) c)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a)) c)) 5. ==[ beta ]==> ((^y.y)(((a a)(a a)) c)) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a)) c)) 7. ==[ beta ]==> (((a a)(a a)) c) REDUCED to normal form. ------ 196451/23365020. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 196452/23365047. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b)) b) REDUCED to normal form. ------ 196453/23365101. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 196454/23365128. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(y y))((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(y y))(^z.z))) 7. ==[ beta ]==> (((^y.(y y))(^z.z))((^y.(y y))(^z.z))) 8. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(z z))(^x1.x1))) 9. ==[ beta ]==> (((^y.y)(^y.y))((^z.(z z))(^x1.x1))) 10. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(^x1.x1))) 11. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.x1))) 12. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.z))) 13. ==[ beta ]==> ((^y.(y y))(^z.z)) 14. ==[ alpha ]==> ((^x.(x x))(^y.y)) 15. ==[ beta ]==> ((^y.y)(^y.y)) 16. ==[ alpha ]==> ((^x.x)(^y.y)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196455/23365155. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 196456/23365245. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((b (^y.y))(a a))) 3. ==[ beta ]==> (((a a)(a a))((b (^y.y))(a a))) 4. ==[ alpha ]==> (((a a)(a a))((b (^x.x))(a a))) REDUCED to normal form. ------ 196457/23365272. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 196458/23365299. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> ((a ((a a) a))(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> ((a ((a a) a))(((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> ((a ((a a) a))(b ((^y.y) a))) 6. ==[ alpha ]==> ((a ((a a) a))(b ((^x.x) a))) 7. ==[ beta ]==> ((a ((a a) a))(b a)) REDUCED to normal form. ------ 196459/23365326. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((a (a a))(^y.y))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 196460/23365353. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((b a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a))((b a)((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a (a a))((b a)((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a (a a))((b a)(^y.y))) 8. ==[ alpha ]==> ((a (a a))((b a)(^x.x))) REDUCED to normal form. ------ 196461/23365380. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> ((((a a) a) a)(((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> ((((a a) a) a)(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 196462/23365407. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((a a)(a b))) REDUCED to normal form. ------ 196463/23365434. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a b)((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((a b)((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)(a a))((a b)(a a))) REDUCED to normal form. ------ 196464/23365461. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a) a)((a a)(^y.y)))) REDUCED to normal form. ------ 196465/23365632. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (b ((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.y))) REDUCED to normal form. ------ 196466/23365641. ------ 1. ==[ start ]==> (((a b) c)((^d.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b) c)((^x.(^y.y))(a a))) 3. ==[ beta ]==> (((a b) c)(^y.y)) 4. ==[ alpha ]==> (((a b) c)(^x.x)) REDUCED to normal form. ------ 196467/23365668. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a a) b)((^y.(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a a) b)((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 196468/23365695. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z) a)) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y) a)) 5. ==[ beta ]==> ((((a a)(^x.x)) a) a) REDUCED to normal form. ------ 196469/23365713. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 196470/23365740. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 196471/23365776. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> ((a (^x.b))(^z.z)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 196472/23365794. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y)(a a))(^z.b))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((a a)(^y.b))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)(^x.b))) REDUCED to normal form. ------ 196473/23365830. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.b)((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.b)((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.b)((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196474/23365884. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 196475/23365911. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 196476/23365938. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 196477/23366694. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(c (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(c (^z.z))) 3. ==[ beta ]==> (((a a)(^y.a))(c (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))(c (^y.y))) REDUCED to normal form. ------ 196478/23366721. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(b (^x1.(a a)))) REDUCED to normal form. ------ 196479/23366766. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((a a)(a a))(^x1.x1))) REDUCED to normal form. ------ 196480/23367045. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196481/23367063. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196482/23367144. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z) b) b)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z) b) b)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z) b) b)) 5. ==[ beta ]==> ((a a)(((^z.z) b) b)) 6. ==[ alpha ]==> ((a a)(((^x.x) b) b)) 7. ==[ beta ]==> ((a a)(b b)) REDUCED to normal form. ------ 196483/23367342. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 196484/23367450. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.(a a))) REDUCED to normal form. ------ 196485/23367522. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1))) c)) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1))) c)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) c)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196486/23367675. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((^x1.x1)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((^x1.x1)(a a))) 6. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((^z.z)(a a))) 7. ==[ beta ]==> (((a a)(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 196487/23367702. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 196488/23367729. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z) a)(b a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z) a)(b a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y) a)(b a))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))(a (b a))) REDUCED to normal form. ------ 196489/23367756. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a (^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(a a))((a (^y.y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))(a a))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 196490/23367783. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a a)((^z.z) b))) 3. ==[ beta ]==> (((^y.y)(a b))((a a)((^z.z) b))) 4. ==[ alpha ]==> (((^x.x)(a b))((a a)((^y.y) b))) 5. ==[ beta ]==> ((a b)((a a)((^y.y) b))) 6. ==[ alpha ]==> ((a b)((a a)((^x.x) b))) 7. ==[ beta ]==> ((a b)((a a) b)) REDUCED to normal form. ------ 196491/23367936. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196492/23367981. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.b))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.b))) 5. ==[ beta ]==> (((a a) a)(^y.b)) 6. ==[ alpha ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 196493/23368008. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(^x2.x2))(^y2.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(a a))) 7. ==[ beta ]==> ((^y.y)(^z.(a a))) 8. ==[ alpha ]==> ((^x.x)(^y.(a a))) 9. ==[ beta ]==> (^y.(a a)) 10. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 196494/23368143. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) b) a)) 3. ==[ beta ]==> (b (((^z.z) b) a)) 4. ==[ alpha ]==> (b (((^x.x) b) a)) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 196495/23368260. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(a a)) REDUCED to normal form. ------ 196496/23368287. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.b)(^z.a))) 3. ==[ beta ]==> ((b a)((^y.b)(^z.a))) 4. ==[ alpha ]==> ((b a)((^x.b)(^y.a))) 5. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 196497/23368314. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 196498/23368341. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(^y1.y1)) REDUCED to normal form. ------ 196499/23368422. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196500/23368449. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.y)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 196501/23368467. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.b) a)) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.y) a)) 3. ==[ beta ]==> (b ((^y.y) a)) 4. ==[ alpha ]==> (b ((^x.x) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196502/23368647. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(^z.z))(a b))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(^y.y))(a b))) 5. ==[ beta ]==> (((a a) b)((^y.y)(a b))) 6. ==[ alpha ]==> (((a a) b)((^x.x)(a b))) 7. ==[ beta ]==> (((a a) b)(a b)) REDUCED to normal form. ------ 196503/23368674. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a (a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a (a a))(a a))) REDUCED to normal form. ------ 196504/23368701. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (b a))(((^y.y) a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (b a))(((^x.x) a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a (b a))(a ((a a)(^y.y)))) 6. ==[ alpha ]==> ((a (b a))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 196505/23368728. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (^y.y))(b a))) REDUCED to normal form. ------ 196506/23368755. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a)((a a)(a (^y.(^z.z))))) 8. ==[ alpha ]==> ((a a)((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 196507/23369007. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 196508/23369142. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((a a)(^z.z)) c)) 3. ==[ beta ]==> (b (((a a)(^z.z)) c)) 4. ==[ alpha ]==> (b (((a a)(^x.x)) c)) REDUCED to normal form. ------ 196509/23369286. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((b b)((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> ((b b)((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> ((b b)((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> ((b b)((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 196510/23369313. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a) a) REDUCED to normal form. ------ 196511/23369367. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 196512/23369610. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(c (^x1.(^y1.y1)))) REDUCED to normal form. ------ 196513/23369664. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 196514/23370501. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a a))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 196515/23370519. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1)(a a))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 196516/23370528. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((^x1.(a a))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 196517/23370600. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196518/23370609. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 196519/23370636. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(z z))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(y y))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.b))(((a a) a)((a a) a))) REDUCED to normal form. ------ 196520/23370717. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 196521/23370744. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 196522/23370771. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 196523/23370942. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(b ((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))(b ((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))(b ((^y.y)(a a)))) 5. ==[ beta ]==> ((b a)(b ((^y.y)(a a)))) 6. ==[ alpha ]==> ((b a)(b ((^x.x)(a a)))) 7. ==[ beta ]==> ((b a)(b (a a))) REDUCED to normal form. ------ 196524/23370969. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 196525/23370996. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y)(a a))(a a))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x)(a a))(a a))) 5. ==[ beta ]==> (((a b)(a a))((a a)(a a))) REDUCED to normal form. ------ 196526/23371023. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((a b)(a (^y.y)))) 3. ==[ beta ]==> (((a a)(a b))((a b)(a (^y.y)))) 4. ==[ alpha ]==> (((a a)(a b))((a b)(a (^x.x)))) REDUCED to normal form. ------ 196527/23371050. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(((a a) a) a)) REDUCED to normal form. ------ 196528/23371104. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a (a a))(^z.z))) REDUCED to normal form. ------ 196529/23371131. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((b a)(((^y.y) a)((a a) a))) 6. ==[ alpha ]==> ((b a)(((^x.x) a)((a a) a))) 7. ==[ beta ]==> ((b a)(a ((a a) a))) REDUCED to normal form. ------ 196530/23371158. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (^y.y))(a b))) REDUCED to normal form. ------ 196531/23371302. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 x1))) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z z))) 9. ==[ beta ]==> ((^y.y)(^z.(z z))) 10. ==[ alpha ]==> ((^x.x)(^y.(y y))) 11. ==[ beta ]==> (^y.(y y)) 12. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 196532/23371383. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.x1))(^y1.b))) 3. ==[ beta ]==> (b ((a (^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.b))) REDUCED to normal form. ------ 196533/23371491. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((a a) a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((a a) a) c)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196534/23371608. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.b))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.b))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 196535/23371653. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(a a)) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(a a)) a)) 5. ==[ beta ]==> ((^y.(a a)) a) 6. ==[ alpha ]==> ((^x.(a a)) a) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196536/23371707. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^c.a) c)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a) c)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a) c)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a) c)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a) c)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a) c)) 7. ==[ beta ]==> ((b b)((^y.a) c)) 8. ==[ alpha ]==> ((b b)((^x.a) c)) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 196537/23371797. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(c (^c.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (^z.a))) REDUCED to normal form. ------ 196538/23371824. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(b (^z.b))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(b (^z.b))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(b (^y.b))) REDUCED to normal form. ------ 196539/23371851. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.(a a)))) REDUCED to normal form. ------ 196540/23371896. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((a a) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196541/23371905. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.a)(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 196542/23371932. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((b (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((b (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 196543/23371959. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((a (a a))(a (a a)))) REDUCED to normal form. ------ 196544/23372013. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a) a))) 7. ==[ beta ]==> ((^y.(^z.z))((a a) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((a a) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196545/23372031. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a a)(^a.b))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a a)(^z.b))) REDUCED to normal form. ------ 196546/23372184. ------ 1. ==[ start ]==> ((((a a) a)(b a))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))(c ((^x.x)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(b a))(c (^y.y))) 4. ==[ alpha ]==> ((((a a) a)(b a))(c (^x.x))) REDUCED to normal form. ------ 196547/23372211. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(b ((a a) a))) REDUCED to normal form. ------ 196548/23372238. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(a (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(a (a b))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(a (a b))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a (a b))) 5. ==[ beta ]==> (((a a)(a a))(a (a b))) REDUCED to normal form. ------ 196549/23372265. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(((a a) a)(a a))) REDUCED to normal form. ------ 196550/23372319. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((a (a a))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((a (a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (a a))((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a (a a)) a)) REDUCED to normal form. ------ 196551/23372346. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y) a)(a (a a)))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x) a)(a (a a)))) 5. ==[ beta ]==> ((b (a (a a)))(a (a (a a)))) REDUCED to normal form. ------ 196552/23372373. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a (^x.x))(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 196553/23372463. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((^z.z)(^x1.x1))(^y1.(^z1.z1)))(^y.y)) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(^y1.y1)) 7. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.y1)) 8. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1)) 9. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196554/23372850. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(c (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(c (^z.(z z)))) 3. ==[ beta ]==> (((^y.y) b)(c (^z.(z z)))) 4. ==[ alpha ]==> (((^x.x) b)(c (^y.(y y)))) 5. ==[ beta ]==> (b (c (^y.(y y)))) 6. ==[ alpha ]==> (b (c (^x.(x x)))) REDUCED to normal form. ------ 196555/23372877. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(b (^y.(^z.z)))) REDUCED to normal form. ------ 196556/23372922. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1)(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196557/23372976. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y) a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x) a)(^y.a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a (^y.a))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a (^x.a))) REDUCED to normal form. ------ 196558/23373012. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 7. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 8. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196559/23373039. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 196560/23373057. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y)(^z.z)) a)) 3. ==[ beta ]==> (b (((^y.y)(^z.z)) a)) 4. ==[ alpha ]==> (b (((^x.x)(^y.y)) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196561/23373120. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 196562/23373282. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b (^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(z z)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196563/23373309. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 196564/23373327. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))(^x1.x1))) REDUCED to normal form. ------ 196565/23373507. ------ 1. ==[ start ]==> (((a b)(b a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a b)(b a))(b ((^x.x) a))) 3. ==[ beta ]==> (((a b)(b a))(b a)) REDUCED to normal form. ------ 196566/23373534. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(a (a (a a)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(a (a (a a)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (a (a a)))) REDUCED to normal form. ------ 196567/23373561. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(((^z.z) a)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(((^z.z) a)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) a)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (a a))) REDUCED to normal form. ------ 196568/23373615. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a a)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))((a a) a)) REDUCED to normal form. ------ 196569/23373741. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(^z.z))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 196570/23373777. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(b (a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b (a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b (a (^z.z)))) REDUCED to normal form. ------ 196571/23373786. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a a) c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a) c)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) c)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) c)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196572/23373813. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^b.a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.a) a)) 3. ==[ beta ]==> ((^y.y)((^y1.a) a)) 4. ==[ alpha ]==> ((^x.x)((^y.a) a)) 5. ==[ beta ]==> ((^y.a) a) 6. ==[ alpha ]==> ((^x.a) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 196573/23373948. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a (^y1.y1)) a)) 3. ==[ beta ]==> (b ((a (^y1.y1)) a)) 4. ==[ alpha ]==> (b ((a (^x.x)) a)) REDUCED to normal form. ------ 196574/23374056. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((a a)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196575/23386038. ------ 1. ==[ start ]==> ((^a.b)((^b.b)(^c.a))) 2. ==[ alpha ]==> ((^x.b)((^y.y)(^z.a))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 196576/23386308. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196577/23386347. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1)(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 196578/23386479. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 196579/23386929. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196580/23387229. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 196581/23387361. ------ 1. ==[ start ]==> ((^a.((a a) a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y)(^z.(^x1.x1)))((^y.y)(^z.(^x1.x1))))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1))))((^x2.x2)(^y2.(^z2.z2)))) 5. ==[ beta ]==> (((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1))))((^x2.x2)(^y2.(^z2.z2)))) 6. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.(^y1.y1))))((^z1.z1)(^x2.(^y2.y2)))) 7. ==[ beta ]==> ((^y.y)((^z1.z1)(^x2.(^y2.y2)))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 9. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 10. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196582/23387694. ------ 1. ==[ start ]==> ((^a.(^a.b))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((^x.(^y.b))(((^z.(^x1.x1)) a)(a a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 196583/23388075. ------ 1. ==[ start ]==> (((^a.a)(a b))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((a b)(^y.((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((a b)(^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a b)(^x.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 196584/23388468. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(b (^y1.y1)))((^z.(^x1.x1))(b (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(b (^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2))))) 5. ==[ beta ]==> (((^y.(^z.z))(b (^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 6. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 7. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(b (^z1.z1)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b (^x1.x1)))) 9. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 10. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196585/23389686. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(^z.(z (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.(y (^z.z)))) REDUCED to normal form. ------ 196586/23389899. ------ 1. ==[ start ]==> ((^a.(b a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.b)(^z.(a a)))) 3. ==[ eta ]==> (b ((^y.b)(^z.(a a)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 196587/23390073. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 196588/23390736. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^x1.a)(a (^y1.(^z1.z1))))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.a)(a (^y.(^z.z))))(^x1.(^y1.y1))) 5. ==[ beta ]==> (a (^x1.(^y1.y1))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 196589/23391339. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a) a)(a b))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a b))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196590/23391654. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.b)((a a) a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 196591/23392152. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.((^z.z) b))) 3. ==[ beta ]==> (b (^y.((^z.z) b))) 4. ==[ alpha ]==> (b (^x.((^y.y) b))) 5. ==[ beta ]==> (b (^x.b)) REDUCED to normal form. ------ 196592/23392467. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 196593/23392653. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(^z.z))(a b))) 3. ==[ beta ]==> ((((^y.(^z.z))(a b))((^y.(^z.z))(a b)))(((^y.(^z.z))(a b))((^y.(^z.z))(a b)))) 4. ==[ alpha ]==> ((((^x.(^y.y))(a b))((^z.(^x1.x1))(a b)))(((^y1.(^z1.z1))(a b))((^x2.(^y2.y2))(a b)))) 5. ==[ beta ]==> (((^y.y)((^z.(^x1.x1))(a b)))(((^y1.(^z1.z1))(a b))((^x2.(^y2.y2))(a b)))) 6. ==[ alpha ]==> (((^x.x)((^y.(^z.z))(a b)))(((^x1.(^y1.y1))(a b))((^z1.(^x2.x2))(a b)))) 7. ==[ beta ]==> (((^y.(^z.z))(a b))(((^x1.(^y1.y1))(a b))((^z1.(^x2.x2))(a b)))) 8. ==[ alpha ]==> (((^x.(^y.y))(a b))(((^z.(^x1.x1))(a b))((^y1.(^z1.z1))(a b)))) 9. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(a b))((^y1.(^z1.z1))(a b)))) 10. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(a b))((^x1.(^y1.y1))(a b)))) 11. ==[ beta ]==> (((^y.(^z.z))(a b))((^x1.(^y1.y1))(a b))) 12. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(a b))) 13. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a b))) 14. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a b))) 15. ==[ beta ]==> ((^y.(^z.z))(a b)) 16. ==[ alpha ]==> ((^x.(^y.y))(a b)) 17. ==[ beta ]==> (^y.y) 18. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196594/23393733. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196595/23393907. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(^z.(b z))) 3. ==[ eta ]==> (((^x.b)(^y.(a a))) b) 4. ==[ beta ]==> (b b) REDUCED to normal form. ------ 196596/23394654. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 196597/23395338. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.((^y1.y1)(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.y1)(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(y y)))) 5. ==[ beta ]==> (^y.((^z.z)(y y))) 6. ==[ alpha ]==> (^x.((^y.y)(x x))) 7. ==[ beta ]==> (^x.(x x)) REDUCED to normal form. ------ 196598/23395734. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(^b.(a b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(^z.(a z))) 3. ==[ eta ]==> (((a a)((^x.(^y.y)) a)) a) 4. ==[ beta ]==> (((a a)(^y.y)) a) 5. ==[ alpha ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 196599/23395923. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(^z.(^x1.z))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(^z.(^x1.z))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.y))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.x))) REDUCED to normal form. ------ 196600/23396112. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(^a.(^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(^z.(^x1.b))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.b))) 5. ==[ beta ]==> ((a a)(^y.(^z.b))) 6. ==[ alpha ]==> ((a a)(^x.(^y.b))) REDUCED to normal form. ------ 196601/23397111. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(a (a a)))) REDUCED to normal form. ------ 196602/23397219. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(^z.(z z)))) REDUCED to normal form. ------ 196603/23397327. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 196604/23397408. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z) a))) 7. ==[ beta ]==> ((a (^x.x))(^y.a)) REDUCED to normal form. ------ 196605/23397459. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196606/23397498. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((^y.y)(^y1.y1)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196607/23397633. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> (b (^y1.c)) 4. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 196608/23397888. ------ 1. ==[ start ]==> ((a b)((^b.b)(^c.a))) 2. ==[ alpha ]==> ((a b)((^x.x)(^y.a))) 3. ==[ beta ]==> ((a b)(^y.a)) 4. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 196609/23398158. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 196610/23398167. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(b (a (a (^z.z))))) 3. ==[ beta ]==> ((^y.a)(b (a (a (^z.z))))) 4. ==[ alpha ]==> ((^x.a)(b (a (a (^y.y))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 196611/23398194. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(a ((^y1.y1)(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(a ((^y1.y1)(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 196612/23398203. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.z))) REDUCED to normal form. ------ 196613/23398230. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(y (^z.z))) b)) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z))) b)) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y))) b)) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 196614/23398248. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (a (((^y.(^z.z)) a)(a (^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.(^y.y)) a)(a (^z.z)))) 7. ==[ beta ]==> (a ((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> (a ((^x.x)(a (^y.y)))) 9. ==[ beta ]==> (a (a (^y.y))) 10. ==[ alpha ]==> (a (a (^x.x))) REDUCED to normal form. ------ 196615/23398275. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((b (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 196616/23398329. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.(x x)))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 196617/23398437. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((((^y.y)(a a))((a a)(^z.z)))(((^y.y)(a a))((a a)(^z.z)))) 6. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 7. ==[ beta ]==> (((a a)((a a)(^y.y)))(((^z.z)(a a))((a a)(^x1.x1)))) 8. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y)(a a))((a a)(^z.z)))) 9. ==[ beta ]==> (((a a)((a a)(^x.x)))((a a)((a a)(^z.z)))) 10. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 196618/23398464. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 196619/23398518. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 9. ==[ beta ]==> ((^y.y)((^z.z) b)) 10. ==[ alpha ]==> ((^x.x)((^y.y) b)) 11. ==[ beta ]==> ((^y.y) b) 12. ==[ alpha ]==> ((^x.x) b) 13. ==[ beta ]==> b REDUCED to normal form. ------ 196620/23398545. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 196621/23398572. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((^y.y) a)(b (^z.z))) 6. ==[ alpha ]==> (((^x.x) a)(b (^y.y))) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 196622/23398626. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a a)(a (a (^y.y))))) 3. ==[ beta ]==> (((a a)(a a))((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> (((a a)(a a))((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 196623/23398671. ------ 1. ==[ start ]==> (((a a)(a (a a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> (((a a)(a (a a)))((a a)(^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 196624/23398743. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((a a)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((b b)(((a a)(a a))(^y.(y y)))) 4. ==[ alpha ]==> ((b b)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 196625/23398779. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 196626/23398878. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 196627/23398932. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 196628/23398959. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 196629/23398986. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((a (a a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((a (a a))(^z.(a a)))) 3. ==[ beta ]==> ((a (^y.a))((a (a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((a (a a))(^y.(a a)))) REDUCED to normal form. ------ 196630/23399076. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> (((a a)(^x.x))(a (a (^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 196631/23399103. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 196632/23399211. ------ 1. ==[ start ]==> ((a ((a a) a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.x)(^y.(^z.z)))) 3. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 196633/23399526. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((((a a) a)(^x.x))(a (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 196634/23399544. ------ 1. ==[ start ]==> ((a (^a.b))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((a (^x.b))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((a (^x.b))((^z.z)(a a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)(a a))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 196635/23399733. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.b)(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.b)(((^y.y)(a a))((^z.z)(a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 196636/23399814. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) IRREDUCIBLE: cycle. ------ 196637/23399895. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> (b ((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> (b ((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 196638/23399922. ------ 1. ==[ start ]==> (((^a.a)(a b))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(a b))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a b)((a a)((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((a b)((a a)((^x.(^y.y)) a))) 5. ==[ beta ]==> ((a b)((a a)(^y.y))) 6. ==[ alpha ]==> ((a b)((a a)(^x.x))) REDUCED to normal form. ------ 196639/23399985. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((b (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 196640/23400012. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 196641/23400039. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.x1) b)(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.x1) b)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.z) b)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.a)(((^z.z) b)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.a)(((^y.y) b)(^z.(z z)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 196642/23400066. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 196643/23400093. ------ 1. ==[ start ]==> (((a b)(^a.a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 196644/23400129. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(^a.a))(a b))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(a b))) 3. ==[ beta ]==> (((a a)(a b))(^y.y)) 4. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 196645/23400156. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 196646/23400183. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 196647/23400237. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(a (^x1.(^y1.y1))))) 7. ==[ beta ]==> (a ((^y.(^z.z))(a (^x1.(^y1.y1))))) 8. ==[ alpha ]==> (a ((^x.(^y.y))(a (^z.(^x1.x1))))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 196648/23400264. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(((^z.z) b)((^z.z) b))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y) b)((^z.z) b))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b ((^z.z) b))) 6. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(b ((^y.y) b))) 7. ==[ beta ]==> ((((a a) a)(a (^x.x)))(b b)) REDUCED to normal form. ------ 196649/23400282. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (b (a (^y.(a a)))) 6. ==[ alpha ]==> (b (a (^x.(a a)))) REDUCED to normal form. ------ 196650/23400291. ------ 1. ==[ start ]==> (((a b)(a a))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)((a a)(a a)))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 196651/23400318. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 196652/23400705. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))(c ((a a)(a a)))) 3. ==[ beta ]==> (b (c ((a a)(a a)))) REDUCED to normal form. ------ 196653/23401029. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1)(^y1.y1))(b a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(b a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(b a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(b a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(b a)) 7. ==[ beta ]==> ((^y.y)(b a)) 8. ==[ alpha ]==> ((^x.x)(b a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196654/23401173. ------ 1. ==[ start ]==> (((a b) c)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b) c)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 196655/23401200. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a) b)(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 196656/23401227. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.a))) REDUCED to normal form. ------ 196657/23401281. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((b a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 196658/23401308. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.b))(((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 196659/23401362. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a b)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a b)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a b)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.(a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196660/23401443. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (a a))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 196661/23401470. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 196662/23401506. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 196663/23401533. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.z)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.z)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.y)(b (^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(b (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(b (^y.y))) REDUCED to normal form. ------ 196664/23401614. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(^y1.a))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.a))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.a))) 7. ==[ beta ]==> ((^y.y)((^z.z)(^x1.a))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 9. ==[ beta ]==> ((^y.y)(^z.a)) 10. ==[ alpha ]==> ((^x.x)(^y.a)) 11. ==[ beta ]==> (^y.a) 12. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 196665/23401641. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 196666/23401722. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(a a))(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 196667/23401749. ------ 1. ==[ start ]==> ((a (b a))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.b)(^y.(a a)))) 3. ==[ beta ]==> ((a (b a)) b) REDUCED to normal form. ------ 196668/23401920. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(a (b (^z.z)))) 3. ==[ beta ]==> (b (a (b (^z.z)))) 4. ==[ alpha ]==> (b (a (b (^x.x)))) REDUCED to normal form. ------ 196669/23401983. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.y) c)) 3. ==[ beta ]==> ((((a a)(^x.x)) b) c) REDUCED to normal form. ------ 196670/23402028. ------ 1. ==[ start ]==> (((^a.a)(b a))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))((b a)(a (a a)))) 3. ==[ beta ]==> ((b a)((b a)(a (a a)))) REDUCED to normal form. ------ 196671/23402055. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 196672/23402109. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a b)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a b)(a b))) 3. ==[ beta ]==> (((a b)(a b))((a b)(a b))) REDUCED to normal form. ------ 196673/23402190. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a (a a))(b a))) 3. ==[ beta ]==> (b ((a (a a))(b a))) REDUCED to normal form. ------ 196674/23402316. ------ 1. ==[ start ]==> (((a a)(b a))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(b a))((^x.(a a))(a a))) 3. ==[ beta ]==> (((a a)(b a))(a a)) REDUCED to normal form. ------ 196675/23402343. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 196676/23402370. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((a (a a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 196677/23402451. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(a a))((a a) a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a a)) REDUCED to normal form. ------ 196678/23402478. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.b)(a b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.b)(a b))) 3. ==[ beta ]==> (((a b)(a (a a))) b) REDUCED to normal form. ------ 196679/23402532. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 196680/23402577. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196681/23402586. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) a) REDUCED to normal form. ------ 196682/23402973. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))(b ((^z.z) b))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))(b ((^z.z) b))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b ((^z.z) b))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))(b ((^z.z) b))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b ((^y.y) b))) 7. ==[ beta ]==> (((a a)(a a))(b ((^y.y) b))) 8. ==[ alpha ]==> (((a a)(a a))(b ((^x.x) b))) 9. ==[ beta ]==> (((a a)(a a))(b b)) REDUCED to normal form. ------ 196683/23403009. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(a a)) a)) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a)) a)) 5. ==[ beta ]==> ((^y.b)((^z.(a a)) a)) 6. ==[ alpha ]==> ((^x.b)((^y.(a a)) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 196684/23403054. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (^z.z)))) REDUCED to normal form. ------ 196685/23403063. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 196686/23403162. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a b)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196687/23403189. ------ 1. ==[ start ]==> ((a (^b.b))(((a a) a)(a b))) 2. ==[ alpha ]==> ((a (^x.x))(((a a) a)(a b))) REDUCED to normal form. ------ 196688/23403315. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(b (^z.z))) 3. ==[ beta ]==> (((^y.y)(a b))(b (^z.z))) 4. ==[ alpha ]==> (((^x.x)(a b))(b (^y.y))) 5. ==[ beta ]==> ((a b)(b (^y.y))) 6. ==[ alpha ]==> ((a b)(b (^x.x))) REDUCED to normal form. ------ 196689/23403369. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((^b.b)(a a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((^z.z)(a a))) 3. ==[ beta ]==> (((a b)(^y.y))((^z.z)(a a))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(a a))) 5. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 196690/23403396. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (a a)))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 196691/23403468. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196692/23403477. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a a)) REDUCED to normal form. ------ 196693/23403504. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.b)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.b)((a a) a))) 3. ==[ beta ]==> ((a b)((^y.b)((a a) a))) 4. ==[ alpha ]==> ((a b)((^x.b)((a a) a))) 5. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 196694/23403999. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(a ((^y.y) b))) 3. ==[ beta ]==> (b (a ((^y.y) b))) 4. ==[ alpha ]==> (b (a ((^x.x) b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 196695/23404008. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.b) a)) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y) a)) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 196696/23404035. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) b)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) b)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 196697/23404107. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((^y1.y1)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196698/23404287. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(a a))(b (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((^x.x)(a a))(b (^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(b (^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 196699/23404314. ------ 1. ==[ start ]==> ((((a a) a)(a b))(a (^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a b))(a (^x.x))) REDUCED to normal form. ------ 196700/23404341. ------ 1. ==[ start ]==> (((a b)((a a) a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a b)((a a) a))((^x.(^y.(^z.z)))(a a))) 3. ==[ beta ]==> (((a b)((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 196701/23404449. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z))) b) REDUCED to normal form. ------ 196702/23404476. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.a)((a a) a))) 3. ==[ beta ]==> ((b (a a))((^y.a)((a a) a))) 4. ==[ alpha ]==> ((b (a a))((^x.a)((a a) a))) 5. ==[ beta ]==> ((b (a a)) a) REDUCED to normal form. ------ 196703/23404503. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))(a b))) 3. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 196704/23404890. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(b (b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(b (b a))) 3. ==[ beta ]==> ((^y.y)(b (b a))) 4. ==[ alpha ]==> ((^x.x)(b (b a))) 5. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 196705/23404926. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2))) a)) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.(^x2.x2))) a)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.(^z1.z1))) a)) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 196706/23404944. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((b a)(a a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((b a)(a a))) 3. ==[ beta ]==> (((b a)(b a))((b a)(a a))) REDUCED to normal form. ------ 196707/23405025. ------ 1. ==[ start ]==> (((^a.b)(a b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a b))((a b)(a (a a)))) 3. ==[ beta ]==> (b ((a b)(a (a a)))) REDUCED to normal form. ------ 196708/23405133. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1) a)((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1) a)((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196709/23405259. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 6. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 196710/23405286. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 196711/23405313. ------ 1. ==[ start ]==> (((a (a a))(b a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.b)(a (a a)))) 3. ==[ beta ]==> (((a (a a))(b a)) b) REDUCED to normal form. ------ 196712/23405367. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> ((((a a) a)(a a))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(a a))(^x.x)) REDUCED to normal form. ------ 196713/23405394. ------ 1. ==[ start ]==> (((a b)(a b))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(x x))(a b))) 3. ==[ beta ]==> (((a b)(a b))((a b)(a b))) REDUCED to normal form. ------ 196714/23405421. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)((a a) a)) a) REDUCED to normal form. ------ 196715/23405448. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 196716/23405529. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 196717/23405556. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(a a))(^y.a))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(a a)) REDUCED to normal form. ------ 196718/23405583. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.b)(^z.(z z)))) 3. ==[ beta ]==> ((a (b (^x.x))) b) REDUCED to normal form. ------ 196719/23405754. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(a (b a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(a (b a))) 3. ==[ beta ]==> (b (a (b a))) REDUCED to normal form. ------ 196720/23405862. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196721/23405970. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((b (^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 196722/23405997. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> ((^y.y)((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((^x.x)((a a)((a a)(^y.y)))) 5. ==[ beta ]==> ((a a)((a a)(^y.y))) 6. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 196723/23406033. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 196724/23406060. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1)(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 196725/23406141. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.(a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 196726/23406168. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a (a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^y.b))((a (a a))(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((a (a a))(^y.a))) REDUCED to normal form. ------ 196727/23406276. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((a a)(^z.z)) a)) 3. ==[ beta ]==> ((b (^y.a))(((a a)(^z.z)) a)) 4. ==[ alpha ]==> ((b (^x.a))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 196728/23406303. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((a a) b)) REDUCED to normal form. ------ 196729/23406366. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(b (^x.x))) a) REDUCED to normal form. ------ 196730/23406393. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.y)) REDUCED to normal form. ------ 196731/23406420. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((a b)((^y.(y y))(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.(x x))(^y.a))) 7. ==[ beta ]==> ((a b)((^y.a)(^y.a))) 8. ==[ alpha ]==> ((a b)((^x.a)(^y.a))) 9. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 196732/23406447. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 196733/23406474. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 196734/23407158. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))(b (a b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))(b (a b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(b (a b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(b (a b))) 5. ==[ beta ]==> ((^y.y)(b (a b))) 6. ==[ alpha ]==> ((^x.x)(b (a b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 196735/23407185. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(a ((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)(a ((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(a a)))) 5. ==[ beta ]==> (a ((^y.y)(a a))) 6. ==[ alpha ]==> (a ((^x.x)(a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 196736/23407239. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(((a a) a)(a (^z.z)))) 5. ==[ beta ]==> ((b ((^y.y) b))(((a a) a)(a (^z.z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(((a a) a)(a (^y.y)))) 7. ==[ beta ]==> ((b b)(((a a) a)(a (^y.y)))) 8. ==[ alpha ]==> ((b b)(((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 196737/23407248. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^c.a) c)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a) c)) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 196738/23407320. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (a ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (a ((^x.x)(^y.y)))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 196739/23407437. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a) a)(^y1.(^z1.z1)))) REDUCED to normal form. ------ 196740/23407464. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> ((b (^x.(x x)))((^z.z)(^x1.a))) 6. ==[ alpha ]==> ((b (^x.(x x)))((^y.y)(^z.a))) 7. ==[ beta ]==> ((b (^x.(x x)))(^z.a)) 8. ==[ alpha ]==> ((b (^x.(x x)))(^y.a)) REDUCED to normal form. ------ 196741/23407491. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 196742/23407581. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.a)(a b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.z)(a b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a b))) 5. ==[ beta ]==> (((a a)(^x.x))(a b)) REDUCED to normal form. ------ 196743/23407608. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.b)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) b) REDUCED to normal form. ------ 196744/23407662. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 196745/23407689. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(x1 x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(x1 x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.(x1 x1))(^x1.(x1 x1)))) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(z z))(^x1.(x1 x1)))) IRREDUCIBLE: cycle. ------ 196746/23407716. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 196747/23407743. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 196748/23407770. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.z)(^x1.b))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.z)(^x1.b))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.y)(^z.b))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^z.b))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.b))) 7. ==[ beta ]==> (((a a)(a a))(^y.b)) 8. ==[ alpha ]==> (((a a)(a a))(^x.b)) REDUCED to normal form. ------ 196749/23407959. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(a (^a.b))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(a (^z.b))) 3. ==[ beta ]==> (((^y.y)(a a))(a (^z.b))) 4. ==[ alpha ]==> (((^x.x)(a a))(a (^y.b))) 5. ==[ beta ]==> ((a a)(a (^y.b))) 6. ==[ alpha ]==> ((a a)(a (^x.b))) REDUCED to normal form. ------ 196750/23407977. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((a a) a)(^z.z))) 3. ==[ beta ]==> ((a (^y.y))(((a a) a)(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))(((a a) a)(^y.y))) REDUCED to normal form. ------ 196751/23408400. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (^x1.x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (a a)))) 7. ==[ beta ]==> ((a (^y.y))(a (a a))) 8. ==[ alpha ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 196752/23408427. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a (^x.x)))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 196753/23408544. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(z z)))) 7. ==[ beta ]==> ((a (^y.y))(^z.(z z))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(y y))) REDUCED to normal form. ------ 196754/23408571. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 196755/23408652. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z) a) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a c)) REDUCED to normal form. ------ 196756/23408697. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(b (a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196757/23408733. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1)) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 196758/23408760. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(y y)) b)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(b b)) REDUCED to normal form. ------ 196759/23408832. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(a (a a)))) REDUCED to normal form. ------ 196760/23408877. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(y y))(a a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))((a a)(a a))) REDUCED to normal form. ------ 196761/23408904. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 196762/23408931. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 196763/23408958. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.x)(a (a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 196764/23408985. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(x1 x1))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(x1 x1))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(z z))(^x1.x1))) 5. ==[ beta ]==> (((^y.y) b)((^z.(z z))(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(^z.z))) 7. ==[ beta ]==> (b ((^y.(y y))(^z.z))) 8. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 9. ==[ beta ]==> (b ((^y.y)(^y.y))) 10. ==[ alpha ]==> (b ((^x.x)(^y.y))) 11. ==[ beta ]==> (b (^y.y)) 12. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196765/23409012. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 196766/23409039. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 196767/23409066. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.(z z))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(y y))) REDUCED to normal form. ------ 196768/23409147. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b (^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b (^z.a))) REDUCED to normal form. ------ 196769/23409174. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a (^z.(z z)))) 5. ==[ beta ]==> ((b (^y.y))(a (^z.(z z)))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 196770/23409201. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.a)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a))) a) REDUCED to normal form. ------ 196771/23409255. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z) a))) 7. ==[ beta ]==> ((a (^x.x))((^z.z) a)) 8. ==[ alpha ]==> ((a (^x.x))((^y.y) a)) 9. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 196772/23409273. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(((^z.z) a) a)) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a) a)) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a) a)) 5. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 196773/23409282. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.a)(^z.z))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a)) a) REDUCED to normal form. ------ 196774/23409309. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 196775/23409318. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (a (^x1.x1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196776/23409345. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(a ((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)(a ((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y) a))) 5. ==[ beta ]==> (a ((^y.y) a)) 6. ==[ alpha ]==> (a ((^x.x) a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196777/23409480. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a c)) 3. ==[ beta ]==> (b (a c)) REDUCED to normal form. ------ 196778/23409588. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(b a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(b a)) 3. ==[ beta ]==> ((^y.(^z.z))(b a)) 4. ==[ alpha ]==> ((^x.(^y.y))(b a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196779/23410500. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196780/23420706. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 196781/23421624. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196782/23421786. ------ 1. ==[ start ]==> ((^a.(^b.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196783/23421897. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 196784/23421906. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) b)(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 196785/23422353. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196786/23422356. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 196787/23422479. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196788/23423229. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 196789/23423634. ------ 1. ==[ start ]==> (((a a)(^a.b))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.b))(^y.((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(^x.b))(^y.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 196790/23423652. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(z (^x1.x1))))) 5. ==[ beta ]==> (^y.(^z.(z (^x1.x1)))) 6. ==[ alpha ]==> (^x.(^y.(y (^z.z)))) REDUCED to normal form. ------ 196791/23424057. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (^y.((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> (^x.((^y.(^z.z)) a)) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196792/23426286. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((^x1.x1) a)(^y1.(^z1.(^x2.x2))))(^y.(^z.z))) 4. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 5. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 196793/23426712. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.((x1 x1)(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.((z z)(z z)))) 5. ==[ beta ]==> ((^y.b)(^z.((z z)(z z)))) 6. ==[ alpha ]==> ((^x.b)(^y.((y y)(y y)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 196794/23427204. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a b)(^c.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a b)(^z.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 196795/23427378. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((^x.b)(^y.a))(^x1.x1)) 4. ==[ alpha ]==> (((^x.b)(^y.a))(^z.z)) 5. ==[ beta ]==> (b (^z.z)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196796/23427702. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(^y.(^z.z))) 3. ==[ beta ]==> (b (^y.(^z.z))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196797/23427711. ------ 1. ==[ start ]==> (((a b)(^c.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.a))(^y.b)) REDUCED to normal form. ------ 196798/23428203. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y)(^z.z))(^x1.b))) 3. ==[ beta ]==> (((((^y.y)(^z.z))(^x1.b))(((^y.y)(^z.z))(^x1.b)))((((^y.y)(^z.z))(^x1.b))(((^y.y)(^z.z))(^x1.b)))) 4. ==[ alpha ]==> (((((^x.x)(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(^z1.b)))((((^x2.x2)(^y2.y2))(^z2.b))(((^x3.x3)(^y3.y3))(^z3.b)))) 5. ==[ beta ]==> ((((^y.y)(^z.b))(((^x1.x1)(^y1.y1))(^z1.b)))((((^x2.x2)(^y2.y2))(^z2.b))(((^x3.x3)(^y3.y3))(^z3.b)))) 6. ==[ alpha ]==> ((((^x.x)(^y.b))(((^z.z)(^x1.x1))(^y1.b)))((((^z1.z1)(^x2.x2))(^y2.b))(((^z2.z2)(^x3.x3))(^y3.b)))) 7. ==[ beta ]==> (((^y.b)(((^z.z)(^x1.x1))(^y1.b)))((((^z1.z1)(^x2.x2))(^y2.b))(((^z2.z2)(^x3.x3))(^y3.b)))) 8. ==[ alpha ]==> (((^x.b)(((^y.y)(^z.z))(^x1.b)))((((^y1.y1)(^z1.z1))(^x2.b))(((^y2.y2)(^z2.z2))(^x3.b)))) 9. ==[ beta ]==> (b ((((^y1.y1)(^z1.z1))(^x2.b))(((^y2.y2)(^z2.z2))(^x3.b)))) 10. ==[ alpha ]==> (b ((((^x.x)(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(^z1.b)))) 11. ==[ beta ]==> (b (((^y.y)(^z.b))(((^x1.x1)(^y1.y1))(^z1.b)))) 12. ==[ alpha ]==> (b (((^x.x)(^y.b))(((^z.z)(^x1.x1))(^y1.b)))) 13. ==[ beta ]==> (b ((^y.b)(((^z.z)(^x1.x1))(^y1.b)))) 14. ==[ alpha ]==> (b ((^x.b)(((^y.y)(^z.z))(^x1.b)))) 15. ==[ beta ]==> (b b) REDUCED to normal form. ------ 196799/23428629. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(y1 (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.(y1 (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(x1 (^y1.(^z1.z1))))) REDUCED to normal form. ------ 196800/23430888. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(a a)))) 5. ==[ beta ]==> (^y.(^z.(a a))) 6. ==[ alpha ]==> (^x.(^y.(a a))) REDUCED to normal form. ------ 196801/23431086. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(^c.(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(^z.(a b))) REDUCED to normal form. ------ 196802/23431263. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 196803/23431686. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((a a) a)(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^z.z))((((a a) a)(^z.z))(^y.y))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((((a a) a)(^y.y))(^z.z))) REDUCED to normal form. ------ 196804/23432292. ------ 1. ==[ start ]==> (((^a.b)(b a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (^y.((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196805/23432436. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^z.(^y1.y1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 196806/23432559. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 196807/23432562. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 196808/23433009. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a (^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196809/23433048. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.y)(^y1.(^z1.a))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 5. ==[ beta ]==> (^y.(^z.a)) 6. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 196810/23433183. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> (b (^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 196811/23433291. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^a.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196812/23433456. ------ 1. ==[ start ]==> (((^a.a)(a a))((^b.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.a))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.a))) 5. ==[ beta ]==> ((a a)(^y.a)) 6. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 196813/23433483. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 196814/23433591. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.b)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.b)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 196815/23433645. ------ 1. ==[ start ]==> ((a (^b.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 196816/23433726. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 196817/23433753. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 196818/23433762. ------ 1. ==[ start ]==> (((a (^a.a)) b)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) b)(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.(^z.z)))) REDUCED to normal form. ------ 196819/23433789. ------ 1. ==[ start ]==> ((((^a.a) a) a)((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a) a)((a (a (^y.y)))(a a))) 3. ==[ beta ]==> ((a a)((a (a (^y.y)))(a a))) 4. ==[ alpha ]==> ((a a)((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 196820/23433816. ------ 1. ==[ start ]==> (((a a)(^b.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.a))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.a))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.a))(a (^y.y))) REDUCED to normal form. ------ 196821/23433843. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((b (^x1.x1)) a)) REDUCED to normal form. ------ 196822/23433870. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 196823/23433978. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a a)(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a a)(((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 196824/23434059. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a b)(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a b)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 196825/23434086. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(^y.y))((^z.z) b))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)((^z.z) b))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)((^y.y) b))) 5. ==[ beta ]==> (((a (a a)) a)((^y.y) b)) 6. ==[ alpha ]==> (((a (a a)) a)((^x.x) b)) 7. ==[ beta ]==> (((a (a a)) a) b) REDUCED to normal form. ------ 196826/23434113. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 196827/23434140. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))(a (b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))(a (b (^z.z)))) REDUCED to normal form. ------ 196828/23434167. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.z))(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 196829/23434185. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(b (^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a)(a a))(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 196830/23434194. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 196831/23434212. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 196832/23434230. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 196833/23434257. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x)) a)((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 196834/23434284. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (a (^y.y)))((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 196835/23434311. ------ 1. ==[ start ]==> (((a (a a))(a a))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 196836/23434338. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 196837/23434347. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196838/23434374. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196839/23434482. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(b a))) 5. ==[ beta ]==> ((^y.y)((^z.b)(b a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 7. ==[ beta ]==> ((^y.b)(b a)) 8. ==[ alpha ]==> ((^x.b)(b a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 196840/23434563. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(z z))((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 196841/23434635. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 196842/23434662. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a (a (^y.y))) a)) REDUCED to normal form. ------ 196843/23434689. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> ((a ((^y.y) a))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> ((a ((^x.x) a))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> ((a a)(((^y.(^z.z)) a) b)) 6. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) b)) 7. ==[ beta ]==> ((a a)((^y.y) b)) 8. ==[ alpha ]==> ((a a)((^x.x) b)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 196844/23434716. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((b (^y.y)) c)) REDUCED to normal form. ------ 196845/23434806. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(^y2.a))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))(^y2.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196846/23434860. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 196847/23434968. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196848/23435031. ------ 1. ==[ start ]==> (((a (a a))(^b.a))(c (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))(c (b (^y.y)))) REDUCED to normal form. ------ 196849/23435058. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(b ((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b ((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b ((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.(^z.z))(b ((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((^x.(^y.y))(b ((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196850/23435085. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(a (a (a (^y.y))))) REDUCED to normal form. ------ 196851/23435274. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.b) a)(((a a)(^y.y))(a b))) 3. ==[ beta ]==> (b (((a a)(^y.y))(a b))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a b))) REDUCED to normal form. ------ 196852/23435436. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a) b)(a ((a a)(a a)))) REDUCED to normal form. ------ 196853/23435454. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (b (c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (c (^x.(^y.y)))) REDUCED to normal form. ------ 196854/23435463. ------ 1. ==[ start ]==> (((a b) a)((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a b) a)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 196855/23435490. ------ 1. ==[ start ]==> (((a a)(^a.b))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.b))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(^x.b))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.y))) REDUCED to normal form. ------ 196856/23435508. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(a (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(a (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(a (^y.(y (^z.z))))) 5. ==[ beta ]==> (a (^y.(y (^z.z)))) 6. ==[ alpha ]==> (a (^x.(x (^y.y)))) REDUCED to normal form. ------ 196857/23435643. ------ 1. ==[ start ]==> (((^a.b)(a a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196858/23435688. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(a b))(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 196859/23435715. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))((a a)(^y.(a a)))) REDUCED to normal form. ------ 196860/23435742. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 196861/23435796. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (a (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> (a (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 9. ==[ beta ]==> (a ((^y.y)(^z.(^x1.(^y1.y1))))) 10. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 11. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 12. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 196862/23435823. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 196863/23435850. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x) a)(^y.(a a)))) 3. ==[ beta ]==> (((a b)(a a))(a (^y.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(a (^x.(a a)))) REDUCED to normal form. ------ 196864/23435886. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196865/23435913. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 7. ==[ beta ]==> ((^y.(^z.z)) a) 8. ==[ alpha ]==> ((^x.(^y.y)) a) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196866/23436048. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196867/23436129. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(a a))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196868/23436264. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196869/23436273. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c ((a a)(a a)))) REDUCED to normal form. ------ 196870/23436300. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))(b (b (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (b (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (b (^y.y)))) REDUCED to normal form. ------ 196871/23436489. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b) c)(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> (b (((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 196872/23436804. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y) a)) 7. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 196873/23436831. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196874/23436966. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196875/23437119. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((b (^y.y)) a)) 3. ==[ beta ]==> ((a (a b))((b (^y.y)) a)) 4. ==[ alpha ]==> ((a (a b))((b (^x.x)) a)) REDUCED to normal form. ------ 196876/23437146. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((a a)(a a)) b)) REDUCED to normal form. ------ 196877/23437173. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((^y1.y1) b) c)) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((^y1.y1) b) c)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((^x1.x1) b) c)) 5. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) b) c)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) b) c)) 7. ==[ beta ]==> ((^y.y)(((^z.z) b) c)) 8. ==[ alpha ]==> ((^x.x)(((^y.y) b) c)) 9. ==[ beta ]==> (((^y.y) b) c) 10. ==[ alpha ]==> (((^x.x) b) c) 11. ==[ beta ]==> (b c) REDUCED to normal form. ------ 196878/23437398. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (b ((^z.(z z))(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 9. ==[ beta ]==> (b (^y.(^z.z))) 10. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196879/23437542. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(b (a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(b (a (^y.y)))) REDUCED to normal form. ------ 196880/23437650. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z)(a a))((a a) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y)(a a))((a a) a))) 5. ==[ beta ]==> ((a (^x.(a a)))((a a)((a a) a))) REDUCED to normal form. ------ 196881/23437677. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a b)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a b)(a b))) REDUCED to normal form. ------ 196882/23437731. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)((a a)(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 196883/23437758. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a (a a))(b a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a (a a))(b a))) REDUCED to normal form. ------ 196884/23437785. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.a))(a (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(^x.a))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 196885/23437812. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (^x1.x1)) b)) REDUCED to normal form. ------ 196886/23437875. ------ 1. ==[ start ]==> (((a a)(b a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(b a))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 196887/23437902. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 196888/23437929. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(^x1.a))) 6. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 196889/23437956. ------ 1. ==[ start ]==> (((a (a a))(a b))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((b a)(^x.(x x)))) REDUCED to normal form. ------ 196890/23437983. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 196891/23438037. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a b)(^a.b))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a b)(^x.b))) REDUCED to normal form. ------ 196892/23438064. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((a a) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((a a) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((a a) a)(^y.(a a)))) 5. ==[ beta ]==> (((a a) a)(((a a) a)(^y.(a a)))) 6. ==[ alpha ]==> (((a a) a)(((a a) a)(^x.(a a)))) REDUCED to normal form. ------ 196893/23438145. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 196894/23438154. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(a (^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196895/23438235. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> ((a a)((^z.(a a))(^x1.x1))) 6. ==[ alpha ]==> ((a a)((^x.(a a))(^y.y))) 7. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 196896/23438451. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 196897/23438532. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.x1))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.z))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 196898/23438541. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(b ((^y.y) b))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(b b)) REDUCED to normal form. ------ 196899/23438568. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(a ((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(a ((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(a ((a a)(a a)))) 5. ==[ beta ]==> ((^y.b)(a ((a a)(a a)))) 6. ==[ alpha ]==> ((^x.b)(a ((a a)(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 196900/23438622. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 196901/23438649. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((b a)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((b a)((^y.y) a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((b a) a)) REDUCED to normal form. ------ 196902/23438676. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 196903/23438730. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a b)((a a) a))) REDUCED to normal form. ------ 196904/23438928. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) b)(^z.z))) 5. ==[ beta ]==> (((a b)(^x.x))(b (^z.z))) 6. ==[ alpha ]==> (((a b)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 196905/23438955. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 196906/23438982. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((b a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((b a)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((b a)(^z.a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((b a)(^y.a))) REDUCED to normal form. ------ 196907/23439036. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 196908/23439063. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a b)(^c.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a b)(^y.a))) 3. ==[ beta ]==> ((a b)((a b)(^y.a))) 4. ==[ alpha ]==> ((a b)((a b)(^x.a))) REDUCED to normal form. ------ 196909/23439072. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z.b)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((a a) a))) 5. ==[ beta ]==> ((^y.b)((a a) a)) 6. ==[ alpha ]==> ((^x.b)((a a) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 196910/23439234. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (b ((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y) b))) 5. ==[ beta ]==> (b ((^y.y) b)) 6. ==[ alpha ]==> (b ((^x.x) b)) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 196911/23439396. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.b)(^z.a))) 5. ==[ beta ]==> (b ((^y.b)(^z.a))) 6. ==[ alpha ]==> (b ((^x.b)(^y.a))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 196912/23439513. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))(c (b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))(c (b a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))(c (b a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))(c (b a))) 5. ==[ beta ]==> ((^y.(a a))(c (b a))) 6. ==[ alpha ]==> ((^x.(a a))(c (b a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 196913/23439540. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 196914/23439558. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.y)(^z.z))) 3. ==[ beta ]==> (b ((^y.y)(^z.z))) 4. ==[ alpha ]==> (b ((^x.x)(^y.y))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196915/23439567. ------ 1. ==[ start ]==> (((a b)(^c.a))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.a))(a ((^y.y) b))) 3. ==[ beta ]==> (((a b)(^x.a))(a b)) REDUCED to normal form. ------ 196916/23439594. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a (^x1.(^y1.y1)))(a a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a (^x1.(^y1.y1)))(a a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 196917/23439621. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((b a)(a (^z.z)))) REDUCED to normal form. ------ 196918/23439675. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(a (a a)))) REDUCED to normal form. ------ 196919/23439702. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.y))((a b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.x))((a b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (^x.x))((a b)(^z.z))) 6. ==[ alpha ]==> ((b (^x.x))((a b)(^y.y))) REDUCED to normal form. ------ 196920/23439900. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 196921/23439927. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((b a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((b a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((b a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 196922/23439954. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 196923/23440008. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a b)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 196924/23440035. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a) a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a) a)(^y.a))) 3. ==[ beta ]==> ((b (a a))(((a a) a)(^y.a))) 4. ==[ alpha ]==> ((b (a a))(((a a) a)(^x.a))) REDUCED to normal form. ------ 196925/23440062. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(^y.y))(^z.b))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(^z.b))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(^y.b))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.b)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.b)) REDUCED to normal form. ------ 196926/23440098. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.z)(a a))) 6. ==[ alpha ]==> ((^x.(x x))((^y.y)(a a))) 7. ==[ beta ]==> (((^y.y)(a a))((^y.y)(a a))) 8. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a a))) 9. ==[ beta ]==> ((a a)((^y.y)(a a))) 10. ==[ alpha ]==> ((a a)((^x.x)(a a))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 196927/23440341. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.a)(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.a)(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196928/23440422. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 196929/23440458. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(b (b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (b a))) REDUCED to normal form. ------ 196930/23440485. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(a (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(a (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 196931/23440566. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((a a)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(^x.(a a)))((a a) a)) REDUCED to normal form. ------ 196932/23440593. ------ 1. ==[ start ]==> (((a b)(^a.b))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.b))((a b)(a (a a)))) REDUCED to normal form. ------ 196933/23440647. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a) a)) REDUCED to normal form. ------ 196934/23440701. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a ((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(a ((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(a (a a))) REDUCED to normal form. ------ 196935/23440728. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 196936/23440755. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a a)(b a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a a)(b a))) REDUCED to normal form. ------ 196937/23440791. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((b a)(^a.a))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((b a)(^x.x))) REDUCED to normal form. ------ 196938/23440818. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 196939/23440845. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> ((a (a (^x.(^y.y))))((a a)(^x1.a))) 6. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(^z.a))) REDUCED to normal form. ------ 196940/23440872. ------ 1. ==[ start ]==> (((a (a a))(b a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 196941/23440899. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 196942/23440953. ------ 1. ==[ start ]==> (((a b)(a b))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(a b))((a (a a))(^x.b))) REDUCED to normal form. ------ 196943/23440980. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((^y.y) a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)((a a) a))(((^y.y) a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))(((^x.x) a)(^y.(a a)))) 5. ==[ beta ]==> (((a a)((a a) a))(a (^y.(a a)))) 6. ==[ alpha ]==> (((a a)((a a) a))(a (^x.(a a)))) REDUCED to normal form. ------ 196944/23441061. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((b a) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((b a) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((b a) a)) REDUCED to normal form. ------ 196945/23441088. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((a a)(^z.z)) b)) 3. ==[ beta ]==> ((b (a (^y.y)))(((a a)(^z.z)) b)) 4. ==[ alpha ]==> ((b (a (^x.x)))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 196946/23441232. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.b))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(x2 x2))(^y2.b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(x2 x2))(^y2.b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196947/23441457. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b c)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b c)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b c)((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((b c)((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((b c)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((b c)((^x.x)(^y.y))) 9. ==[ beta ]==> ((b c)(^y.y)) 10. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 196948/23441484. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a (a a))((a a) a))) REDUCED to normal form. ------ 196949/23441529. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(c (^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(c (^z.(a a)))) 3. ==[ beta ]==> ((b (^y.y))(c (^z.(a a)))) 4. ==[ alpha ]==> ((b (^x.x))(c (^y.(a a)))) REDUCED to normal form. ------ 196950/23441556. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 196951/23441691. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.a)(a (a a)))) 3. ==[ beta ]==> (b ((^z.a)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.a)(a (a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196952/23441799. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196953/23442087. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^c.(^a.a)) a)) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 196954/23442114. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(a a)) b)) 3. ==[ beta ]==> (((a a)(a b))((^y.(a a)) b)) 4. ==[ alpha ]==> (((a a)(a b))((^x.(a a)) b)) 5. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 196955/23442141. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.b) c)) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) b) REDUCED to normal form. ------ 196956/23442393. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) a))) 7. ==[ beta ]==> ((^y.a)((^z.z) a)) 8. ==[ alpha ]==> ((^x.a)((^y.y) a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 196957/23442474. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)((a a) a))) 3. ==[ beta ]==> (b ((^x1.a)((a a) a))) 4. ==[ alpha ]==> (b ((^x.a)((a a) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 196958/23442582. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.b)(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b)(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196959/23442717. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196960/23442744. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(a a)))) 5. ==[ beta ]==> ((^y.y)(^z.(a a))) 6. ==[ alpha ]==> ((^x.x)(^y.(a a))) 7. ==[ beta ]==> (^y.(a a)) 8. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 196961/23442807. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 196962/23442834. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))((^y2.y2) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))((^y2.y2) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((^x2.x2) a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))((^x2.x2) a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 196963/23442888. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 196964/23442915. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 196965/23442942. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a a)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a a)(a b))) REDUCED to normal form. ------ 196966/23442987. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((^z1.b)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196967/23443122. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 196968/23443140. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a a)(^a.b))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a a)(^z.b))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(^z.b))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.b))) REDUCED to normal form. ------ 196969/23443167. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a b) a)) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a b) a)) REDUCED to normal form. ------ 196970/23443194. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((a a) a) b)) 3. ==[ beta ]==> ((a ((a a)(a a)))(((a a) a) b)) REDUCED to normal form. ------ 196971/23443221. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> (((a (a a)) b)(((^y.y)(^z.z)) c)) 4. ==[ alpha ]==> (((a (a a)) b)(((^x.x)(^y.y)) c)) 5. ==[ beta ]==> (((a (a a)) b)((^y.y) c)) 6. ==[ alpha ]==> (((a (a a)) b)((^x.x) c)) 7. ==[ beta ]==> (((a (a a)) b) c) REDUCED to normal form. ------ 196972/23443356. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.b) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) b) REDUCED to normal form. ------ 196973/23443410. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.(^z1.z1)) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.(^z1.z1)) c)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.(^y1.y1)) c)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.y1)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.x1)) REDUCED to normal form. ------ 196974/23443545. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((a a) a)(^a.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((a a) a)(^y.y))) REDUCED to normal form. ------ 196975/23443941. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (b (((^y.y) a)((^z.z) a))) 6. ==[ alpha ]==> (b (((^x.x) a)((^y.y) a))) 7. ==[ beta ]==> (b (a ((^y.y) a))) 8. ==[ alpha ]==> (b (a ((^x.x) a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 196976/23443968. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 196977/23443986. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(^z.z)))) REDUCED to normal form. ------ 196978/23443995. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((a a)(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 196979/23444067. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 196980/23444103. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(c d)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(c d)) 3. ==[ beta ]==> (((^y.y)(^z.z))(c d)) 4. ==[ alpha ]==> (((^x.x)(^y.y))(c d)) 5. ==[ beta ]==> ((^y.y)(c d)) 6. ==[ alpha ]==> ((^x.x)(c d)) 7. ==[ beta ]==> (c d) REDUCED to normal form. ------ 196981/23444148. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.y)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 196982/23444256. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196983/23444292. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 196984/23444319. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (a a))(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (a a))(a a))) REDUCED to normal form. ------ 196985/23444373. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 196986/23444391. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b (^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 196987/23444400. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a a)(a (a a)))) REDUCED to normal form. ------ 196988/23444418. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 196989/23444436. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (a a))(^y.y))) REDUCED to normal form. ------ 196990/23444463. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 196991/23444490. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))(^z.a))) REDUCED to normal form. ------ 196992/23444517. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a a)(^x.(x x)))) REDUCED to normal form. ------ 196993/23444544. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (a a)) a)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (a a)) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (a a)) a)) 5. ==[ beta ]==> (((^y.y) b)((a (a a)) a)) 6. ==[ alpha ]==> (((^x.x) b)((a (a a)) a)) 7. ==[ beta ]==> (b ((a (a a)) a)) REDUCED to normal form. ------ 196994/23444571. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(((^z.z) a) b)) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a b)) REDUCED to normal form. ------ 196995/23444598. ------ 1. ==[ start ]==> (((a b)(b a))((a (^a.a)) c)) 2. ==[ alpha ]==> (((a b)(b a))((a (^x.x)) c)) REDUCED to normal form. ------ 196996/23444652. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(z z)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(z z)) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(y y)) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a a)) REDUCED to normal form. ------ 196997/23444760. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(((^x.x) a)(^y.y))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(a (^y.y))) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 196998/23444814. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a a)(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a a)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)(^z.a))) 5. ==[ beta ]==> ((a (^y.y))((a a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 196999/23444841. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(((^a.a) a) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(((^y.y) a) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(a a)) REDUCED to normal form. ------ 197000/23444868. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a (^x1.x1)) b)) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1)) b)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 197001/23444877. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197002/23444904. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.y1)(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 197003/23445039. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> (b ((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 197004/23445147. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(a (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(a (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197005/23457483. ------ 1. ==[ start ]==> (((a (^a.a)) b)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 197006/23457705. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((^z.z)(a a)))((((a a)(^y.y))((^z.z)(a a)))(((a a)(^y.y))((^z.z)(a a))))) 4. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((((a a)(^z.z))((^x1.x1)(a a)))(((a a)(^y1.y1))((^z1.z1)(a a))))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))((((a a)(^z.z))((^x1.x1)(a a)))(((a a)(^y1.y1))((^z1.z1)(a a))))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))((((a a)(^y.y))((^z.z)(a a)))(((a a)(^x1.x1))((^y1.y1)(a a))))) 7. ==[ beta ]==> ((((a a)(^x.x))(a a))((((a a)(^y.y))(a a))(((a a)(^x1.x1))((^y1.y1)(a a))))) 8. ==[ alpha ]==> ((((a a)(^x.x))(a a))((((a a)(^y.y))(a a))(((a a)(^z.z))((^x1.x1)(a a))))) 9. ==[ beta ]==> ((((a a)(^x.x))(a a))((((a a)(^y.y))(a a))(((a a)(^z.z))(a a)))) REDUCED to normal form. ------ 197007/23458806. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 197008/23458821. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(z (^x1.x1))) a)) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197009/23459001. ------ 1. ==[ start ]==> ((^a.(a b))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((^x.(x b))(((a a)(^y.y))(a b))) 3. ==[ beta ]==> ((((a a)(^y.y))(a b)) b) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b)) b) REDUCED to normal form. ------ 197010/23459388. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b a)(^z.a))) 3. ==[ beta ]==> (^y.(((b a)(^z.a))((b a)(^z.a)))) 4. ==[ alpha ]==> (^x.(((b a)(^y.a))((b a)(^z.a)))) REDUCED to normal form. ------ 197011/23460057. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a a)((^x.x)(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(^y.(^z.z))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 197012/23460270. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a b)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a b)((^z.z)(a a)))((a b)((^z.z)(a a))))(^y.y)) 4. ==[ alpha ]==> ((((a b)((^x.x)(a a)))((a b)((^y.y)(a a))))(^z.z)) 5. ==[ beta ]==> ((((a b)(a a))((a b)((^y.y)(a a))))(^z.z)) 6. ==[ alpha ]==> ((((a b)(a a))((a b)((^x.x)(a a))))(^y.y)) 7. ==[ beta ]==> ((((a b)(a a))((a b)(a a)))(^y.y)) 8. ==[ alpha ]==> ((((a b)(a a))((a b)(a a)))(^x.x)) REDUCED to normal form. ------ 197013/23462289. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))(^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(^z.(^x1.(a a)))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 197014/23462955. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(^c.(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(^x1.x1))) 3. ==[ beta ]==> (b (^z.(^x1.x1))) 4. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 197015/23463288. ------ 1. ==[ start ]==> (((a b)(^c.a))(^b.(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 197016/23463594. ------ 1. ==[ start ]==> ((((a a) a)(a b))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 197017/23464206. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 197018/23465556. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 197019/23465808. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.((y y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a a))(^y.((y y)(^z.z)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 197020/23466021. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a a)((^x1.x1)(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))((a a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197021/23467077. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^a.(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(y b))) REDUCED to normal form. ------ 197022/23467257. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(^z.(^x1.b))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.b))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.b))) REDUCED to normal form. ------ 197023/23467869. ------ 1. ==[ start ]==> (((^a.b)(b a))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197024/23468013. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 197025/23468373. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(z (z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(z (z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(y (y y)))) REDUCED to normal form. ------ 197026/23468454. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((b (^y.y))(^z.((^x1.x1) a))) 6. ==[ alpha ]==> ((b (^x.x))(^y.((^z.z) a))) 7. ==[ beta ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 197027/23468553. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 197028/23468760. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (b (^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197029/23468868. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^b.b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.y1)) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197030/23469051. ------ 1. ==[ start ]==> (((a a)(^a.a))((^b.b)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.a)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 197031/23469078. ------ 1. ==[ start ]==> (((^a.a) b)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.b))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.b))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 197032/23469132. ------ 1. ==[ start ]==> (((a a) b)((^c.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) b)(^y.y)) 4. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 197033/23469186. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 197034/23469348. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 197035/23469393. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> (((^y.y) a)((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> (a ((^y.(y (^z.z))) b)) 6. ==[ alpha ]==> (a ((^x.(x (^y.y))) b)) 7. ==[ beta ]==> (a (b (^y.y))) 8. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 197036/23469492. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)(((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(((^x.x) b)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a) a)(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> (((a a) a)(b (^y.y))) 8. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 197037/23469519. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((a (^z.(^x1.x1)))((a a) a))) REDUCED to normal form. ------ 197038/23469546. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((b a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((b a)(a b))) 3. ==[ beta ]==> ((a (a a))((b a)(a b))) REDUCED to normal form. ------ 197039/23469573. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((a (a (a a)))(((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> ((a (a (a a)))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 197040/23469780. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 197041/23469933. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197042/23470014. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.(a a)))) 5. ==[ beta ]==> ((^y.y)(((a a)(^y1.y1))(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 197043/23470023. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> (((a (a a)) b)(^y.y)) 4. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 197044/23470050. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (a ((^y.(a a))((a a)(^z.z)))) 6. ==[ alpha ]==> (a ((^x.(a a))((a a)(^y.y)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 197045/23470077. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 197046/23470095. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197047/23470131. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 197048/23470158. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 197049/23470185. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)(b (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)(b (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)(b (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(b (^z.z)))) 7. ==[ beta ]==> ((^y.a)(b (^z.z))) 8. ==[ alpha ]==> ((^x.a)(b (^y.y))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 197050/23470482. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 197051/23470563. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 197052/23470671. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 197053/23470689. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.b))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((a (^x.b))(a (^z.z))) 4. ==[ alpha ]==> ((a (^x.b))(a (^y.y))) REDUCED to normal form. ------ 197054/23470707. ------ 1. ==[ start ]==> (((a a)((a a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a a)((a a) a))(((^x.(^y.y)) a)(a a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.y)(a a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(a a))) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 197055/23470734. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((b (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 197056/23470761. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> ((a (a (a a)))(((a a)(a a))((^y.y) a))) 4. ==[ alpha ]==> ((a (a (a a)))(((a a)(a a))((^x.x) a))) 5. ==[ beta ]==> ((a (a (a a)))(((a a)(a a)) a)) REDUCED to normal form. ------ 197057/23470788. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.x) b)(a (a a)))) 5. ==[ beta ]==> (((a (a a)) a)(b (a (a a)))) REDUCED to normal form. ------ 197058/23470815. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> ((a (^x.x))((a (^y.(^z.z)))(^y1.y1))) 8. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 197059/23470842. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b a)((a a) a))) REDUCED to normal form. ------ 197060/23470869. ------ 1. ==[ start ]==> ((a (a b))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> ((a (a b))(((a a)(^x.x))(a b))) REDUCED to normal form. ------ 197061/23471049. ------ 1. ==[ start ]==> (((a b) a)(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) a)(c (^x.(^y.y)))) REDUCED to normal form. ------ 197062/23471148. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 197063/23471184. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> ((^y.a)((^z.(a a))((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.a)((^y.(a a))((^z.z) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 197064/23471211. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 197065/23471229. ------ 1. ==[ start ]==> (((^a.b)(a a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 197066/23471238. ------ 1. ==[ start ]==> (((a b)(^a.a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a b)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 197067/23471256. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((b a)(^y.a))) REDUCED to normal form. ------ 197068/23471427. ------ 1. ==[ start ]==> (((^a.b) b)((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> (b ((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> (b (((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> (b (((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> (b (b ((^y.y) b))) 8. ==[ alpha ]==> (b (b ((^x.x) b))) 9. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 197069/23471553. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b (^x1.x1)) b)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b (^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1)) b)) 5. ==[ beta ]==> ((^y.y)((b (^y1.y1)) b)) 6. ==[ alpha ]==> ((^x.x)((b (^y.y)) b)) 7. ==[ beta ]==> ((b (^y.y)) b) 8. ==[ alpha ]==> ((b (^x.x)) b) REDUCED to normal form. ------ 197070/23471643. ------ 1. ==[ start ]==> (((a b) b)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b) b)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a b) b)(^x.(^y.y))) REDUCED to normal form. ------ 197071/23471697. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 197072/23471724. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(a a)) REDUCED to normal form. ------ 197073/23471778. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 197074/23471805. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((^y.(y y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (((^y.(^z.z))(^x1.(^y1.(^z1.z1))))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 8. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3))))) 9. ==[ beta ]==> ((^y.y)((^z1.(^x2.x2))(^y2.(^z2.(^x3.x3))))) 10. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 11. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197075/23471832. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(y y))(^z.z))) 3. ==[ beta ]==> ((((a a) a)(^x.a))((^z.z)(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.y)(^z.z))) 5. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 197076/23471859. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 197077/23471922. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(a a))(a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a a)(a a))(a ((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a a)(a a))(a (^y.y))) 6. ==[ alpha ]==> (((a a)(a a))(a (^x.x))) REDUCED to normal form. ------ 197078/23471949. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((b (^y.y))(a a))) REDUCED to normal form. ------ 197079/23471976. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> ((a ((a a) a))(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> ((a ((a a) a))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 197080/23472003. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(b ((^z.z) a))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(b ((^y.y) a))) 7. ==[ beta ]==> (((a (a a))(^x.x))(b a)) REDUCED to normal form. ------ 197081/23472030. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((a (^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((a (^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))(a (a a)))) 6. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 197082/23472057. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a) a) a)((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((((a a) a) a)((b a)(^y.y))) 6. ==[ alpha ]==> ((((a a) a) a)((b a)(^x.x))) REDUCED to normal form. ------ 197083/23472084. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 197084/23472111. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(a a))(a b))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(a a))(a b))) 5. ==[ beta ]==> (((a a)(a a))((a a)(a b))) REDUCED to normal form. ------ 197085/23472138. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)((^y.y)(a a)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((a b)(a a))) REDUCED to normal form. ------ 197086/23472390. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (((a a)(^x.x))(b (^z.a))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.a))) REDUCED to normal form. ------ 197087/23472417. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 197088/23472426. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 197089/23472507. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(a a))(a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(a a))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(a b))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197090/23472534. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x))) b) REDUCED to normal form. ------ 197091/23472552. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 197092/23472561. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 197093/23472588. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(b a))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197094/23472615. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a (^x1.(^y1.y1)))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (^z.(^x1.x1)))(a (^y1.(^z1.z1))))) REDUCED to normal form. ------ 197095/23473722. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197096/23473740. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197097/23473821. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((a a)(a a)) a)) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((a a)(a a)) a)) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((a a)(a a)) a)) 5. ==[ beta ]==> ((a a)(((a a)(a a)) a)) REDUCED to normal form. ------ 197098/23474046. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 197099/23474127. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 197100/23474154. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(^z.(a a)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 197101/23474199. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.x1) b)) 3. ==[ beta ]==> (b ((^x1.x1) b)) 4. ==[ alpha ]==> (b ((^x.x) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 197102/23474352. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a) a)(a b))) REDUCED to normal form. ------ 197103/23474379. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((^z.z)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(b a))((^z.z)(a a))) 6. ==[ alpha ]==> (((a (^x.x))(b a))((^y.y)(a a))) 7. ==[ beta ]==> (((a (^x.x))(b a))(a a)) REDUCED to normal form. ------ 197104/23474406. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 197105/23474433. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y) a)(b a))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x) a)(b a))) 5. ==[ beta ]==> (((a (a a))(a a))(a (b a))) REDUCED to normal form. ------ 197106/23474460. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)((a (^y.y))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a b)((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 197107/23474487. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a a)((^x.x) b))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a a) b)) REDUCED to normal form. ------ 197108/23474613. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197109/23474658. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^z.a))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 197110/23474685. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((a a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a)(^z1.b))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^z1.b))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.b))) 5. ==[ beta ]==> (((a a) a)(^y.b)) 6. ==[ alpha ]==> (((a a) a)(^x.b)) REDUCED to normal form. ------ 197111/23474820. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a a)(^z.z))) 3. ==[ beta ]==> (b ((a a)(^z.z))) 4. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 197112/23474937. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 197113/23474964. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b a)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b a)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 197114/23474991. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 197115/23475126. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 197116/23475153. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.y)(^z.z))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 197117/23475324. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((a a) b)(((a a) a)((a a) a))) REDUCED to normal form. ------ 197118/23475351. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((^y1.y1)(a b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((^x1.x1)(a b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(a b)) REDUCED to normal form. ------ 197119/23475378. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> ((a (b a))((a (a a))((^y.y)(a a)))) 4. ==[ alpha ]==> ((a (b a))((a (a a))((^x.x)(a a)))) 5. ==[ beta ]==> ((a (b a))((a (a a))(a a))) REDUCED to normal form. ------ 197120/23475405. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y) a)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a ((a a)(^z.z)))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 197121/23475432. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (^x1.x1))(b a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (^x1.x1))(b a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (^z.z))(b a))) 5. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))(b a))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))(b a))) 7. ==[ beta ]==> ((a a)((a (^y.y))(b a))) 8. ==[ alpha ]==> ((a a)((a (^x.x))(b a))) REDUCED to normal form. ------ 197122/23475459. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 197123/23475684. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a (a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a (a a))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(^y.(a a))) 6. ==[ alpha ]==> ((a (a a))(^x.(a a))) REDUCED to normal form. ------ 197124/23475819. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((b a) b)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((b a) b)) 3. ==[ beta ]==> (b ((b a) b)) REDUCED to normal form. ------ 197125/23475963. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 197126/23475990. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(x x))(^y.(a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(a a))(^y.(a a)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(a a))(^y.(a a)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 197127/23476071. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 197128/23476089. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((b a)(b a))((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (((b a)(b a))((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (((b a)(b a))(^y.(^z.z))) 6. ==[ alpha ]==> (((b a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 197129/23476314. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(c (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 197130/23477196. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((a a)(^y1.y1))(^z1.z1))) REDUCED to normal form. ------ 197131/23477277. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (b (((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> (b (((a a) a)(^x.(x x)))) REDUCED to normal form. ------ 197132/23477286. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.a)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.(a a))) a) REDUCED to normal form. ------ 197133/23477313. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 197134/23477385. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((a (^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197135/23477394. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))((^z1.z1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 197136/23477421. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> ((b (^x.a))((a a)(^z.z))) 6. ==[ alpha ]==> ((b (^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 197137/23477619. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))(c (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))(c (a b))) 3. ==[ beta ]==> (((^y.y)(b a))(c (a b))) 4. ==[ alpha ]==> (((^x.x)(b a))(c (a b))) 5. ==[ beta ]==> ((b a)(c (a b))) REDUCED to normal form. ------ 197138/23477646. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(b (a a))) REDUCED to normal form. ------ 197139/23477673. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(a ((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)(a a))(a ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a b)(a a))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 197140/23477700. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> (((a a)(a b))(((^y.y)(a a))(a a))) 4. ==[ alpha ]==> (((a a)(a b))(((^x.x)(a a))(a a))) 5. ==[ beta ]==> (((a a)(a b))((a a)(a a))) REDUCED to normal form. ------ 197141/23477727. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((a b)(a (^y.y)))) REDUCED to normal form. ------ 197142/23477781. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a (a a))) REDUCED to normal form. ------ 197143/23477808. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)((a (a a))((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((b a)((a (a a))((^x.x)(^y.y)))) 7. ==[ beta ]==> ((b a)((a (a a))(^y.y))) 8. ==[ alpha ]==> ((b a)((a (a a))(^x.x))) REDUCED to normal form. ------ 197144/23477835. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y) a)((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 197145/23477889. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(a a))) REDUCED to normal form. ------ 197146/23477979. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(^z.a))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a)(^z.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.a))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.a))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.a))) 7. ==[ beta ]==> (((a a) a)(^y.a)) 8. ==[ alpha ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 197147/23478060. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> (b (((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 197148/23478168. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a b) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a b) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a b) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197149/23478285. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.a)(^x1.a))) 3. ==[ beta ]==> (((^y.y) a)((^z.a)(^x1.a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.a)(^z.a))) 5. ==[ beta ]==> (a ((^y.a)(^z.a))) 6. ==[ alpha ]==> (a ((^x.a)(^y.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 197150/23478384. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.b) b)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.b) b)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.b) b)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.b) b)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.b) b)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.b) b)) 7. ==[ beta ]==> ((b b)((^y.b) b)) 8. ==[ alpha ]==> ((b b)((^x.b) b)) 9. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 197151/23478474. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(d (^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(d (^z.(^x1.x1)))) REDUCED to normal form. ------ 197152/23478501. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(c (^z.a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(c (^z.a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(c (^y.a))) REDUCED to normal form. ------ 197153/23478528. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(b (^z.b))) REDUCED to normal form. ------ 197154/23478573. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a b)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197155/23478582. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((^a.b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.b)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) b) REDUCED to normal form. ------ 197156/23478609. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((b (^x.(x x))) a) REDUCED to normal form. ------ 197157/23478636. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 197158/23478690. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.a)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.a)((^y.y)(^z.z))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 197159/23478888. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(c (^z.z))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(c (^y.y))) REDUCED to normal form. ------ 197160/23478915. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))(b ((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))(b ((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b ((a a) a))) 5. ==[ beta ]==> (((a a)(a a))(b ((a a) a))) REDUCED to normal form. ------ 197161/23478942. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(a (a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(a (a b))) REDUCED to normal form. ------ 197162/23478996. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((^y1.y1)(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((^y1.y1)(a (^z1.z1)))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(a (^y1.y1)))) 7. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(a (^y1.y1))) 8. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (^x1.x1))) REDUCED to normal form. ------ 197163/23479023. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((a (a a))((^y.y) a))) 3. ==[ beta ]==> ((b (a (a a)))((a (a a))((^y.y) a))) 4. ==[ alpha ]==> ((b (a (a a)))((a (a a))((^x.x) a))) 5. ==[ beta ]==> ((b (a (a a)))((a (a a)) a)) REDUCED to normal form. ------ 197164/23479050. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y) a)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x) a)(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a)) a)(a (a (a a)))) REDUCED to normal form. ------ 197165/23479104. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a a)((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a a)((a a) a))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)((a a) a))) 5. ==[ beta ]==> ((a a)((a a)((a a) a))) REDUCED to normal form. ------ 197166/23479122. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(a (^a.b))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(a (^z.b))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.b))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.b))) REDUCED to normal form. ------ 197167/23479140. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((a a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((a a) a)(^x1.x1))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((a a) a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((a a) a)(^z.z))) 5. ==[ beta ]==> ((((a a) a)(^z.z))(^y.y)) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 197168/23479581. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(b (^z.(^x1.x1)))) REDUCED to normal form. ------ 197169/23479653. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 197170/23479689. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) a))) 7. ==[ beta ]==> ((^y.a)((^z.z) a)) 8. ==[ alpha ]==> ((^x.a)((^y.y) a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 197171/23479716. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 197172/23479734. ------ 1. ==[ start ]==> (((^a.b)(b a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a a)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 197173/23479797. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 197174/23479878. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 197175/23479986. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(b (^z.(z z)))) REDUCED to normal form. ------ 197176/23480076. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(c c)) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(c c)) 3. ==[ beta ]==> ((a (b (^y.y)))(c c)) 4. ==[ alpha ]==> ((a (b (^x.x)))(c c)) REDUCED to normal form. ------ 197177/23480184. ------ 1. ==[ start ]==> (((a b)(b a))(c (a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))(c (a (^x.x)))) REDUCED to normal form. ------ 197178/23480211. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(b ((^z.z) a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(b ((^y.y) a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(b a)) REDUCED to normal form. ------ 197179/23480238. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(a (a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (a (a a)))) REDUCED to normal form. ------ 197180/23480292. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a (^z.z))(a (^x1.x1)))) REDUCED to normal form. ------ 197181/23480319. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a a)((^x1.x1) a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a a)((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))((a a)((^z.z) a))) 6. ==[ alpha ]==> ((b (^x.x))((a a)((^y.y) a))) 7. ==[ beta ]==> ((b (^x.x))((a a) a)) REDUCED to normal form. ------ 197182/23480400. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(b c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(b c)) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b c)) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b c)) 5. ==[ beta ]==> ((a (^y.y))(b c)) 6. ==[ alpha ]==> ((a (^x.x))(b c)) REDUCED to normal form. ------ 197183/23480418. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x))((^z.z) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 197184/23480463. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1)) b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1)) b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197185/23480625. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 197186/23480733. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((^a.a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.y1) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197187/23481663. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(a (a (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197188/23482554. ------ 1. ==[ start ]==> ((^a.(^a.b))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(z (z (^x1.x1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197189/23490996. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(^z.(^x1.b))) 3. ==[ beta ]==> ((^z.(^x1.b))((^z.(^x1.b))(^y.y))) 4. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.b))(^y1.y1))) 5. ==[ beta ]==> (^y.b) 6. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197190/23491869. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^c.(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(a (a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 197191/23492769. ------ 1. ==[ start ]==> ((^a.b)((^c.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 197192/23493210. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 197193/23493534. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(a (a (^x1.x1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197194/23493537. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(a (a (^x1.x1))))) REDUCED to normal form. ------ 197195/23493555. ------ 1. ==[ start ]==> (((a a)(a (a a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 197196/23493987. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 197197/23494425. ------ 1. ==[ start ]==> ((^a.(^a.b))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))(a (a (a (^z.z))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197198/23494428. ------ 1. ==[ start ]==> ((a (^a.b))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(y (y (^z.z))))) REDUCED to normal form. ------ 197199/23495199. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.a)((a a)(a a)))((^z.a)((a a)(a a))))) 4. ==[ alpha ]==> ((^x.x)(((^y.a)((a a)(a a)))((^z.a)((a a)(a a))))) 5. ==[ beta ]==> (((^y.a)((a a)(a a)))((^z.a)((a a)(a a)))) 6. ==[ alpha ]==> (((^x.a)((a a)(a a)))((^y.a)((a a)(a a)))) 7. ==[ beta ]==> (a ((^y.a)((a a)(a a)))) 8. ==[ alpha ]==> (a ((^x.a)((a a)(a a)))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 197200/23496048. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(^z.(b (^x1.x1)))) 3. ==[ beta ]==> (b (^z.(b (^x1.x1)))) 4. ==[ alpha ]==> (b (^x.(b (^y.y)))) REDUCED to normal form. ------ 197201/23496444. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(y (^z.z)))) 3. ==[ beta ]==> ((a (a b))(^y.(y (^z.z)))) 4. ==[ alpha ]==> ((a (a b))(^x.(x (^y.y)))) REDUCED to normal form. ------ 197202/23496630. ------ 1. ==[ start ]==> ((^a.(b a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(a a))(^z.b))) 3. ==[ eta ]==> (b ((^y.(a a))(^z.b))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 197203/23497179. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)((a a)(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 197204/23497467. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(x1 x1))(b a))) 3. ==[ beta ]==> (((^x1.(x1 x1))(b a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(^z.z))) 5. ==[ beta ]==> (((b a)(b a))(^y.(^z.z))) 6. ==[ alpha ]==> (((b a)(b a))(^x.(^y.y))) REDUCED to normal form. ------ 197205/23498070. ------ 1. ==[ start ]==> ((^a.(^b.b))((a b)((a a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((a b)((a a) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197206/23498253. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.(^z.(y y)))) REDUCED to normal form. ------ 197207/23498385. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 197208/23499225. ------ 1. ==[ start ]==> (((a b)((a a) a))(^a.(^b.b))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 197209/23499828. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> (((b a)(b a))(^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 197210/23500116. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 197211/23500386. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(^b.(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(^x1.(x1 a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.(x1 a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.(z a))) REDUCED to normal form. ------ 197212/23500464. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197213/23501160. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 197214/23501412. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197215/23501625. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(b (^x1.(a a)))) 3. ==[ eta ]==> ((^y.(^z.z))(b (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197216/23502492. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^b.(a b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(a z))) 3. ==[ eta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 197217/23502681. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.(^z.y))) REDUCED to normal form. ------ 197218/23502867. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(a (^a.b))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(a (^z.b))) 3. ==[ beta ]==> ((a (^z.b))((a (^z.b))(^y.y))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.b))(^z.z))) REDUCED to normal form. ------ 197219/23502870. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(^y.(^z.b))) REDUCED to normal form. ------ 197220/23503740. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a a)(a (a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 197221/23503743. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^c.(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(a (a a)))) REDUCED to normal form. ------ 197222/23503761. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 197223/23503869. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(a (a a)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(a (a a)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(a (a a)))) 7. ==[ beta ]==> (b (^y.(a (a a)))) 8. ==[ alpha ]==> (b (^x.(a (a a)))) REDUCED to normal form. ------ 197224/23503977. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.(z z)))) REDUCED to normal form. ------ 197225/23504085. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 197226/23504157. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.a))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.a))) REDUCED to normal form. ------ 197227/23504166. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^y.a)) REDUCED to normal form. ------ 197228/23504190. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197229/23504472. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^c.(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197230/23504646. ------ 1. ==[ start ]==> ((a b)((^c.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 197231/23504700. ------ 1. ==[ start ]==> (((a a)(a a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((a a)(a a))((^x.(^y.(^z.z)))(^x1.b))) 3. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 197232/23504862. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 197233/23504925. ------ 1. ==[ start ]==> (((^a.a)(^b.a))(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.x)(^y.a))(c ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.a)(c ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.a)(c ((^y.(^z.z)) a))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 197234/23504952. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(b (a (a (^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(b (a (a (^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 197235/23504988. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 197236/23505006. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> (((^y.y) a)((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> (a ((a (a (^y.y)))(a a))) 6. ==[ alpha ]==> (a ((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 197237/23505015. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (((a a)(^x.a))(b (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))(b (^y.y))) REDUCED to normal form. ------ 197238/23505033. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 7. ==[ beta ]==> ((^y.y)(a (^z.z))) 8. ==[ alpha ]==> ((^x.x)(a (^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 197239/23505087. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 197240/23505195. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.(y y))(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((((a a)(^y.y))((^z.z)(a a)))(((a a)(^y.y))((^z.z)(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(((a a)(^z.z))((^x1.x1)(a a)))) 7. ==[ beta ]==> ((((a a)(^x.x))(a a))(((a a)(^z.z))((^x1.x1)(a a)))) 8. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))((^z.z)(a a)))) 9. ==[ beta ]==> ((((a a)(^x.x))(a a))(((a a)(^y.y))(a a))) REDUCED to normal form. ------ 197241/23505222. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1)(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 197242/23505276. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a) a)(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a) a)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 7. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 8. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 197243/23505303. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (a a))((^y.y)((^z.z) b))) 6. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y) b))) 7. ==[ beta ]==> ((a (a a))((^y.y) b)) 8. ==[ alpha ]==> ((a (a a))((^x.x) b)) 9. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 197244/23505330. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)(a a))) REDUCED to normal form. ------ 197245/23505384. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.y))((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.x))((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a a)(a a))((a (^x.x))(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 197246/23505411. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(a (a (^z.z))))) REDUCED to normal form. ------ 197247/23505429. ------ 1. ==[ start ]==> (((a a)(a (a a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 197248/23505456. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> (((a (^x.x)) a)((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> (((a (^x.x)) a)((a a)(^z.z))) 6. ==[ alpha ]==> (((a (^x.x)) a)((a a)(^y.y))) REDUCED to normal form. ------ 197249/23505501. ------ 1. ==[ start ]==> (((^a.(a a)) b)((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((b (^y.y))(^z.a))) 3. ==[ beta ]==> ((b b)((b (^y.y))(^z.a))) 4. ==[ alpha ]==> ((b b)((b (^x.x))(^y.a))) REDUCED to normal form. ------ 197250/23505636. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 197251/23505717. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 197252/23505744. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.a))((^y.y)(^z.z))) 7. ==[ beta ]==> ((a (^x.a))(^z.z)) 8. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 197253/23505834. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 197254/23505861. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(a (a (^y.y)))) REDUCED to normal form. ------ 197255/23505888. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(^x1.x1))) 6. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(^z.z))) 7. ==[ beta ]==> ((a a)((^z.z)(^y.y))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 197256/23506302. ------ 1. ==[ start ]==> ((a (^a.b))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))(a (a (a (^y.y))))) REDUCED to normal form. ------ 197257/23506491. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> ((^y.b)(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> ((^x.b)(((a a)(^y.y))(a b))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 197258/23506572. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a) a)(b a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a) a)(b a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a) a)(b a))) IRREDUCIBLE: cycle. ------ 197259/23506653. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> (b (((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> (b (((^x.x) a)((a a)(a a)))) 5. ==[ beta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 197260/23506680. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> ((a b)((a (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> ((a b)((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 197261/23506707. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((a a)((^z.(^x1.x1)) a))) 3. ==[ beta ]==> ((^y.y)((a a)((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 197262/23506743. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.(^x1.x1)) a)(^y1.y1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197263/23506770. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 197264/23506797. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((a a)(a a))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((a a)(a a))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((a a)(a a))(^z.a))) 5. ==[ beta ]==> ((^y.a)(((a a)(a a))(^z.a))) 6. ==[ alpha ]==> ((^x.a)(((a a)(a a))(^y.a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 197265/23506824. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(b (^z.(z z)))) REDUCED to normal form. ------ 197266/23506851. ------ 1. ==[ start ]==> (((a b)(^a.a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 197267/23506941. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 197268/23506968. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> (((a (a a))(a (a a))) b) REDUCED to normal form. ------ 197269/23507022. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 197270/23507040. ------ 1. ==[ start ]==> (((^a.b) b)((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b) b)((a (a a))(^y.y))) 3. ==[ beta ]==> (b ((a (a a))(^y.y))) 4. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 197271/23507049. ------ 1. ==[ start ]==> (((a b)(a a))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(x x))((^y.y) b))) 3. ==[ beta ]==> (((a b)(a a))(((^y.y) b)((^y.y) b))) 4. ==[ alpha ]==> (((a b)(a a))(((^x.x) b)((^y.y) b))) 5. ==[ beta ]==> (((a b)(a a))(b ((^y.y) b))) 6. ==[ alpha ]==> (((a b)(a a))(b ((^x.x) b))) 7. ==[ beta ]==> (((a b)(a a))(b b)) REDUCED to normal form. ------ 197272/23507076. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.a)((a a)(a a)))) 3. ==[ beta ]==> ((a (a a))((^y.a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (a a))((^x.a)((a a)(a a)))) 5. ==[ beta ]==> ((a (a a)) a) REDUCED to normal form. ------ 197273/23507787. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((a a) a)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)((a a)(^y.y)))) 5. ==[ beta ]==> (((a a) a)((a a)(^y.y))) 6. ==[ alpha ]==> (((a a) a)((a a)(^x.x))) REDUCED to normal form. ------ 197274/23507922. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a a)(b (^z.z)))) 3. ==[ beta ]==> (b ((a a)(b (^z.z)))) 4. ==[ alpha ]==> (b ((a a)(b (^x.x)))) REDUCED to normal form. ------ 197275/23507958. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((b (^y.y))(^z.z))) 3. ==[ beta ]==> (((a a) b)((b (^y.y))(^z.z))) 4. ==[ alpha ]==> (((a a) b)((b (^x.x))(^y.y))) REDUCED to normal form. ------ 197276/23507985. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 197277/23508039. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) REDUCED to normal form. ------ 197278/23508066. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 197279/23508120. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1)(a a))(^z1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))(^y1.b))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(^x1.b))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197280/23508147. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a b)(^y.(a a)))) REDUCED to normal form. ------ 197281/23508174. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 197282/23508228. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a))(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 197283/23508264. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a)((^z.z) b))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 197284/23508291. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.x1))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))((a a)(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))((a a)(a a)))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 197285/23508318. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> ((a (a b))((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> ((a (a b))((^x.x)(b (^y.y)))) 5. ==[ beta ]==> ((a (a b))(b (^y.y))) 6. ==[ alpha ]==> ((a (a b))(b (^x.x))) REDUCED to normal form. ------ 197286/23508399. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.x)(^y.a))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.a)) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.a)) REDUCED to normal form. ------ 197287/23508426. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a b) a)((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a b) a)((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (((a b) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a b) a)(^x.(^y.y))) REDUCED to normal form. ------ 197288/23508507. ------ 1. ==[ start ]==> ((a (b a))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> ((a (b a))((^x.(a a))(^y.b))) 3. ==[ beta ]==> ((a (b a))(a a)) REDUCED to normal form. ------ 197289/23508678. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(b ((a a)(a a)))) 3. ==[ beta ]==> (b (b ((a a)(a a)))) REDUCED to normal form. ------ 197290/23508741. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^c.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(a a)) b)) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(a a)) REDUCED to normal form. ------ 197291/23508786. ------ 1. ==[ start ]==> (((^a.a)(b a))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b a))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> ((b a)((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 197292/23508813. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((b a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)((b a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((b a)(a (a a)))) 5. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 197293/23508867. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> (((a b)(a b))((a a)((a a) a))) REDUCED to normal form. ------ 197294/23508948. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((a a)(^z.z)))) 5. ==[ beta ]==> (b ((^y.y)((a a)(^z.z)))) 6. ==[ alpha ]==> (b ((^x.x)((a a)(^y.y)))) 7. ==[ beta ]==> (b ((a a)(^y.y))) 8. ==[ alpha ]==> (b ((a a)(^x.x))) REDUCED to normal form. ------ 197295/23509056. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)((a a)(a a)))) REDUCED to normal form. ------ 197296/23509128. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a (a a))((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 197297/23509155. ------ 1. ==[ start ]==> (((a (a a))(a b))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a b))(^x.(^y.y))) REDUCED to normal form. ------ 197298/23509236. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(a (a a)))(a a)) REDUCED to normal form. ------ 197299/23509263. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.b)(a b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.b)(a b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.b)(a b))) 5. ==[ beta ]==> (((a a) a)((^y.b)(a b))) 6. ==[ alpha ]==> (((a a) a)((^x.b)(a b))) 7. ==[ beta ]==> (((a a) a) b) REDUCED to normal form. ------ 197300/23509344. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.(a a))(b a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(z z))(b a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))((b a)(b a))) REDUCED to normal form. ------ 197301/23509812. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> (b (((^x1.x1) b)(a a))) 4. ==[ alpha ]==> (b (((^x.x) b)(a a))) 5. ==[ beta ]==> (b (b (a a))) REDUCED to normal form. ------ 197302/23509821. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.b) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 197303/23509920. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197304/23509947. ------ 1. ==[ start ]==> ((a (^b.b))((a b)((a a) a))) 2. ==[ alpha ]==> ((a (^x.x))((a b)((a a) a))) REDUCED to normal form. ------ 197305/23510073. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(a b))(c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(a b))(c (^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)(c (^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a b)(c (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 197306/23510100. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(b (^b.b))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(b (^x.x))) REDUCED to normal form. ------ 197307/23510127. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(a (^c.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(a (^z.(a a)))) 3. ==[ beta ]==> (((a b)(^y.y))(a (^z.(a a)))) 4. ==[ alpha ]==> (((a b)(^x.x))(a (^y.(a a)))) REDUCED to normal form. ------ 197308/23510154. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((^b.b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((^y.y)(a a))) 3. ==[ beta ]==> (((a a)(a (a a)))((^y.y)(a a))) 4. ==[ alpha ]==> (((a a)(a (a a)))((^x.x)(a a))) 5. ==[ beta ]==> (((a a)(a (a a)))(a a)) REDUCED to normal form. ------ 197309/23510181. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 197310/23510226. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((a a)(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197311/23510262. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^y.(a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a b)((^x.(a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 197312/23510757. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(b (a (^y.(^z.z))))) 3. ==[ beta ]==> (b (b (a (^y.(^z.z))))) 4. ==[ alpha ]==> (b (b (a (^x.(^y.y))))) REDUCED to normal form. ------ 197313/23510793. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1) a)) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1) a)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z) a)) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) a) REDUCED to normal form. ------ 197314/23510820. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 197315/23510865. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(((a a)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197316/23511072. ------ 1. ==[ start ]==> ((((a a) a)(a b))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a b))(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 197317/23511099. ------ 1. ==[ start ]==> (((a b)((a a) a))(a (^b.b))) 2. ==[ alpha ]==> (((a b)((a a) a))(a (^x.x))) REDUCED to normal form. ------ 197318/23511126. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))(a a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.(^y1.y1)))(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 197319/23511207. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(a a)) REDUCED to normal form. ------ 197320/23511234. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((b (a a))((^y.b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((b (a a))((^x.b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b (a a)) b) REDUCED to normal form. ------ 197321/23511648. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))(c ((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(c ((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(c ((a a)(^y.y)))) 5. ==[ beta ]==> (c ((a a)(^y.y))) 6. ==[ alpha ]==> (c ((a a)(^x.x))) REDUCED to normal form. ------ 197322/23511702. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> (((b a)(b a))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((b a)(b a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 197323/23511765. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 197324/23511783. ------ 1. ==[ start ]==> (((^a.b)(a b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a b))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (b (((^y.y)(a a))((^z.z) a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((^y.y) a))) 5. ==[ beta ]==> (b ((a a)((^y.y) a))) 6. ==[ alpha ]==> (b ((a a)((^x.x) a))) 7. ==[ beta ]==> (b ((a a) a)) REDUCED to normal form. ------ 197325/23511891. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a (a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a (a a))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197326/23511990. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 197327/23512071. ------ 1. ==[ start ]==> (((a (a a))(b a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> (((a (a a))(b a))(a a)) REDUCED to normal form. ------ 197328/23512098. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.b)(a (a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.b)(a (a a)))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.b)(a (a a)))) 7. ==[ beta ]==> (((a a)(^x.x)) b) REDUCED to normal form. ------ 197329/23512152. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))((a a) a))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 197330/23512179. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(y y))(a b))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(y y))(a b))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(x x))(a b))) 5. ==[ beta ]==> (((a a)((a a) a))((a b)(a b))) REDUCED to normal form. ------ 197331/23512206. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) a) REDUCED to normal form. ------ 197332/23512260. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.a)(b a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.x1)(b a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.x1)(b a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.z)(b a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(b a)) REDUCED to normal form. ------ 197333/23512341. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> ((a (b (^x.x)))(a a)) REDUCED to normal form. ------ 197334/23512512. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(b ((a a)(^z.z)))) 3. ==[ beta ]==> (b (b ((a a)(^z.z)))) 4. ==[ alpha ]==> (b (b ((a a)(^x.x)))) REDUCED to normal form. ------ 197335/23512620. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((a b)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197336/23512728. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z) a)(a b))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)(a b))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)(a b))) 5. ==[ beta ]==> ((b (^x.x))(a (a b))) REDUCED to normal form. ------ 197337/23512755. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 7. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 197338/23512818. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((a a)(^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 197339/23512899. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 197340/23512926. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.b))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((a a)(^x.b))(^z.(^x1.x1))) 8. ==[ alpha ]==> (((a a)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 197341/23513007. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((a (^x1.x1))(^y1.(a a)))) REDUCED to normal form. ------ 197342/23513034. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.a))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 197343/23513061. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((a a)(^z.z)) a)) REDUCED to normal form. ------ 197344/23513124. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a a)(b (^x.x))) b) REDUCED to normal form. ------ 197345/23513178. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 197346/23513232. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.b))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.b))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.b))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 197347/23513259. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 197348/23513286. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a b)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a b)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 197349/23513502. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(b (^b.(a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(b (^z.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(a a)))) REDUCED to normal form. ------ 197350/23513943. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(b (a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(b (a b))) 3. ==[ beta ]==> ((^y.y)(b (a b))) 4. ==[ alpha ]==> ((^x.x)(b (a b))) 5. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 197351/23513997. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((a b)(a a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((a b)(a a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((a b)(a a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((a b)(a a))) 5. ==[ beta ]==> ((b ((^y.y) b))((a b)(a a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((a b)(a a))) 7. ==[ beta ]==> ((b b)((a b)(a a))) REDUCED to normal form. ------ 197352/23514006. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.b) b)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.b) b)) 3. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 197353/23514078. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a (a a))(a (a a)))) 3. ==[ beta ]==> (b ((a (a a))(a (a a)))) REDUCED to normal form. ------ 197354/23514195. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a b)(^y1.y1))) REDUCED to normal form. ------ 197355/23514222. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(((a a) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b (^y.(y y)))(((a a) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 197356/23514249. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((^y.y)(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a))((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.y)(^z.a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.a))(^z.a)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.a)) REDUCED to normal form. ------ 197357/23514303. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(^z.z))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 197358/23514339. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((a a) a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 197359/23514366. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.z)(a b))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a b)) REDUCED to normal form. ------ 197360/23514393. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.b)(^z.z))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.b)(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.b)(^y.y))) 5. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 197361/23514420. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 197362/23514447. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))(^z1.a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(^z1.a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(^y1.a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197363/23514474. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.(y y))(^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 197364/23514501. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 197365/23514555. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.y)(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.b)) REDUCED to normal form. ------ 197366/23514717. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(b (^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(b (^z.a))) 3. ==[ beta ]==> (((^y.y)(a a))(b (^z.a))) 4. ==[ alpha ]==> (((^x.x)(a a))(b (^y.a))) 5. ==[ beta ]==> ((a a)(b (^y.a))) 6. ==[ alpha ]==> ((a a)(b (^x.a))) REDUCED to normal form. ------ 197367/23514744. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(a (^a.b))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(a (^y.b))) REDUCED to normal form. ------ 197368/23515140. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(a a)) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(z z)) c)) 3. ==[ beta ]==> (((^y.y) b)((^z.(z z)) c)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(y y)) c)) 5. ==[ beta ]==> (b ((^y.(y y)) c)) 6. ==[ alpha ]==> (b ((^x.(x x)) c)) 7. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 197369/23515158. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1) a)((^y1.y1) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1) a)((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)((^x1.x1) a))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)((^x1.x1) a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) a))) 7. ==[ beta ]==> (((^y.y) a)((^z.z) a)) 8. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 9. ==[ beta ]==> (a ((^y.y) a)) 10. ==[ alpha ]==> (a ((^x.x) a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 197370/23515185. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (^z.z))(a (a a)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(a (a a)))) REDUCED to normal form. ------ 197371/23515212. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 197372/23515302. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1) a)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> ((^y.y)(((^z.z) a)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.a))) 7. ==[ beta ]==> (((^y.y) a)(^z.a)) 8. ==[ alpha ]==> (((^x.x) a)(^y.a)) 9. ==[ beta ]==> (a (^y.a)) 10. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 197373/23515329. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(^y1.(y1 y1)))) REDUCED to normal form. ------ 197374/23515410. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (a a)) b)) REDUCED to normal form. ------ 197375/23515518. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z)) a)) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 197376/23515572. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^b.a) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.a) c)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.a) c)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.a) c)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.a) c)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.a) c)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197377/23515590. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.x))((a (^y.y)) a)) REDUCED to normal form. ------ 197378/23515617. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(a (a a)))) REDUCED to normal form. ------ 197379/23515635. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (^y.(^z.z)))) REDUCED to normal form. ------ 197380/23515662. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a a)(a a))) REDUCED to normal form. ------ 197381/23515689. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.a)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.a)(a (^z.z)))) 5. ==[ beta ]==> ((a (b (^x.x))) a) REDUCED to normal form. ------ 197382/23515716. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 197383/23515743. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.z)(a (a a)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(a (a a)))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(a (a a)))) 7. ==[ beta ]==> (b ((^y.y)(a (a a)))) 8. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 9. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 197384/23515770. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 6. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 197385/23515797. ------ 1. ==[ start ]==> (((a b)(b a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 197386/23515824. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 197387/23515851. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(z z))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(y y))) REDUCED to normal form. ------ 197388/23515932. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b (^x1.a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b (^x1.a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b (^z.a))) 5. ==[ beta ]==> ((b (^y.y))(b (^z.a))) 6. ==[ alpha ]==> ((b (^x.x))(b (^y.a))) REDUCED to normal form. ------ 197389/23515959. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(a (^x.(x x)))) REDUCED to normal form. ------ 197390/23516013. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(a (^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.z)) 8. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 197391/23516031. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a)(^z.a))) 3. ==[ beta ]==> ((b (^y.y))((a a)(^z.a))) 4. ==[ alpha ]==> ((b (^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 197392/23516040. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))((^z.z) a)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.y) a)) 5. ==[ beta ]==> (((a (a (^x.x)))(a a)) a) REDUCED to normal form. ------ 197393/23516067. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.a)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 197394/23516076. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(c (a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(c (a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(c (a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(c (a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197395/23516103. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(b (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(b (a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(b (a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(b (a (^y.y)))) 5. ==[ beta ]==> (b (a (^y.y))) 6. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 197396/23516238. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(b b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(b b)) 3. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 197397/23516346. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((a a)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((a a)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197398/23518176. ------ 1. ==[ start ]==> ((^a.(^a.b))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))(^z.(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197399/23528436. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^b.b)(^c.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197400/23528598. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.a)(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (^y.((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (^x.((^y.a)(^z.z))) 5. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 197401/23528745. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(^x.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197402/23529165. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197403/23529291. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197404/23530056. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.z)(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197405/23530059. ------ 1. ==[ start ]==> ((a (^a.b))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 197406/23530623. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2))))) 4. ==[ alpha ]==> (^x.(((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))((^x2.(^y2.(^z2.z2)))((^x3.x3)(^y3.y3))))) 5. ==[ beta ]==> (^x.((^z.(^x1.x1))((^x2.(^y2.(^z2.z2)))((^x3.x3)(^y3.y3))))) 6. ==[ alpha ]==> (^x.((^y.(^z.z))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2))))) 7. ==[ beta ]==> (^x.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197407/23531688. ------ 1. ==[ start ]==> (((a b) c)(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(b (^y.y)))) REDUCED to normal form. ------ 197408/23532075. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197409/23532810. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(b (^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (^y1.(a a)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 197410/23533191. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.((a a)(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.((a a)(a a)))) 5. ==[ beta ]==> ((a a)(^z.((a a)(a a)))) 6. ==[ alpha ]==> ((a a)(^x.((a a)(a a)))) REDUCED to normal form. ------ 197411/23534016. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 197412/23534523. ------ 1. ==[ start ]==> (((a b)(^c.a))(^d.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(^y.(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 197413/23534550. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.((^y1.y1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.((^x1.x1) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^z.b)) REDUCED to normal form. ------ 197414/23535459. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((b a)(b a))(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((b a)(b a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 197415/23536095. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((^z.z)(a a)) c)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197416/23536548. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 197417/23537943. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(^z1.(^x2.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197418/23538075. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 197419/23538123. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(^c.(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.(^x1.b))) REDUCED to normal form. ------ 197420/23538510. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(^a.(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(^x1.(^y1.b))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.(^y1.b))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.b))) 5. ==[ beta ]==> ((^z.(^x1.b))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.b))(^z.z)) 7. ==[ beta ]==> (^y.b) 8. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197421/23539275. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^y.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 197422/23539371. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(b (^y1.(y1 y1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 197423/23539500. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^c.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(z z)))) 7. ==[ beta ]==> (b (^y.(^z.(z z)))) 8. ==[ alpha ]==> (b (^x.(^y.(y y)))) REDUCED to normal form. ------ 197424/23539821. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(((^y1.y1) a) a)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197425/23540322. ------ 1. ==[ start ]==> ((a (^a.(^a.a)))((^b.b)(^c.a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 197426/23540457. ------ 1. ==[ start ]==> (((^a.(^a.a))(a a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a a))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 197427/23540484. ------ 1. ==[ start ]==> ((a (^b.a))((^c.a)(^b.b))) 2. ==[ alpha ]==> ((a (^x.a))((^y.a)(^z.z))) 3. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 197428/23540592. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(x2 (^y2.y2))))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(x2 (^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197429/23540601. ------ 1. ==[ start ]==> (((a (^a.a)) b)(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)(b (a (a (^y.y))))) REDUCED to normal form. ------ 197430/23540628. ------ 1. ==[ start ]==> ((((^a.a) a) a)(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(a ((^y.y)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a a)(a ((^x.x)(^y.(^z.z))))) 5. ==[ beta ]==> ((a a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 197431/23540655. ------ 1. ==[ start ]==> (((a a)(^b.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)(^x.a))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 197432/23540682. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(((^x1.(^y1.y1)) a)(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(a (^y1.y1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.x1))) REDUCED to normal form. ------ 197433/23540709. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (^x.x))((b (^y.y)) a)) REDUCED to normal form. ------ 197434/23540817. ------ 1. ==[ start ]==> (((^a.(a a)) a)((b a)(a b))) 2. ==[ alpha ]==> (((^x.(x x)) a)((b a)(a b))) 3. ==[ beta ]==> ((a a)((b a)(a b))) REDUCED to normal form. ------ 197435/23540898. ------ 1. ==[ start ]==> ((((^a.a) a) b)((a b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a) b)((a b)(b a))) 3. ==[ beta ]==> ((a b)((a b)(b a))) REDUCED to normal form. ------ 197436/23540925. ------ 1. ==[ start ]==> (((a (a a)) a)(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a)) a)(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 197437/23540952. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))((^z.z) b)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y) b)) 7. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 197438/23540979. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 197439/23541006. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(b (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (b (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 197440/23541033. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^x.x))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 197441/23541051. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(b (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 197442/23541096. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x)) a)((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 197443/23541123. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 197444/23541150. ------ 1. ==[ start ]==> (((a (a a))(a a))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a a))((b (^x.x))(^y.a))) REDUCED to normal form. ------ 197445/23541177. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((a (^y.y))(((a a)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))(^y.(y y)))) REDUCED to normal form. ------ 197446/23541186. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197447/23541213. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197448/23541321. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 7. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 8. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 197449/23541348. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.b)(b a))) 3. ==[ beta ]==> ((^y.y)((^z.b)(b a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 5. ==[ beta ]==> ((^y.b)(b a)) 6. ==[ alpha ]==> ((^x.b)(b a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 197450/23541402. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 197451/23541501. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 197452/23541528. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a (a (^z.z))) a)) 3. ==[ beta ]==> ((a ((^y.y) a))((a (a (^z.z))) a)) 4. ==[ alpha ]==> ((a ((^x.x) a))((a (a (^y.y))) a)) 5. ==[ beta ]==> ((a a)((a (a (^y.y))) a)) 6. ==[ alpha ]==> ((a a)((a (a (^x.x))) a)) REDUCED to normal form. ------ 197453/23541555. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((^z.z) b)) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y) b)) 5. ==[ beta ]==> (((a (a a))(a (^x.x))) b) REDUCED to normal form. ------ 197454/23541582. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((b (^z.z)) c)) 3. ==[ beta ]==> (((^y.y)(a a))((b (^z.z)) c)) 4. ==[ alpha ]==> (((^x.x)(a a))((b (^y.y)) c)) 5. ==[ beta ]==> ((a a)((b (^y.y)) c)) 6. ==[ alpha ]==> ((a a)((b (^x.x)) c)) REDUCED to normal form. ------ 197455/23541645. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197456/23541924. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(b (^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 197457/23541942. ------ 1. ==[ start ]==> ((a (^a.b))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((a (^x.b))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^x.b))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))(^y.(y (^z.z)))) REDUCED to normal form. ------ 197458/23541960. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.(x (^y.y))) a)) 3. ==[ beta ]==> (((a a)((a a) a))(a (^y.y))) 4. ==[ alpha ]==> (((a a)((a a) a))(a (^x.x))) REDUCED to normal form. ------ 197459/23542113. ------ 1. ==[ start ]==> (((^a.b) a)((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.b) a)((b a)((a a) a))) 3. ==[ beta ]==> (b ((b a)((a a) a))) REDUCED to normal form. ------ 197460/23542275. ------ 1. ==[ start ]==> ((((a a) a) b)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> ((((a a) a) b)((a (a a))((^x.x) b))) 3. ==[ beta ]==> ((((a a) a) b)((a (a a)) b)) REDUCED to normal form. ------ 197461/23542302. ------ 1. ==[ start ]==> (((a b) a)(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a b) a)(((^x.x) a)((a a)(a a)))) 3. ==[ beta ]==> (((a b) a)(a ((a a)(a a)))) REDUCED to normal form. ------ 197462/23542320. ------ 1. ==[ start ]==> (((^a.a)(a b))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(c (^y.(^z.z)))) 3. ==[ beta ]==> ((a b)(c (^y.(^z.z)))) 4. ==[ alpha ]==> ((a b)(c (^x.(^y.y)))) REDUCED to normal form. ------ 197463/23542329. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 197464/23542482. ------ 1. ==[ start ]==> (((^a.b)(a a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (b ((^y.y)(a (a a)))) 4. ==[ alpha ]==> (b ((^x.x)(a (a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 197465/23542509. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 197466/23542527. ------ 1. ==[ start ]==> (((a a)(a b))((b a)(^c.a))) 2. ==[ alpha ]==> (((a a)(a b))((b a)(^x.a))) REDUCED to normal form. ------ 197467/23542554. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 197468/23542581. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> ((a (^x.x))((a a)(^z.(a a)))) 8. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(a a)))) REDUCED to normal form. ------ 197469/23542608. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 197470/23542662. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((((a a) a)(a (^x.x)))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 197471/23542689. ------ 1. ==[ start ]==> (((a b)(a a))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((a b)(a a))((a (a a))(^x.x))) REDUCED to normal form. ------ 197472/23542725. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)((a a)(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 197473/23542752. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197474/23542887. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (b (^y.(y y))) 6. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 197475/23542968. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197476/23543022. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.b)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(^y1.(^z1.z1)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.x1)))) 11. ==[ beta ]==> ((^y.b)(^z.(^x1.x1))) 12. ==[ alpha ]==> ((^x.b)(^y.(^z.z))) 13. ==[ beta ]==> b REDUCED to normal form. ------ 197477/23543103. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.y))) 5. ==[ beta ]==> (b ((^y.y)(^y.y))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197478/23543328. ------ 1. ==[ start ]==> (((^a.b) c)((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (b ((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (b ((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (b ((b a)(^y.y))) 6. ==[ alpha ]==> (b ((b a)(^x.x))) REDUCED to normal form. ------ 197479/23543571. ------ 1. ==[ start ]==> (((a b) c)((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b) c)((a a)(b (^x.x)))) REDUCED to normal form. ------ 197480/23543670. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 197481/23543805. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> (b ((^z.b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y)(a a)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 197482/23543904. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (^z.z))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(a (^y.y))) REDUCED to normal form. ------ 197483/23543985. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a (a a))((a a) a))((b (^x.x)) a)) REDUCED to normal form. ------ 197484/23544012. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(a a)) b)) 5. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(a a)) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(a a)) b)) 7. ==[ beta ]==> ((^y.y)(((a a)(a a)) b)) 8. ==[ alpha ]==> ((^x.x)(((a a)(a a)) b)) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 197485/23544039. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(((^x.x) b) c)) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(b c)) REDUCED to normal form. ------ 197486/23544318. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197487/23544381. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(((a a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(((a a)(a a))(a a))) REDUCED to normal form. ------ 197488/23544489. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(a a)))(((a a)(^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 197489/23544516. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a a)((a a) a))) REDUCED to normal form. ------ 197490/23544570. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(((a a) a)(a a))) REDUCED to normal form. ------ 197491/23544597. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((^z.z)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(x x)))((^y.y)((a a)(^z.z)))) 5. ==[ beta ]==> (((a b)(^x.(x x)))((a a)(^z.z))) 6. ==[ alpha ]==> (((a b)(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 197492/23544624. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a (a a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a (a a))(b a))) 3. ==[ beta ]==> (((a a)(^y.a))((a (a a))(b a))) 4. ==[ alpha ]==> (((a a)(^x.a))((a (a a))(b a))) REDUCED to normal form. ------ 197493/23544651. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(a (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 197494/23544696. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(b (^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.(a a)))) REDUCED to normal form. ------ 197495/23544741. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((a a)(a a))(^z.z))) REDUCED to normal form. ------ 197496/23544768. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (a a))(((^y.y) b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) b)(^y.(^z.z)))) 7. ==[ beta ]==> ((a (a a))(b (^y.(^z.z)))) 8. ==[ alpha ]==> ((a (a a))(b (^x.(^y.y)))) REDUCED to normal form. ------ 197497/23544795. ------ 1. ==[ start ]==> (((a (a a))(a b))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a b))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 197498/23544822. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((b a)(^y.(y y)))) 5. ==[ beta ]==> (((a a) a)((b a)(^y.(y y)))) 6. ==[ alpha ]==> (((a a) a)((b a)(^x.(x x)))) REDUCED to normal form. ------ 197499/23544849. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 197500/23544876. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((^a.a)(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> (((a b)(a (a a)))((a a)(^y.a))) 4. ==[ alpha ]==> (((a b)(a (a a)))((a a)(^x.a))) REDUCED to normal form. ------ 197501/23544903. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((a b)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((a b)(^z.b))) 3. ==[ beta ]==> (((a a)((^y.y) a))((a b)(^z.b))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((a b)(^y.b))) 5. ==[ beta ]==> (((a a) a)((a b)(^y.b))) 6. ==[ alpha ]==> (((a a) a)((a b)(^x.b))) REDUCED to normal form. ------ 197502/23544930. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((a a) a)(^z.(a a)))) REDUCED to normal form. ------ 197503/23544993. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(b a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(y1 y1))(b a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 x1))(b a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197504/23545074. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.z)((a a)(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.z)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.z)((a a)(a a)))) 5. ==[ beta ]==> ((a a)((^z.z)((a a)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.x)((a a)(a a)))) 7. ==[ beta ]==> ((a a)((a a)(a a))) REDUCED to normal form. ------ 197505/23545155. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.(^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.a))) 3. ==[ beta ]==> (b ((^x1.(^y1.(^z1.z1)))(^x2.a))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 197506/23545263. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.b)(^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197507/23545317. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197508/23545371. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(^x1.(^y1.y1))))) 8. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(^z.(^x1.x1))))) 9. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 197509/23545380. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))(c (a (^y.(^z.z))))) REDUCED to normal form. ------ 197510/23545407. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(b ((^x1.x1) b))) 3. ==[ beta ]==> (((^y.y)(^z.b))(b ((^x1.x1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(b ((^z.z) b))) 5. ==[ beta ]==> ((^y.b)(b ((^z.z) b))) 6. ==[ alpha ]==> ((^x.b)(b ((^y.y) b))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 197511/23545461. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b (a a))) REDUCED to normal form. ------ 197512/23545488. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((a (^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 197513/23545515. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((b a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))((b a) a)) REDUCED to normal form. ------ 197514/23545569. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((^x1.x1)(a a))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a a)(^x1.x1))) REDUCED to normal form. ------ 197515/23545794. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y) b)(^z.z))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y) b)(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x) b)(^y.y))) 5. ==[ beta ]==> (((a a)(a (a a)))(b (^y.y))) 6. ==[ alpha ]==> (((a a)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 197516/23545821. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 197517/23545875. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((a a)(^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 197518/23545902. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> ((a b)((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 197519/23545911. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 197520/23545938. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^a.b)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b)((a a) a))) 3. ==[ beta ]==> ((^y.y)((^z1.b)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((a a) a))) 5. ==[ beta ]==> ((^y.b)((a a) a)) 6. ==[ alpha ]==> ((^x.b)((a a) a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 197521/23546073. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197522/23546235. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 197523/23546262. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.b)(^z1.a))) 3. ==[ beta ]==> ((^y.y)((^y1.b)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.a))) 5. ==[ beta ]==> ((^y.b)(^z.a)) 6. ==[ alpha ]==> ((^x.b)(^y.a)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 197524/23546316. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 197525/23546379. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))(c (b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))(c (b a))) REDUCED to normal form. ------ 197526/23546397. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197527/23546406. ------ 1. ==[ start ]==> (((a b)(^c.a))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))(b (a (^y.(^z.z))))) REDUCED to normal form. ------ 197528/23546433. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(a ((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(a ((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(a ((^z.z) b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a b)) REDUCED to normal form. ------ 197529/23546460. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((a (^z.(^x1.x1)))(a a))) REDUCED to normal form. ------ 197530/23546514. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a)(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((a a)(^y1.y1)) a)) REDUCED to normal form. ------ 197531/23546541. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((^z.z)(a a))(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(a a))(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(a a))(a (a a)))) 5. ==[ beta ]==> ((b (^x.x))((a a)(a (a a)))) REDUCED to normal form. ------ 197532/23546766. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.(^x1.x1)))(^y1.y1))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 197533/23546793. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 197534/23546847. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 197535/23546874. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((b (a a))((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 197536/23546937. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.y1))(a b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(a b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a b))) 5. ==[ beta ]==> ((^y.(^z.z))(a b)) 6. ==[ alpha ]==> ((^x.(^y.y))(a b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197537/23547072. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (b ((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 197538/23547180. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.b)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.b)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197539/23547261. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 197540/23547288. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.z))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 197541/23547297. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))(c ((a a)(^z.z)))) REDUCED to normal form. ------ 197542/23547324. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))(b (b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))(b (b a))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))(b (b a))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (b a))) REDUCED to normal form. ------ 197543/23547342. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((b a)(b a))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((b a)(b a))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((b a)(b a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((b a)(b a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197544/23547405. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 197545/23547432. ------ 1. ==[ start ]==> (((a b)(^a.b))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.b))(((^y.y)(a a))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.b))((a a)((^z.z) a))) 4. ==[ alpha ]==> (((a b)(^x.b))((a a)((^y.y) a))) 5. ==[ beta ]==> (((a b)(^x.b))((a a) a)) REDUCED to normal form. ------ 197546/23547486. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 197547/23547540. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a (a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a (a a))(a b))) REDUCED to normal form. ------ 197548/23547567. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a)((^x1.x1)(a a)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a ((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(a ((^z.z)(a a)))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(a (a a))) REDUCED to normal form. ------ 197549/23547594. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 197550/23547657. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((b a)(^z.z))) 3. ==[ beta ]==> (((a (^x.x)) b)((b a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) b)((b a)(^y.y))) REDUCED to normal form. ------ 197551/23547684. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 197552/23547711. ------ 1. ==[ start ]==> (((a (a a))(b a))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))(b a))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> (((a (a a))(b a))((a a)(^y.a))) 4. ==[ alpha ]==> (((a (a a))(b a))((a a)(^x.a))) REDUCED to normal form. ------ 197553/23547738. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((a b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((a b)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a b)(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))((a b)(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(^x.x))((a b)(^y.(y y)))) REDUCED to normal form. ------ 197554/23547765. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 197555/23547792. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(^y.y))(^z.a))) 3. ==[ beta ]==> (((a b)(a b))((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a b)(a b))((^x.x)(^y.a))) 5. ==[ beta ]==> (((a b)(a b))(^y.a)) 6. ==[ alpha ]==> (((a b)(a b))(^x.a)) REDUCED to normal form. ------ 197556/23547819. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a (a a))(^y.b))) 3. ==[ beta ]==> (((a a)((a a) a))((a (a a))(^y.b))) 4. ==[ alpha ]==> (((a a)((a a) a))((a (a a))(^x.b))) REDUCED to normal form. ------ 197557/23547846. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a (^x1.(a a)))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(a (^z.(a a)))) REDUCED to normal form. ------ 197558/23547927. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((b a) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((b a) a)) 3. ==[ beta ]==> ((b (a (^y.y)))((b a) a)) 4. ==[ alpha ]==> ((b (a (^x.x)))((b a) a)) REDUCED to normal form. ------ 197559/23547954. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(((a a)(^x.x)) b)) REDUCED to normal form. ------ 197560/23547981. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((^a.a)(a a)) c)) 2. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y)(a a)) c)) 3. ==[ beta ]==> ((a (b (^x.x)))((a a) c)) REDUCED to normal form. ------ 197561/23548071. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(^y2.y2))(^z2.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(^y2.y2))(^z2.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197562/23548152. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197563/23548296. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((b c)(((a a) a)(a (a a)))) REDUCED to normal form. ------ 197564/23548323. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) b)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a)) b)((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 197565/23548431. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (^y.y))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 197566/23548530. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (b ((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> (b ((^x.b)((^y.y) a))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 197567/23548638. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197568/23548764. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a b) c)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a b) c)) REDUCED to normal form. ------ 197569/23548953. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^c.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(^z.z)) a)) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 197570/23548980. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(a a)) b)) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(a a)) REDUCED to normal form. ------ 197571/23549232. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.b)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.b)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.b)(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(a (^z.z)))) 7. ==[ beta ]==> ((^y.b)(a (^z.z))) 8. ==[ alpha ]==> ((^x.b)(a (^y.y))) 9. ==[ beta ]==> b REDUCED to normal form. ------ 197572/23549313. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.(x1 x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.(x x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (b ((^y.y)((^z.z)(^x1.x1)))) 8. ==[ alpha ]==> (b ((^x.x)((^y.y)(^z.z)))) 9. ==[ beta ]==> (b ((^y.y)(^z.z))) 10. ==[ alpha ]==> (b ((^x.x)(^y.y))) 11. ==[ beta ]==> (b (^y.y)) 12. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197573/23549421. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(a a))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(a a))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197574/23549556. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.a)(^y1.a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.a)(^y1.a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.a)(^x1.a))) 5. ==[ beta ]==> ((^y.y)((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 7. ==[ beta ]==> ((^y.a)(^z.a)) 8. ==[ alpha ]==> ((^x.a)(^y.a)) 9. ==[ beta ]==> a REDUCED to normal form. ------ 197575/23549583. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197576/23549646. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((a b)(a a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a b)(a a))) REDUCED to normal form. ------ 197577/23549673. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((a a) a)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((a a) a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a)(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a)(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(a (^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197578/23549727. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 197579/23549754. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.(a a)))(a ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))(a ((^y.y)(^z.z)))) 7. ==[ beta ]==> (((a a)(^x.(a a)))(a (^z.z))) 8. ==[ alpha ]==> (((a a)(^x.(a a)))(a (^y.y))) REDUCED to normal form. ------ 197580/23549781. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (^z.z))((a a) a))) REDUCED to normal form. ------ 197581/23549826. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(a (^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197582/23549961. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y)))) a) REDUCED to normal form. ------ 197583/23550006. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 197584/23550033. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a b) a)) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a b) a)) 3. ==[ beta ]==> ((a ((a a)(a a)))((a b) a)) REDUCED to normal form. ------ 197585/23550060. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(((a a) a) b)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(((a a) a) b)) 3. ==[ beta ]==> (((a (a a)) b)(((a a) a) b)) REDUCED to normal form. ------ 197586/23550276. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y)) c)) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 197587/23550375. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((a a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((a a) a))) REDUCED to normal form. ------ 197588/23550393. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(a (^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(a (^x1.b))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(a (^x1.b))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(a (^z.b))) 5. ==[ beta ]==> ((a (^z.b))(^y.y)) 6. ==[ alpha ]==> ((a (^x.b))(^y.y)) REDUCED to normal form. ------ 197589/23550780. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((a (a a))(a (^z.z)))) 3. ==[ beta ]==> (((^y.y) b)((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x) b)((a (a a))(a (^y.y)))) 5. ==[ beta ]==> (b ((a (a a))(a (^y.y)))) 6. ==[ alpha ]==> (b ((a (a a))(a (^x.x)))) REDUCED to normal form. ------ 197590/23550807. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)(a ((^z.z) a))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(a ((^y.y) a))) 5. ==[ beta ]==> (((a (a (^x.x))) a)(a a)) REDUCED to normal form. ------ 197591/23550834. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (^z.z))(a (a a)))) REDUCED to normal form. ------ 197592/23550852. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 197593/23550906. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.(^z.z))(a a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.(^y.y))(a a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 197594/23550987. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197595/23551095. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197596/23551131. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(b (a (a a)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(b (a (a a)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(b (a (a a)))) REDUCED to normal form. ------ 197597/23551158. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(a (^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 197598/23551212. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(((^y1.y1) a)(a (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) a)(a (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) a)(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(a (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(a (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197599/23551239. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))((a (^z.z)) a)) REDUCED to normal form. ------ 197600/23551257. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(b (^x1.(x1 x1)))) REDUCED to normal form. ------ 197601/23551302. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (a a))(^z.z))) REDUCED to normal form. ------ 197602/23551329. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (b (^x.x)))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 197603/23551356. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 197604/23551383. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a a)(^z.(z z)))) 5. ==[ beta ]==> (((^y.y) b)((a a)(^z.(z z)))) 6. ==[ alpha ]==> (((^x.x) b)((a a)(^y.(y y)))) 7. ==[ beta ]==> (b ((a a)(^y.(y y)))) 8. ==[ alpha ]==> (b ((a a)(^x.(x x)))) REDUCED to normal form. ------ 197605/23551410. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a (a a)) a)) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a (a a)) a)) REDUCED to normal form. ------ 197606/23551437. ------ 1. ==[ start ]==> (((a b)(b a))(((^a.a) a) b)) 2. ==[ alpha ]==> (((a b)(b a))(((^x.x) a) b)) 3. ==[ beta ]==> (((a b)(b a))(a b)) REDUCED to normal form. ------ 197607/23551545. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^b.a) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.a) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a)) a) REDUCED to normal form. ------ 197608/23551572. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(^y1.y1)) c)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(^x1.x1)) c)) 5. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) c)) 6. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) c)) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 197609/23551653. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 197610/23551671. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(b c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(b c)) 3. ==[ beta ]==> ((b (^y.y))(b c)) 4. ==[ alpha ]==> ((b (^x.x))(b c)) REDUCED to normal form. ------ 197611/23551680. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a a)(^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a a)(^y.a))) REDUCED to normal form. ------ 197612/23551707. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(((^x1.x1) a) a)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a) a)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a) a)) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 197613/23551716. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197614/23551743. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.(^z1.z1))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197615/23551878. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a a))) 3. ==[ beta ]==> (b ((^y1.(^z1.z1))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197616/23551986. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(b (^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(b (^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197617/23564403. ------ 1. ==[ start ]==> ((((^a.a) a) a)(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 197618/23564598. ------ 1. ==[ start ]==> ((^a.(a (a a)))((b a)(a b))) 2. ==[ alpha ]==> ((^x.(x (x x)))((b a)(a b))) 3. ==[ beta ]==> (((b a)(a b))(((b a)(a b))((b a)(a b)))) REDUCED to normal form. ------ 197619/23565735. ------ 1. ==[ start ]==> (((a a)((a a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 197620/23565894. ------ 1. ==[ start ]==> ((^a.(a b))((b a)((a a) a))) 2. ==[ alpha ]==> ((^x.(x b))((b a)((a a) a))) 3. ==[ beta ]==> (((b a)((a a) a)) b) REDUCED to normal form. ------ 197621/23566158. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 197622/23566281. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(((a (^z.(^x1.x1)))(^y1.(^z1.z1)))((a (^z.(^x1.x1)))(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (^x.(((a (^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.(^x2.x2)))(^y2.(^z2.z2))))) REDUCED to normal form. ------ 197623/23566977. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> (((a (^x.x))(a b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(^y.(^z.z))) REDUCED to normal form. ------ 197624/23567163. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((^z.z)(a a))(a b))) 3. ==[ beta ]==> (((((^z.z)(a a))(a b))(((^z.z)(a a))(a b)))(^y.y)) 4. ==[ alpha ]==> (((((^x.x)(a a))(a b))(((^y.y)(a a))(a b)))(^z.z)) 5. ==[ beta ]==> ((((a a)(a b))(((^y.y)(a a))(a b)))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a b))(((^x.x)(a a))(a b)))(^y.y)) 7. ==[ beta ]==> ((((a a)(a b))((a a)(a b)))(^y.y)) 8. ==[ alpha ]==> ((((a a)(a b))((a a)(a b)))(^x.x)) REDUCED to normal form. ------ 197625/23567346. ------ 1. ==[ start ]==> (((a b) c)(^d.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197626/23568489. ------ 1. ==[ start ]==> (((a a)(b a))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(^x.((a a)(a a)))) REDUCED to normal form. ------ 197627/23568849. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(^z.(^x1.(a a)))) 5. ==[ beta ]==> ((a a)(^z.(^x1.(a a)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(a a)))) REDUCED to normal form. ------ 197628/23569542. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(^c.((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> (((a b)(^y.y))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> (((a b)(^x.x))(^y.((^z.z) b))) 5. ==[ beta ]==> (((a b)(^x.x))(^y.b)) REDUCED to normal form. ------ 197629/23570208. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 197630/23570514. ------ 1. ==[ start ]==> (((a b)((a a) a))(^c.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 197631/23572476. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.((a a)(^x1.x1)))) REDUCED to normal form. ------ 197632/23572728. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.((y y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a b))(^y.((y y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.((x x)(^y.y)))) REDUCED to normal form. ------ 197633/23572914. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (^x1.x1))(a b))) 3. ==[ eta ]==> ((^y.(^z.z))((a (^x1.x1))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197634/23573610. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.(y1 y1)))) REDUCED to normal form. ------ 197635/23573733. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 197636/23574156. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a a)((a a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a a)((a a) a))) 3. ==[ beta ]==> (((a a)((a a) a))(((a a)((a a) a))(^y.y))) 4. ==[ alpha ]==> (((a a)((a a) a))(((a a)((a a) a))(^x.x))) REDUCED to normal form. ------ 197637/23574933. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 197638/23575998. ------ 1. ==[ start ]==> (((^a.a) b)((^b.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.a))) 3. ==[ beta ]==> (b ((^y.y)(^z.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 197639/23576025. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.(^y1.y1)))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197640/23576133. ------ 1. ==[ start ]==> (((a (^a.a))(^a.a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) b) REDUCED to normal form. ------ 197641/23576187. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197642/23576268. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 197643/23576295. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197644/23576313. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> (a ((^y.(^z.(^x1.x1))) a)) 6. ==[ alpha ]==> (a ((^x.(^y.(^z.z))) a)) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 197645/23576340. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(x1 (^y1.y1))) b)) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1))) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((^y.(y (^z.z))) b) 6. ==[ alpha ]==> ((^x.(x (^y.y))) b) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197646/23576412. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a) a)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 197647/23576439. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(b (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(b (^z.z))) REDUCED to normal form. ------ 197648/23576466. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a (a a))((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> ((a (a a))((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 197649/23576493. ------ 1. ==[ start ]==> ((a (a (a a)))((b a)(a b))) REDUCED to normal form. ------ 197650/23576736. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 197651/23576853. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(a a))(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197652/23576880. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 197653/23576934. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((b a)(^x1.b))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b a)(^y1.b))) 5. ==[ beta ]==> ((^y.y)((b a)(^y1.b))) 6. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 7. ==[ beta ]==> ((b a)(^y.b)) 8. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 197654/23576997. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 197655/23577024. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.b)(b a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y))) b) REDUCED to normal form. ------ 197656/23577051. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.a))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.a))((^y.a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.a)) a) REDUCED to normal form. ------ 197657/23577069. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(^x1.x1))) 7. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(^z.z)) REDUCED to normal form. ------ 197658/23577078. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197659/23577105. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))((a a)(a a)))) 7. ==[ beta ]==> ((^y.(y y))((a a)(a a))) 8. ==[ alpha ]==> ((^x.(x x))((a a)(a a))) 9. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 197660/23577402. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197661/23577429. ------ 1. ==[ start ]==> ((((a a) a) a)((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) a)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a) a)(a a)) REDUCED to normal form. ------ 197662/23577483. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z))) a) REDUCED to normal form. ------ 197663/23577510. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((a (^x.(x x)))(^y.y)) REDUCED to normal form. ------ 197664/23577537. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.a))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> (((a (a a))(^x.a))(a a)) REDUCED to normal form. ------ 197665/23577627. ------ 1. ==[ start ]==> (((a a)((a a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))(a (a (a (^x.x))))) REDUCED to normal form. ------ 197666/23577654. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.(^y1.y1)) a)(a a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.x1)(a a))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(a a))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 197667/23577681. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))((b (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> ((a (a (a a)))((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 197668/23577708. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> (((a (a a)) a)(((a a)(a a))((^y.y) a))) 4. ==[ alpha ]==> (((a (a a)) a)(((a a)(a a))((^x.x) a))) 5. ==[ beta ]==> (((a (a a)) a)(((a a)(a a)) a)) REDUCED to normal form. ------ 197669/23577735. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.x1) b)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) b)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) b)(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) b)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) b)(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(b (a (a a)))) REDUCED to normal form. ------ 197670/23577762. ------ 1. ==[ start ]==> ((((a a) a)(a a))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 197671/23577789. ------ 1. ==[ start ]==> ((a (a b))((b a)((a a) a))) REDUCED to normal form. ------ 197672/23577996. ------ 1. ==[ start ]==> (((a a)(^a.b))(c (^d.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(c (^y.(^z.z)))) REDUCED to normal form. ------ 197673/23578050. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(a (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 197674/23578068. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.(^z.z)) a)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.(^y.y)) a)(^z.z))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a (a a))(a (a a)))(^y.y)) 8. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.x)) REDUCED to normal form. ------ 197675/23578149. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (b (((^y.y) b)(^z.(z z)))) 4. ==[ alpha ]==> (b (((^x.x) b)(^y.(y y)))) 5. ==[ beta ]==> (b (b (^y.(y y)))) 6. ==[ alpha ]==> (b (b (^x.(x x)))) REDUCED to normal form. ------ 197676/23578158. ------ 1. ==[ start ]==> (((a b)(^a.a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a b)(^x.x))(a (a a))) REDUCED to normal form. ------ 197677/23578176. ------ 1. ==[ start ]==> ((a (^b.(a a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 197678/23578347. ------ 1. ==[ start ]==> (((^a.b) b)((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197679/23578392. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 197680/23578473. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a) a)) 5. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a) a)) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) a)) 7. ==[ beta ]==> (((^y.(^z.z)) a) a) 8. ==[ alpha ]==> (((^x.(^y.y)) a) a) 9. ==[ beta ]==> ((^y.y) a) 10. ==[ alpha ]==> ((^x.x) a) 11. ==[ beta ]==> a REDUCED to normal form. ------ 197681/23578563. ------ 1. ==[ start ]==> (((a b) b)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b) b)((^x.x)(^y.(y y)))) 3. ==[ beta ]==> (((a b) b)(^y.(y y))) 4. ==[ alpha ]==> (((a b) b)(^x.(x x))) REDUCED to normal form. ------ 197682/23578590. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 6. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 197683/23578644. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.z)) REDUCED to normal form. ------ 197684/23578698. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 197685/23578752. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.a))(^y.y)) REDUCED to normal form. ------ 197686/23578779. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197687/23578806. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 197688/23578842. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))(b (b (^y.y)))) 3. ==[ beta ]==> (((a a)(a a))(b (b (^y.y)))) 4. ==[ alpha ]==> (((a a)(a a))(b (b (^x.x)))) REDUCED to normal form. ------ 197689/23578869. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x))(a b))(a (^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a b))(a (^y.y))) REDUCED to normal form. ------ 197690/23578896. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((b (^y.y))(a a))) 3. ==[ beta ]==> ((a ((a a) a))((b (^y.y))(a a))) 4. ==[ alpha ]==> ((a ((a a) a))((b (^x.x))(a a))) REDUCED to normal form. ------ 197691/23578923. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^y.y))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 197692/23578950. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((^z.z) b)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((^z.z) b)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y) b)((^z.z) a))) 5. ==[ beta ]==> ((a (a a))(((^y.y) b)((^z.z) a))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) b)((^y.y) a))) 7. ==[ beta ]==> ((a (a a))(b ((^y.y) a))) 8. ==[ alpha ]==> ((a (a a))(b ((^x.x) a))) 9. ==[ beta ]==> ((a (a a))(b a)) REDUCED to normal form. ------ 197693/23578977. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> ((((a a) a) a)((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> ((((a a) a) a)((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 197694/23579004. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a (^x.x)))((b a)(^z.z))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))((b a)(^y.y))) REDUCED to normal form. ------ 197695/23579031. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((a a)(^y.y))((a a) a))) 3. ==[ beta ]==> (((a a)(a a))(((a a)(^y.y))((a a) a))) 4. ==[ alpha ]==> (((a a)(a a))(((a a)(^x.x))((a a) a))) REDUCED to normal form. ------ 197696/23579058. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))(a b))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(a b))) REDUCED to normal form. ------ 197697/23579238. ------ 1. ==[ start ]==> (((a b) c)(b (^d.(^a.a)))) 2. ==[ alpha ]==> (((a b) c)(b (^x.(^y.y)))) REDUCED to normal form. ------ 197698/23579310. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 197699/23579337. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((^x1.x1) b)(^y1.a))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.a))) 5. ==[ beta ]==> (((^y.y) b)(^z.a)) 6. ==[ alpha ]==> (((^x.x) b)(^y.a)) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 197700/23579346. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))((^x1.x1) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.z) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 197701/23579373. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(^x1.(^y1.y1)))(a (a a)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(^x1.(^y1.y1)))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(^z.(^x1.x1)))(a (a a)))) 5. ==[ beta ]==> ((a (^x.b))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 197702/23579391. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 197703/23579427. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((a a) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197704/23579454. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(a a))(a b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(a a)) REDUCED to normal form. ------ 197705/23579472. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((a b)(^z.(a a)))) 3. ==[ beta ]==> (b ((a b)(^z.(a a)))) 4. ==[ alpha ]==> (b ((a b)(^x.(a a)))) REDUCED to normal form. ------ 197706/23579481. ------ 1. ==[ start ]==> (((a b)(^b.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a b)(^x.a)) b) REDUCED to normal form. ------ 197707/23579535. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 197708/23580093. ------ 1. ==[ start ]==> (((^a.a)(b a))((^b.b) c)) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.y) c)) 3. ==[ beta ]==> ((b a)((^y.y) c)) 4. ==[ alpha ]==> ((b a)((^x.x) c)) 5. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 197709/23580381. ------ 1. ==[ start ]==> (((a a)(b a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 197710/23580642. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197711/23580741. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a a)(^z.(a a)))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a a)(^z.(a a)))) 5. ==[ beta ]==> ((a a)((a a)(^z.(a a)))) 6. ==[ alpha ]==> ((a a)((a a)(^x.(a a)))) REDUCED to normal form. ------ 197712/23580822. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a (^a.(^a.a))) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (b ((a (^x1.(^y1.y1))) c)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) c)) REDUCED to normal form. ------ 197713/23580939. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.b)(^x1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a) b) REDUCED to normal form. ------ 197714/23581047. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 197715/23581074. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 197716/23581119. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(a a)) a)) 3. ==[ beta ]==> (b ((^x1.(a a)) a)) 4. ==[ alpha ]==> (b ((^x.(a a)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 197717/23581272. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((a b)((a a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a b)((a a) a))) REDUCED to normal form. ------ 197718/23581299. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a) a)(a b))) REDUCED to normal form. ------ 197719/23581326. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)((^z.z)(a a)))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))((^z.z)(a a))) 8. ==[ alpha ]==> ((a ((a a)(^x.x)))((^y.y)(a a))) 9. ==[ beta ]==> ((a ((a a)(^x.x)))(a a)) REDUCED to normal form. ------ 197720/23581353. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a (a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a (a a))(a a))((a (a a))((a a)(^y.y)))) 4. ==[ alpha ]==> (((a (a a))(a a))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 197721/23581380. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) a)(b a))) 5. ==[ beta ]==> ((a b)(((^y.y) a)(b a))) 6. ==[ alpha ]==> ((a b)(((^x.x) a)(b a))) 7. ==[ beta ]==> ((a b)(a (b a))) REDUCED to normal form. ------ 197722/23581407. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 197723/23581434. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a a)((^z.z) b))) 3. ==[ beta ]==> (((a b)(^y.y))((a a)((^z.z) b))) 4. ==[ alpha ]==> (((a b)(^x.x))((a a)((^y.y) b))) 5. ==[ beta ]==> (((a b)(^x.x))((a a) b)) REDUCED to normal form. ------ 197724/23581578. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 197725/23581605. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((a b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((a b)(^z1.a))) 3. ==[ beta ]==> ((^y.y)((a b)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.a))) 5. ==[ beta ]==> ((a b)(^y.a)) 6. ==[ alpha ]==> ((a b)(^x.a)) REDUCED to normal form. ------ 197726/23581740. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((a (^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 197727/23581848. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((b a) c)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197728/23581884. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(z z)))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 197729/23581911. ------ 1. ==[ start ]==> (((a a)(^b.b))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 197730/23581938. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1)))) b) REDUCED to normal form. ------ 197731/23582019. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 197732/23582073. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 197733/23582100. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197734/23582244. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a) b)((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a) b)((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a) b)((a b)(^y.y))) 6. ==[ alpha ]==> (((a a) b)((a b)(^x.x))) REDUCED to normal form. ------ 197735/23582271. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a) a)((a a) a))) REDUCED to normal form. ------ 197736/23582298. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(^z.z))(a b))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(^y.y))(a b))) 5. ==[ beta ]==> ((a (b a))((^y.y)(a b))) 6. ==[ alpha ]==> ((a (b a))((^x.x)(a b))) 7. ==[ beta ]==> ((a (b a))(a b)) REDUCED to normal form. ------ 197737/23582325. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a (a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a (a a))(a a))) REDUCED to normal form. ------ 197738/23582352. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)((a a)(^z.z)))) 7. ==[ beta ]==> ((a a)(((^y.y) a)((a a)(^z.z)))) 8. ==[ alpha ]==> ((a a)(((^x.x) a)((a a)(^y.y)))) 9. ==[ beta ]==> ((a a)(a ((a a)(^y.y)))) 10. ==[ alpha ]==> ((a a)(a ((a a)(^x.x)))) REDUCED to normal form. ------ 197739/23582379. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (^x.x))(b a))) REDUCED to normal form. ------ 197740/23582406. ------ 1. ==[ start ]==> (((a b)((a a) a))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))((a a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 197741/23582604. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.b))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.b)) 7. ==[ beta ]==> ((^y.y)(^z.b)) 8. ==[ alpha ]==> ((^x.x)(^y.b)) 9. ==[ beta ]==> (^y.b) 10. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197742/23582739. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a (^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a (^z.(^x1.x1))) a)) 3. ==[ beta ]==> (b ((a (^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (b ((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 197743/23582883. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.a)(^z.a))) 3. ==[ beta ]==> ((b b)((^y.a)(^z.a))) 4. ==[ alpha ]==> ((b b)((^x.a)(^y.a))) 5. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 197744/23582910. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y))(^z.b))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 197745/23582964. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 197746/23583090. ------ 1. ==[ start ]==> (((^a.b)(a b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.z)) c)) 3. ==[ beta ]==> (b ((^y.(^z.z)) c)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) c)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197747/23583297. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a a)(b a))) REDUCED to normal form. ------ 197748/23583927. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))((^b.(a a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))((^y1.(a a)) c)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197749/23584098. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(b (^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(b (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 197750/23584197. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a b)(^z.a))) 3. ==[ beta ]==> (b ((a b)(^z.a))) 4. ==[ alpha ]==> (b ((a b)(^x.a))) REDUCED to normal form. ------ 197751/23584206. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.b)((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.(a a))) b) REDUCED to normal form. ------ 197752/23584233. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.a)(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.a)(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.a)(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.b)) a) REDUCED to normal form. ------ 197753/23584305. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) a)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197754/23584314. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.a)(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z))) a) REDUCED to normal form. ------ 197755/23584341. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 197756/23584368. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.z)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 197757/23584593. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a a))(b ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a b)(a a))(b ((^x.x)(a a)))) 5. ==[ beta ]==> (((a b)(a a))(b (a a))) REDUCED to normal form. ------ 197758/23584620. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(a ((a a)(^y.y)))) 3. ==[ beta ]==> (((a a)(a b))(a ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a a)(a b))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 197759/23584647. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(((^y.y)(a a))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))((a a)(a a))) REDUCED to normal form. ------ 197760/23584701. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(((a a) a) a)) REDUCED to normal form. ------ 197761/23584728. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((b a)(((^y.y)(^z.z))(a (a a)))) 6. ==[ alpha ]==> ((b a)(((^x.x)(^y.y))(a (a a)))) 7. ==[ beta ]==> ((b a)((^y.y)(a (a a)))) 8. ==[ alpha ]==> ((b a)((^x.x)(a (a a)))) 9. ==[ beta ]==> ((b a)(a (a a))) REDUCED to normal form. ------ 197762/23584755. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (a a))((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 197763/23584809. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (^a.a))(a b))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a (^z.z))(a b))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a b))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a b))) REDUCED to normal form. ------ 197764/23584899. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a b)(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)(^y.(^z.z))) 8. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 197765/23584980. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a (a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 197766/23585088. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a)(a a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1)(a a)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1)(a a)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197767/23585205. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(z z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(z z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.(y y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.(x x))(^y.(^z.z)))) 7. ==[ beta ]==> (a ((^y.(^z.z))(^y.(^z.z)))) 8. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 197768/23585304. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(a a)) a)) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(a a)) a)) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(a a)) a)) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(a a)) a)) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(a a)) a)) 7. ==[ beta ]==> ((b b)((^y.(a a)) a)) 8. ==[ alpha ]==> ((b b)((^x.(a a)) a)) 9. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 197769/23585448. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(c (^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(c (^z.a))) REDUCED to normal form. ------ 197770/23585502. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(a (^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.(a a)))) REDUCED to normal form. ------ 197771/23585529. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((^z.b)(a a))) 3. ==[ beta ]==> ((b (^y.(y y)))((^z.b)(a a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((^y.b)(a a))) 5. ==[ beta ]==> ((b (^x.(x x))) b) REDUCED to normal form. ------ 197772/23585556. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^c.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.a)(a (^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) a) REDUCED to normal form. ------ 197773/23585610. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a (a a)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(a (a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (a a)))) 7. ==[ beta ]==> ((^y.(y y))(a (a a))) 8. ==[ alpha ]==> ((^x.(x x))(a (a a))) 9. ==[ beta ]==> ((a (a a))(a (a a))) REDUCED to normal form. ------ 197774/23585628. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 197775/23585862. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(b ((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(b ((a a) a))) REDUCED to normal form. ------ 197776/23585916. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(((a a) a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(((a a) a)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(((a a) a)(a a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a) a)(a a))) REDUCED to normal form. ------ 197777/23585943. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((b (a (a a)))(((^y.y)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((b (a (a a)))(((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((b (a (a a)))((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((b (a (a a)))((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((b (a (a a)))(a (^y.y))) 8. ==[ alpha ]==> ((b (a (a a)))(a (^x.x))) REDUCED to normal form. ------ 197778/23585970. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((a (a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a)) a)((a (a a))((^y.y) a))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((a (a a))((^x.x) a))) 5. ==[ beta ]==> ((((a a)(a a)) a)((a (a a)) a)) REDUCED to normal form. ------ 197779/23586024. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a a)((a (^y.y))((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a a)((a (^x.x))((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((a (^x.x))(^z.z))) 8. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 197780/23586042. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(b (^c.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(b (^z.a))) 3. ==[ beta ]==> ((a (^y.y))(b (^z.a))) 4. ==[ alpha ]==> ((a (^x.x))(b (^y.a))) REDUCED to normal form. ------ 197781/23586051. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a a)((a a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a a)((a a) a))) REDUCED to normal form. ------ 197782/23586573. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((^y.y)(^z.z))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((^x.x)(^y.y))) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(^y.y)) 8. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 197783/23586609. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(x1 x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(a (^z.z)))) 7. ==[ beta ]==> ((^y.(y y))(a (^z.z))) 8. ==[ alpha ]==> ((^x.(x x))(a (^y.y))) 9. ==[ beta ]==> ((a (^y.y))(a (^y.y))) 10. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 197784/23586636. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 197785/23586654. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (^y.y))(^z.(z z)))) 3. ==[ beta ]==> (b ((a (^y.y))(^z.(z z)))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.(y y)))) REDUCED to normal form. ------ 197786/23586717. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 197787/23586798. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197788/23586825. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 197789/23586897. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^b.a) c)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.a) c)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a) c)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a) c)) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 197790/23586942. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a a)(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a a)(a (a a)))) REDUCED to normal form. ------ 197791/23587158. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(b ((^z.z) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b ((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(b ((^y.y) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(b a)) REDUCED to normal form. ------ 197792/23587212. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(((^a.a) a)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(((^z.z) a)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(a (a a))) REDUCED to normal form. ------ 197793/23587239. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))((a (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 197794/23587266. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a a)((^x.x) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))((a a) a)) REDUCED to normal form. ------ 197795/23587338. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 197796/23587347. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(b c)) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(b c)) REDUCED to normal form. ------ 197797/23587383. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a) a)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a) a)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a) a)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197798/23587410. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a (^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a (^y1.y1)) b)) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1)) b)) 4. ==[ alpha ]==> ((^x.x)((a (^y.y)) b)) 5. ==[ beta ]==> ((a (^y.y)) b) 6. ==[ alpha ]==> ((a (^x.x)) b) REDUCED to normal form. ------ 197799/23587545. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (b ((a (^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (b ((a (^x.x))(^y.y))) REDUCED to normal form. ------ 197800/23587653. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((^a.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197801/23587787. ------ 1. ==[ start ]==> (^a.((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (^x.((^y.(y (^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^x.((^x1.(^y1.y1))(^z.z))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197802/23587788. ------ 1. ==[ start ]==> (a ((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (a ((^x.(x (^y.y)))(^z.(^x1.x1)))) 3. ==[ beta ]==> (a ((^z.(^x1.x1))(^y.y))) 4. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 197803/23599266. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197804/23599683. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a))) a) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1))) a) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y)) a) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z)) a) 5. ==[ beta ]==> ((^y.y) a) 6. ==[ alpha ]==> ((^x.x) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 197805/23599689. ------ 1. ==[ start ]==> ((^a.a)((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> ((^z.(^x1.x1))(^y.y)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197806/23599824. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.b))) 3. ==[ beta ]==> (((^z.(^x1.(^y1.y1)))(^z1.b))(^y.y)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.y1)) 5. ==[ beta ]==> ((^y.(^z.z))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197807/23600106. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) a)(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) a)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (a (^y.((^z.z)(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (a (^x.((^y.y)(^z.(^x1.x1))))) 7. ==[ beta ]==> (a (^x.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197808/23600184. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 197809/23600508. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197810/23600556. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 197811/23600988. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y) a))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))(^y.(a (a (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(a (a (^z.z))))) 6. ==[ alpha ]==> ((a a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 197812/23601399. ------ 1. ==[ start ]==> ((^a.(^a.b))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((^x.(^y.b))(b ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 197813/23601420. ------ 1. ==[ start ]==> (((a a)((a a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 197814/23602173. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.y)(((^z.(z z))((^x1.x1) b))((^z.(z z))((^x1.x1) b)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(y y))((^z.z) b))((^x1.(x1 x1))((^y1.y1) b)))) 5. ==[ beta ]==> (((^y.(y y))((^z.z) b))((^x1.(x1 x1))((^y1.y1) b))) 6. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(z z))((^x1.x1) b))) 7. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(z z))((^x1.x1) b))) 8. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(z z))((^x1.x1) b))) 9. ==[ beta ]==> ((b ((^y.y) b))((^z.(z z))((^x1.x1) b))) 10. ==[ alpha ]==> ((b ((^x.x) b))((^y.(y y))((^z.z) b))) 11. ==[ beta ]==> ((b b)((^y.(y y))((^z.z) b))) 12. ==[ alpha ]==> ((b b)((^x.(x x))((^y.y) b))) 13. ==[ beta ]==> ((b b)(((^y.y) b)((^y.y) b))) 14. ==[ alpha ]==> ((b b)(((^x.x) b)((^y.y) b))) 15. ==[ beta ]==> ((b b)(b ((^y.y) b))) 16. ==[ alpha ]==> ((b b)(b ((^x.x) b))) 17. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 197815/23603445. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 197816/23603604. ------ 1. ==[ start ]==> ((^a.(b a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.z))(^x1.a))) 3. ==[ eta ]==> (b ((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197817/23604153. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 197818/23604441. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((^x1.(^y1.y1))((a a)(^z1.z1)))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197819/23604912. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.((x1 x1)(x1 x1)))) 3. ==[ beta ]==> (b (^x1.((x1 x1)(x1 x1)))) 4. ==[ alpha ]==> (b (^x.((x x)(x x)))) REDUCED to normal form. ------ 197820/23605044. ------ 1. ==[ start ]==> ((^a.(^b.b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197821/23605359. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 197822/23606226. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(^x1.(^y1.y1))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 197823/23606358. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.b)((^z.z)(^x1.x1)))((^y.b)((^z.z)(^x1.x1))))(((^y.b)((^z.z)(^x1.x1)))((^y.b)((^z.z)(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.b)((^y.y)(^z.z)))((^x1.b)((^y1.y1)(^z1.z1))))(((^x2.b)((^y2.y2)(^z2.z2)))((^x3.b)((^y3.y3)(^z3.z3))))) 5. ==[ beta ]==> ((b ((^x1.b)((^y1.y1)(^z1.z1))))(((^x2.b)((^y2.y2)(^z2.z2)))((^x3.b)((^y3.y3)(^z3.z3))))) 6. ==[ alpha ]==> ((b ((^x.b)((^y.y)(^z.z))))(((^x1.b)((^y1.y1)(^z1.z1)))((^x2.b)((^y2.y2)(^z2.z2))))) 7. ==[ beta ]==> ((b b)(((^x1.b)((^y1.y1)(^z1.z1)))((^x2.b)((^y2.y2)(^z2.z2))))) 8. ==[ alpha ]==> ((b b)(((^x.b)((^y.y)(^z.z)))((^x1.b)((^y1.y1)(^z1.z1))))) 9. ==[ beta ]==> ((b b)(b ((^x1.b)((^y1.y1)(^z1.z1))))) 10. ==[ alpha ]==> ((b b)(b ((^x.b)((^y.y)(^z.z))))) 11. ==[ beta ]==> ((b b)(b b)) REDUCED to normal form. ------ 197824/23607117. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 197825/23607387. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^b.(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(z a))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.(z a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.(y a))) REDUCED to normal form. ------ 197826/23607438. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197827/23608413. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197828/23609097. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.((^x1.x1)(z z)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.((^x1.x1)(z z)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.((^z.z)(y y)))) 7. ==[ beta ]==> ((b b)(^y.((^z.z)(y y)))) 8. ==[ alpha ]==> ((b b)(^x.((^y.y)(x x)))) 9. ==[ beta ]==> ((b b)(^x.(x x))) REDUCED to normal form. ------ 197829/23609493. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(^y.(a y))) 3. ==[ eta ]==> ((((^x.x) a)((a a)(a a))) a) 4. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 197830/23609841. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(b (^c.a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(b (^z.a))) 3. ==[ beta ]==> ((b (^z.a))((b (^z.a))(^y.y))) 4. ==[ alpha ]==> ((b (^x.a))((b (^y.a))(^z.z))) REDUCED to normal form. ------ 197831/23610714. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 197832/23610762. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 197833/23610870. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.(a (a a)))) REDUCED to normal form. ------ 197834/23611164. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.y1)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197835/23611167. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^z.a)) REDUCED to normal form. ------ 197836/23611446. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^a.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197837/23611581. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(^a.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(^y1.y1)) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(^y1.y1)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.x1)) 5. ==[ beta ]==> ((^y.y)(^x1.x1)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197838/23611593. ------ 1. ==[ start ]==> ((a a)((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y.y))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 197839/23611701. ------ 1. ==[ start ]==> (((a a)(a a))((^b.b)(^c.a))) 2. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.a))) 3. ==[ beta ]==> (((a a)(a a))(^y.a)) 4. ==[ alpha ]==> (((a a)(a a))(^x.a)) REDUCED to normal form. ------ 197840/23611728. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 197841/23611890. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 197842/23612007. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y) a)(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x) a)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (a ((^y.y)(^z.(^x1.x1))))) 6. ==[ alpha ]==> (a (a ((^x.x)(^y.(^z.z))))) 7. ==[ beta ]==> (a (a (^y.(^z.z)))) 8. ==[ alpha ]==> (a (a (^x.(^y.y)))) REDUCED to normal form. ------ 197843/23612016. ------ 1. ==[ start ]==> (((a a)(^b.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 197844/23612034. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((a (a (^x1.x1)))(a a))) 3. ==[ beta ]==> ((^y.y)((a (a (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y)))(a a))) 5. ==[ beta ]==> ((a (a (^y.y)))(a a)) 6. ==[ alpha ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 197845/23612043. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(x1 (^y1.y1))) b)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(b (^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (^x1.x1))) REDUCED to normal form. ------ 197846/23612088. ------ 1. ==[ start ]==> ((a (^a.(a a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.(x x)))((b (^y.y)) a)) REDUCED to normal form. ------ 197847/23612196. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((b a)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((b a)(a b))) 3. ==[ beta ]==> ((^y.(y y))((b a)(a b))) 4. ==[ alpha ]==> ((^x.(x x))((b a)(a b))) 5. ==[ beta ]==> (((b a)(a b))((b a)(a b))) REDUCED to normal form. ------ 197848/23612223. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((a a)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 197849/23612277. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a b)(b a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a b)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(b a))) 5. ==[ beta ]==> ((^y.y)((a b)(b a))) 6. ==[ alpha ]==> ((^x.x)((a b)(b a))) 7. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 197850/23612304. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> ((a (a a))(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> ((a (a a))(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 197851/23612331. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1) b)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z) b)) 7. ==[ beta ]==> ((^y.y)((^z.z) b)) 8. ==[ alpha ]==> ((^x.x)((^y.y) b)) 9. ==[ beta ]==> ((^y.y) b) 10. ==[ alpha ]==> ((^x.x) b) 11. ==[ beta ]==> b REDUCED to normal form. ------ 197852/23612385. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) a)(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) a)(b (^y.y)))) 5. ==[ beta ]==> (((a a)(a a))(a (b (^y.y)))) 6. ==[ alpha ]==> (((a a)(a a))(a (b (^x.x)))) REDUCED to normal form. ------ 197853/23612412. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((a (^z.z))(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.x1))) REDUCED to normal form. ------ 197854/23612430. ------ 1. ==[ start ]==> (((a a)(a (a a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(a (a a)))(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 197855/23612457. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 197856/23612484. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((a (a (^x.x)))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (a (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 197857/23612502. ------ 1. ==[ start ]==> (((^a.(a a)) b)(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) b)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b b)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b b)(((^x.(^y.y)) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((b b)((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b b)((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> ((b b)(^y.(^z.z))) 8. ==[ alpha ]==> ((b b)(^x.(^y.y))) REDUCED to normal form. ------ 197858/23612637. ------ 1. ==[ start ]==> (((a (a a)) b)((b a)(^a.b))) 2. ==[ alpha ]==> (((a (a a)) b)((b a)(^x.b))) REDUCED to normal form. ------ 197859/23612664. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (a (((a a)(^y.y))(^z.(a a)))) 6. ==[ alpha ]==> (a (((a a)(^x.x))(^y.(a a)))) REDUCED to normal form. ------ 197860/23612691. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 197861/23612745. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.a))(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.a))(((a a) a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 197862/23612772. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197863/23612835. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)(b (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 197864/23612862. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 197865/23612889. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((a a)((^y.y)(a (a (^z.z))))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (a (^y.y))))) 7. ==[ beta ]==> ((a a)(a (a (^y.y)))) 8. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 197866/23612916. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))((^x1.x1)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 197867/23613303. ------ 1. ==[ start ]==> ((a (^a.b))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((a (^x.b))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (^x.b))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.b))(b (^y.y))) REDUCED to normal form. ------ 197868/23613321. ------ 1. ==[ start ]==> (((a a)((a a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)((a a) a))((^x.x)(^y.(y (^z.z))))) 3. ==[ beta ]==> (((a a)((a a) a))(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))(^x.(x (^y.y)))) REDUCED to normal form. ------ 197869/23613492. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((b a)((a a) a))) 3. ==[ beta ]==> ((^y.b)((b a)((a a) a))) 4. ==[ alpha ]==> ((^x.b)((b a)((a a) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 197870/23613573. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((a b)((a a)(^z.z)))) IRREDUCIBLE: cycle. ------ 197871/23613654. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a (a a))((^z.z) b))) 3. ==[ beta ]==> (b ((a (a a))((^z.z) b))) 4. ==[ alpha ]==> (b ((a (a a))((^x.x) b))) 5. ==[ beta ]==> (b ((a (a a)) b)) REDUCED to normal form. ------ 197872/23613681. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> ((a b)(((^y.y) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a b)(((^x.x) a)((a a)(a a)))) 5. ==[ beta ]==> ((a b)(a ((a a)(a a)))) REDUCED to normal form. ------ 197873/23613708. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((a (^z.z))(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.z))(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(b (^z.z)))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 197874/23613771. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (a a))(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 197875/23613798. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((b (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.a))((b (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((b (^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.a)((b (^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.a)((b (^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 197876/23613825. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(a a))(^z.a))) REDUCED to normal form. ------ 197877/23613852. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a b)(^x.x))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a b)(^x.x))(b (^y.(y y)))) REDUCED to normal form. ------ 197878/23613888. ------ 1. ==[ start ]==> (((a a)(a b))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 197879/23613969. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a a)) REDUCED to normal form. ------ 197880/23613996. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.b)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.b)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.b)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)((^z.b)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.b)((a a)(^z.z)))) 7. ==[ beta ]==> (a ((^y.b)((a a)(^z.z)))) 8. ==[ alpha ]==> (a ((^x.b)((a a)(^y.y)))) 9. ==[ beta ]==> (a b) REDUCED to normal form. ------ 197881/23614041. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 197882/23614050. ------ 1. ==[ start ]==> (((a b)(a a))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b)(a a))(^y.y)) 4. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 197883/23614077. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(y y))((^z.z) b))) 3. ==[ beta ]==> ((a (a a))((^y.(y y))((^z.z) b))) 4. ==[ alpha ]==> ((a (a a))((^x.(x x))((^y.y) b))) 5. ==[ beta ]==> ((a (a a))(((^y.y) b)((^y.y) b))) 6. ==[ alpha ]==> ((a (a a))(((^x.x) b)((^y.y) b))) 7. ==[ beta ]==> ((a (a a))(b ((^y.y) b))) 8. ==[ alpha ]==> ((a (a a))(b ((^x.x) b))) 9. ==[ beta ]==> ((a (a a))(b b)) REDUCED to normal form. ------ 197884/23614788. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((a b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((a b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((^y.y)((a b)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((^x.x)((a b)((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)((^y.y)(a a))) 6. ==[ alpha ]==> ((a b)((^x.x)(a a))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 197885/23614923. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (b ((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (b ((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 197886/23614986. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((b (^y.y))(^z.z))) REDUCED to normal form. ------ 197887/23615040. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(b (^x1.a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(b (^z.a))) REDUCED to normal form. ------ 197888/23615067. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.b))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.b))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 197889/23615121. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((a a)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((a a)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197890/23615148. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))((a a)(^z.b))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a a)(^y.b))) REDUCED to normal form. ------ 197891/23615175. ------ 1. ==[ start ]==> (((a b)(^b.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((a b)(^y.(a a)))) REDUCED to normal form. ------ 197892/23615265. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 197893/23615292. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.a)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.a)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.a)((^z.z) b))) 5. ==[ beta ]==> (((a (^x.x))(a a)) a) REDUCED to normal form. ------ 197894/23615319. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))((a a)(a a)))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))((a a)(a a)))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))((a a)(a a)))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 197895/23615346. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.x)(b (^y.y)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(b (^y.y))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(b (^x.x))) REDUCED to normal form. ------ 197896/23615427. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^b.b)(^b.a))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.y)(^z.a))) 3. ==[ beta ]==> (((a b) a)((^y.y)(^z.a))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(^y.a))) 5. ==[ beta ]==> (((a b) a)(^y.a)) 6. ==[ alpha ]==> (((a b) a)(^x.a)) REDUCED to normal form. ------ 197897/23615454. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.(^z.z))) REDUCED to normal form. ------ 197898/23615508. ------ 1. ==[ start ]==> ((a (b a))((^c.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((a (b a))(^y.y)) 4. ==[ alpha ]==> ((a (b a))(^x.x)) REDUCED to normal form. ------ 197899/23615679. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))(c ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))(c ((^z.z) b))) 3. ==[ beta ]==> (b (c ((^z.z) b))) 4. ==[ alpha ]==> (b (c ((^x.x) b))) 5. ==[ beta ]==> (b (c b)) REDUCED to normal form. ------ 197900/23615787. ------ 1. ==[ start ]==> (((^a.a)(b a))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> ((b a)(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> ((b a)(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> ((b a)(b (a (^y.y)))) 6. ==[ alpha ]==> ((b a)(b (a (^x.x)))) REDUCED to normal form. ------ 197901/23615814. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((a (^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 197902/23615868. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a b))(((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a b)(a b))(((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (((a b)(a b))(((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 197903/23615949. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> (b (((a a) a)((^y.y)(a a)))) 4. ==[ alpha ]==> (b (((a a) a)((^x.x)(a a)))) 5. ==[ beta ]==> (b (((a a) a)(a a))) REDUCED to normal form. ------ 197904/23616057. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1)) b)) REDUCED to normal form. ------ 197905/23616075. ------ 1. ==[ start ]==> (((a a)(b a))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a a)(b a))(b (^x.(a a)))) REDUCED to normal form. ------ 197906/23616156. ------ 1. ==[ start ]==> (((a (a a))(a b))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))(a b))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))(a b))(a (^x.x))) REDUCED to normal form. ------ 197907/23616183. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 197908/23616237. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^c.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.y)) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.x)) REDUCED to normal form. ------ 197909/23616264. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(a a))((a a) a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(a a))((a a) a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(a a))((a a) a))) 5. ==[ beta ]==> (((a a) a)((^y.(a a))((a a) a))) 6. ==[ alpha ]==> (((a a) a)((^x.(a a))((a a) a))) 7. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 197910/23616291. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^a.b)(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.b)(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 197911/23616345. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 197912/23616813. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(a ((a a)(a a)))) 3. ==[ beta ]==> (b (a ((a a)(a a)))) REDUCED to normal form. ------ 197913/23616822. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^c.(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 197914/23616849. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^b.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.z) b)) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.z) b)) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.y) b)) 5. ==[ beta ]==> (((a a)(^x.(x x))) b) REDUCED to normal form. ------ 197915/23616876. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.x1))) REDUCED to normal form. ------ 197916/23616921. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((a a)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197917/23616948. ------ 1. ==[ start ]==> ((a (^b.b))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^x.x))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 197918/23617128. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(b (^b.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(b (^z.z))) 3. ==[ beta ]==> (((a b)(^y.y))(b (^z.z))) 4. ==[ alpha ]==> (((a b)(^x.x))(b (^y.y))) REDUCED to normal form. ------ 197919/23617182. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((^b.b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((^z.z)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((^z.z)(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((^y.y)(a a))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(a a)) REDUCED to normal form. ------ 197920/23617227. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((b a)(^x1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197921/23617263. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(a (a a)))) 3. ==[ beta ]==> ((a b)((^y.(^z.z))(a (a a)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 197922/23617551. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((b a) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((b a) c)) REDUCED to normal form. ------ 197923/23617758. ------ 1. ==[ start ]==> (((^a.b)((a a) a))(c (b a))) 2. ==[ alpha ]==> (((^x.b)((a a) a))(c (b a))) 3. ==[ beta ]==> (b (c (b a))) REDUCED to normal form. ------ 197924/23617821. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^b.b) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y))) a) REDUCED to normal form. ------ 197925/23617866. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((b a)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)(a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197926/23617902. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^c.(^a.a)) d)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) d)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) d)) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 197927/23618073. ------ 1. ==[ start ]==> ((((a a) a)(a b))(c (^d.a))) 2. ==[ alpha ]==> ((((a a) a)(a b))(c (^x.a))) REDUCED to normal form. ------ 197928/23618100. ------ 1. ==[ start ]==> (((a b)((a a) a))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((a a) a))(b (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 197929/23618127. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(a (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(a (^x1.x1))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(a (^x1.x1))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(a (^z.z))) 5. ==[ beta ]==> (((a a)(^y.y))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 197930/23618154. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.z))) REDUCED to normal form. ------ 197931/23618235. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((b (a a))((^y.(a a))(a (a a)))) 4. ==[ alpha ]==> ((b (a a))((^x.(a a))(a (a a)))) 5. ==[ beta ]==> ((b (a a))(a a)) REDUCED to normal form. ------ 197932/23618262. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(a a))) b) REDUCED to normal form. ------ 197933/23618703. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(b (b a))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(b (b a))) 3. ==[ beta ]==> (((b a)(b a))(b (b a))) REDUCED to normal form. ------ 197934/23618784. ------ 1. ==[ start ]==> (((^a.b)(a b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a b))(((a a)(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (b (((a a)(^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(a (^y.y)))) REDUCED to normal form. ------ 197935/23618793. ------ 1. ==[ start ]==> (((a b)(^a.b))((^c.(^a.a)) c)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.z)) c)) 3. ==[ beta ]==> (((a b)(^x.b))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.y)) REDUCED to normal form. ------ 197936/23618892. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1)(^z1.z1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(^z1.z1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197937/23619018. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x)) b)(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x)) b)(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 197938/23619072. ------ 1. ==[ start ]==> (((a (a a))(b a))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a))(b a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))(b a))(^x.x)) REDUCED to normal form. ------ 197939/23619099. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((^x1.(a a))((^y1.y1) a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((^x1.(a a))((^y1.y1) a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((^z.(a a))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^y.y))((^z.(a a))((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.(a a))((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 197940/23619126. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.b)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.b)(a (a a)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.b)(a (a a)))) 5. ==[ beta ]==> ((((a a) a)(a a)) b) REDUCED to normal form. ------ 197941/23619153. ------ 1. ==[ start ]==> (((a b)(a b))((^c.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a b)(a b)) a) REDUCED to normal form. ------ 197942/23619180. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 197943/23619207. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(z z))(a b))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a b)(a b))) REDUCED to normal form. ------ 197944/23619261. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))((a a)(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))((a a)(^y1.y1)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 197945/23619288. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.z)(b a))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.z)(b a))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.y)(b a))) 5. ==[ beta ]==> ((b (a (^x.x)))(b a)) REDUCED to normal form. ------ 197946/23619342. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^c.(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 197947/23619513. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))(c ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))(c ((^z.z)(a a)))) 3. ==[ beta ]==> (b (c ((^z.z)(a a)))) 4. ==[ alpha ]==> (b (c ((^x.x)(a a)))) 5. ==[ beta ]==> (b (c (a a))) REDUCED to normal form. ------ 197948/23619621. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((^y1.y1)(a a))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197949/23619657. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^a.b) d)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.b) d)) 3. ==[ beta ]==> ((b c)((^y.b) d)) 4. ==[ alpha ]==> ((b c)((^x.b) d)) 5. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 197950/23619729. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a (a a))((a a) a))) 3. ==[ beta ]==> ((b (^y.y))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((b (^x.x))((a (a a))((a a) a))) REDUCED to normal form. ------ 197951/23619756. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z) a)(a b))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)(a b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(a b))) 5. ==[ beta ]==> (((^y.y) a)(a b)) 6. ==[ alpha ]==> (((^x.x) a)(a b)) 7. ==[ beta ]==> (a (a b)) REDUCED to normal form. ------ 197952/23619810. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a a)((a a)(^y1.y1)))) REDUCED to normal form. ------ 197953/23619900. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((a b)(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((a b)(^y.a))) REDUCED to normal form. ------ 197954/23619927. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a) a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.b))(((a a) a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a) a)(^y.(y y)))) REDUCED to normal form. ------ 197955/23620008. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1) a)(^y1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^y1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(a (^x1.b))) REDUCED to normal form. ------ 197956/23620035. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((b (^y.a))((a (^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((b (^x.a))((a (^y.y))(^z.(a a)))) REDUCED to normal form. ------ 197957/23620125. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(a a)) REDUCED to normal form. ------ 197958/23620152. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.b)(^z.a))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a))) b) REDUCED to normal form. ------ 197959/23620179. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((a b)((^y.a)(^z.(z z)))) 6. ==[ alpha ]==> ((a b)((^x.a)(^y.(y y)))) 7. ==[ beta ]==> ((a b) a) REDUCED to normal form. ------ 197960/23620206. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 197961/23620233. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(z z))(^x1.a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(z z))(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(y y))(^z.a))) 5. ==[ beta ]==> ((b a)((^y.(y y))(^z.a))) 6. ==[ alpha ]==> ((b a)((^x.(x x))(^y.a))) 7. ==[ beta ]==> ((b a)((^y.a)(^y.a))) 8. ==[ alpha ]==> ((b a)((^x.a)(^y.a))) 9. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 197962/23620260. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.a)(^z.b))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x))) a) REDUCED to normal form. ------ 197963/23620287. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 197964/23620314. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.y)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a b))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a b))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a b))(^x.(^y.y))) REDUCED to normal form. ------ 197965/23620944. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))(c ((a a) a))) 3. ==[ beta ]==> ((^y.y)(c ((a a) a))) 4. ==[ alpha ]==> ((^x.x)(c ((a a) a))) 5. ==[ beta ]==> (c ((a a) a)) REDUCED to normal form. ------ 197966/23620998. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(a ((^z.z)(a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(a ((^z.z)(a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))(a ((^z.z)(a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(a ((^y.y)(a a)))) 7. ==[ beta ]==> ((b b)(a ((^y.y)(a a)))) 8. ==[ alpha ]==> ((b b)(a ((^x.x)(a a)))) 9. ==[ beta ]==> ((b b)(a (a a))) REDUCED to normal form. ------ 197967/23621007. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(a a)) a)) 3. ==[ beta ]==> (((a (a a))(^x.x))(a a)) REDUCED to normal form. ------ 197968/23621034. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.b) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.b) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b) b)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b) b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b) b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 197969/23621079. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))((^z.z) a))) 5. ==[ beta ]==> (b ((^y.y)((^z.z) a))) 6. ==[ alpha ]==> (b ((^x.x)((^y.y) a))) 7. ==[ beta ]==> (b ((^y.y) a)) 8. ==[ alpha ]==> (b ((^x.x) a)) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 197970/23621088. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(^a.a)) d)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1)) d)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 197971/23621187. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a a)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197972/23621223. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a b)(^z.z))) 3. ==[ beta ]==> ((b (^y.(y y)))((a b)(^z.z))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a b)(^y.y))) REDUCED to normal form. ------ 197973/23621250. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(((a a) a)(^y.(^z.z)))) REDUCED to normal form. ------ 197974/23621304. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a (a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.(z z)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(y y)))) 7. ==[ beta ]==> ((a (a a))(^y.(y y))) 8. ==[ alpha ]==> ((a (a a))(^x.(x x))) REDUCED to normal form. ------ 197975/23621340. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x)) a) REDUCED to normal form. ------ 197976/23621367. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 197977/23621394. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.y)(a b))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.y)(a b))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.x)(a b))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a b)) REDUCED to normal form. ------ 197978/23621421. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a (a a)) b)((^y.b)(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.b)(^y.y))) 5. ==[ beta ]==> (((a (a a)) b) b) REDUCED to normal form. ------ 197979/23621475. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.(^y.y))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(b a))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(b a))(^x.x)) REDUCED to normal form. ------ 197980/23621502. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 197981/23621529. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 197982/23621556. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 197983/23621745. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(b (^c.a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(b (^y.a))) REDUCED to normal form. ------ 197984/23621754. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a a)((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a a)((a a) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a a)((a a) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a a)((a a) a))) 5. ==[ beta ]==> (((a a)((a a) a))(^y.y)) 6. ==[ alpha ]==> (((a a)((a a) a))(^x.x)) REDUCED to normal form. ------ 197985/23622141. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^b.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z)) b)) 5. ==[ beta ]==> (b ((^y.(^z.z)) b)) 6. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 197986/23622159. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((a (a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))((a (a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(a (^z.z)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(a (^z.z)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.y)))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 197987/23622186. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z) a)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> ((a (a (^x.x)))(a ((^z.z) a))) 6. ==[ alpha ]==> ((a (a (^x.x)))(a ((^y.y) a))) 7. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 197988/23622213. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (^y1.y1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))(a (a a))) 6. ==[ alpha ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 197989/23622303. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a (a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a (a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a (a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a (a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 197990/23622330. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1) a)(^y1.a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^y1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(a (^x1.a))) REDUCED to normal form. ------ 197991/23622348. ------ 1. ==[ start ]==> (((^a.b)(b a))(c d)) 2. ==[ alpha ]==> (((^x.b)(b a))(c d)) 3. ==[ beta ]==> (b (c d)) REDUCED to normal form. ------ 197992/23622411. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z)(^x1.x1)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))((^x1.x1) a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z) a)) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 197993/23622573. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(a a)) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(y1 y1)) b)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(y1 y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 x1)) b)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1)) b)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z)) b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 197994/23622591. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (a (^z.z)))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (a (^y.y)))) REDUCED to normal form. ------ 197995/23622600. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^b.a) c)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.a) c)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y)) a) REDUCED to normal form. ------ 197996/23622618. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a (^x1.x1)) a)) REDUCED to normal form. ------ 197997/23622636. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(b (^y.(y y)))) REDUCED to normal form. ------ 197998/23622663. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 197999/23622690. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((^z.(z z))(a a))) 3. ==[ beta ]==> ((a (b (^y.y)))((^z.(z z))(a a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((^y.(y y))(a a))) 5. ==[ beta ]==> ((a (b (^x.x)))((a a)(a a))) REDUCED to normal form. ------ 198000/23622717. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.a)(a (^y.y)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a))) a) REDUCED to normal form. ------ 198001/23622744. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> (b ((^y.(^z.z))((^x1.x1) a))) 8. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z) a))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198002/23622771. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a (a a))) REDUCED to normal form. ------ 198003/23622798. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.(x x))(^y.y))) 3. ==[ beta ]==> (((a b)(b a))((^y.y)(^y.y))) 4. ==[ alpha ]==> (((a b)(b a))((^x.x)(^y.y))) 5. ==[ beta ]==> (((a b)(b a))(^y.y)) 6. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 198004/23622825. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x))) a) REDUCED to normal form. ------ 198005/23622852. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 198006/23622933. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(c (^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(c (^z.(^x1.x1)))) 5. ==[ beta ]==> ((b (^y.y))(c (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((b (^x.x))(c (^y.(^z.z)))) REDUCED to normal form. ------ 198007/23622960. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(b (^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(b (^x.a))) REDUCED to normal form. ------ 198008/23623014. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((^b.a)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((^x1.a)(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((^x1.a)(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.a)(a a))) 5. ==[ beta ]==> ((a (^y.y))((^z.a)(a a))) 6. ==[ alpha ]==> ((a (^x.x))((^y.a)(a a))) 7. ==[ beta ]==> ((a (^x.x)) a) REDUCED to normal form. ------ 198009/23623032. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 198010/23623041. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.y)) REDUCED to normal form. ------ 198011/23623068. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.x1)((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 198012/23623239. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(c a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(c a)) 3. ==[ beta ]==> (b (c a)) REDUCED to normal form. ------ 198013/23623347. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(a (a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(a (a (^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198014/23623482. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(a a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(a a)) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(a a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a a)) 5. ==[ beta ]==> ((^y.y)(a a)) 6. ==[ alpha ]==> ((^x.x)(a a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198015/23623490. ------ 1. ==[ start ]==> (^a.((a (a (^a.a))) b)) 2. ==[ alpha ]==> (^x.((x (x (^y.y))) b)) REDUCED to normal form. ------ 198016/23623491. ------ 1. ==[ start ]==> (a ((a (a (^a.a))) b)) 2. ==[ alpha ]==> (a ((a (a (^x.x))) b)) REDUCED to normal form. ------ 198017/23635386. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a))) b) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1))) b) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y)) b) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z)) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 198018/23635395. ------ 1. ==[ start ]==> (((a (a (^a.a))) b) a) 2. ==[ alpha ]==> (((a (a (^x.x))) b) a) REDUCED to normal form. ------ 198019/23635401. ------ 1. ==[ start ]==> ((^a.a)((a (a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) b)) 3. ==[ beta ]==> ((a (a (^y.y))) b) 4. ==[ alpha ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 198020/23635410. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198021/23635653. ------ 1. ==[ start ]==> ((^a.(^b.a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.((^z.b)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (^x.((^y.b)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^x.b) REDUCED to normal form. ------ 198022/23635818. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) a)(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) a)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (a (^y.(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 198023/23635827. ------ 1. ==[ start ]==> (((a a)(^b.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.a))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 198024/23636346. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198025/23636778. ------ 1. ==[ start ]==> ((^a.((a a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((^x.((x x) x))((b (^y.y)) c)) 3. ==[ beta ]==> ((((b (^y.y)) c)((b (^y.y)) c))((b (^y.y)) c)) 4. ==[ alpha ]==> ((((b (^x.x)) c)((b (^y.y)) c))((b (^z.z)) c)) REDUCED to normal form. ------ 198026/23637555. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^z.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 198027/23637573. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 198028/23637678. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (^y.(((^z.z)(a (a a)))((^z.z)(a (a a))))) 4. ==[ alpha ]==> (^x.(((^y.y)(a (a a)))((^z.z)(a (a a))))) 5. ==[ beta ]==> (^x.((a (a a))((^z.z)(a (a a))))) 6. ==[ alpha ]==> (^x.((a (a a))((^y.y)(a (a a))))) 7. ==[ beta ]==> (^x.((a (a a))(a (a a)))) REDUCED to normal form. ------ 198029/23637885. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a (a a))(^z.z))) 3. ==[ beta ]==> ((^y.y)(((a (a a))(^z.z))((a (a a))(^z.z)))) 4. ==[ alpha ]==> ((^x.x)(((a (a a))(^y.y))((a (a a))(^z.z)))) 5. ==[ beta ]==> (((a (a a))(^y.y))((a (a a))(^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 198030/23637978. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(^y1.((^z1.(^x2.x2)) a))) 5. ==[ beta ]==> ((^y.y)(^y1.((^z1.(^x2.x2)) a))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.(^x1.x1)) a))) 7. ==[ beta ]==> (^y.((^z.(^x1.x1)) a)) 8. ==[ alpha ]==> (^x.((^y.(^z.z)) a)) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198031/23638770. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(^c.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(^y.(b (^z.z)))) 3. ==[ beta ]==> (((a a) b)(^y.(b (^z.z)))) 4. ==[ alpha ]==> (((a a) b)(^x.(b (^y.y)))) REDUCED to normal form. ------ 198032/23639553. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(^a.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.(b (^z.z)))) REDUCED to normal form. ------ 198033/23640624. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (b (^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 198034/23640633. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((z z)(z z)))) REDUCED to normal form. ------ 198035/23641071. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 198036/23641632. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^z.b)) REDUCED to normal form. ------ 198037/23642070. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((a b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a b)(^y.(^z.z)))((a b)(^y.(^z.z))))(((a b)(^y.(^z.z)))((a b)(^y.(^z.z))))) 4. ==[ alpha ]==> ((((a b)(^x.(^y.y)))((a b)(^z.(^x1.x1))))(((a b)(^y1.(^z1.z1)))((a b)(^x2.(^y2.y2))))) REDUCED to normal form. ------ 198038/23642244. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^b.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^z.(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(a (^y.(^z.z))))) REDUCED to normal form. ------ 198039/23643099. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(^c.(^d.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(^z.(^x1.a))) 3. ==[ beta ]==> ((b (a (^y.y)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((b (a (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 198040/23643150. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(((a a)(^z.z)) b)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198041/23644593. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^b.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198042/23644809. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(^z.(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(^z.(^x1.(a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))(^z.(^x1.(a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))(^y.(^z.(a a)))) 7. ==[ beta ]==> ((b b)(^y.(^z.(a a)))) 8. ==[ alpha ]==> ((b b)(^x.(^y.(a a)))) REDUCED to normal form. ------ 198043/23644818. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.((^z.z)(y y)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^y.(y y))) REDUCED to normal form. ------ 198044/23645007. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(^c.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(a b))) REDUCED to normal form. ------ 198045/23645130. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(x1 x1))(a (a a)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 198046/23646426. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(c (^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(c (^y1.a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198047/23646876. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198048/23646888. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((^y1.y1) a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198049/23647050. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(^z1.y1))) 3. ==[ beta ]==> (b (^y1.(^z1.y1))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 198050/23647158. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^b.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198051/23647293. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198052/23647302. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^a.a)) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.y)) REDUCED to normal form. ------ 198053/23647314. ------ 1. ==[ start ]==> ((a a)((a (a (^a.a))) b)) 2. ==[ alpha ]==> ((a a)((a (a (^x.x))) b)) REDUCED to normal form. ------ 198054/23647323. ------ 1. ==[ start ]==> ((a (^a.a))((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.x))((^x1.(^y1.y1))(^z.z))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 198055/23647458. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198056/23647566. ------ 1. ==[ start ]==> ((a (^b.a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.a))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 198057/23647683. ------ 1. ==[ start ]==> (((a (^a.a)) b)(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x)) b)(c ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (^x.x)) b)(c (^z.z))) 4. ==[ alpha ]==> (((a (^x.x)) b)(c (^y.y))) REDUCED to normal form. ------ 198058/23647710. ------ 1. ==[ start ]==> ((((^a.a) a) a)(b (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)(b (a (a (^y.y))))) 3. ==[ beta ]==> ((a a)(b (a (a (^y.y))))) 4. ==[ alpha ]==> ((a a)(b (a (a (^x.x))))) REDUCED to normal form. ------ 198059/23647728. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (a (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 198060/23647737. ------ 1. ==[ start ]==> (((a a)(^b.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^x.a))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(a (^y.(^z.z)))) REDUCED to normal form. ------ 198061/23647764. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((a (a (^x1.x1)))(a a))) REDUCED to normal form. ------ 198062/23647791. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (^z.z)))) 7. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 198063/23647899. ------ 1. ==[ start ]==> (((^a.(a a)) a)((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x)) a)((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> ((a a)((a (^y.(^z.z)))((a a) a))) 4. ==[ alpha ]==> ((a a)((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 198064/23647980. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a b)(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a b)(((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a b)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 198065/23648007. ------ 1. ==[ start ]==> (((a (a a)) a)((a b)(b a))) REDUCED to normal form. ------ 198066/23648034. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((a a) a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 198067/23648061. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (((a (^x.x))(^y.a))((^x1.x1) b)) 6. ==[ alpha ]==> (((a (^x.x))(^y.a))((^z.z) b)) 7. ==[ beta ]==> (((a (^x.x))(^y.a)) b) REDUCED to normal form. ------ 198068/23648088. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (a a))((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 198069/23648115. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y) a)(b (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (b (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a (b (^y.y)))) REDUCED to normal form. ------ 198070/23648205. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 198071/23648232. ------ 1. ==[ start ]==> (((a (a a))(a a))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a a))(((^x.(^y.y)) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (((a (a a))(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.y))) REDUCED to normal form. ------ 198072/23648259. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b (^z.z))(^x1.a))) 3. ==[ beta ]==> ((a (^y.y))((b (^z.z))(^x1.a))) 4. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(^z.a))) REDUCED to normal form. ------ 198073/23648349. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))((a a) a))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.(^x2.x2)))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198074/23648430. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((^y.(a a))((a a)(^z.z))) 6. ==[ alpha ]==> ((^x.(a a))((a a)(^y.y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198075/23648610. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a ((^y.y) a))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a ((^x.x) a))((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)((a a)(^y.(y (^z.z))))) 6. ==[ alpha ]==> ((a a)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 198076/23648637. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a (a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a (a (^y.y))) a)) REDUCED to normal form. ------ 198077/23648664. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(((^z.(^x1.x1)) a) b)) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.(^x1.x1)) a) b)) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> ((a a)(((^y.(^z.z)) a) b)) 6. ==[ alpha ]==> ((a a)(((^x.(^y.y)) a) b)) 7. ==[ beta ]==> ((a a)((^y.y) b)) 8. ==[ alpha ]==> ((a a)((^x.x) b)) 9. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 198078/23648691. ------ 1. ==[ start ]==> ((a ((a a) a))((b (^a.a)) c)) 2. ==[ alpha ]==> ((a ((a a) a))((b (^x.x)) c)) REDUCED to normal form. ------ 198079/23648727. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(z z)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(z z))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(y y))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198080/23648781. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(^x1.(^y1.y1)))(^z1.a))) 5. ==[ beta ]==> (a ((^z.(^x1.(^y1.y1)))(^z1.a))) 6. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 198081/23648862. ------ 1. ==[ start ]==> (((^a.a)((a a) a))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a) a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a) a)(a a)) REDUCED to normal form. ------ 198082/23648943. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((((^y.y) a)((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.x1))) 7. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.x1))) 8. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 198083/23649069. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.(x1 (^y1.y1))) a)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.(x1 (^y1.y1))) a)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z (^x1.x1))) a)) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 198084/23649195. ------ 1. ==[ start ]==> (((^a.b) a)((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) a)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (b ((a (^x.(^y.y)))(^x1.x1))) 6. ==[ alpha ]==> (b ((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 198085/23649357. ------ 1. ==[ start ]==> ((((a a) a) b)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a) b)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((((a a) a) b)((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((((a a) a) b)((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> ((((a a) a) b)(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((((a a) a) b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 198086/23649384. ------ 1. ==[ start ]==> (((a b) a)((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a b) a)((a (a a))((^x.x) b))) 3. ==[ beta ]==> (((a b) a)((a (a a)) b)) REDUCED to normal form. ------ 198087/23649411. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^x.b))(a ((a a)(a a)))) REDUCED to normal form. ------ 198088/23649465. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((a a)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.z))) REDUCED to normal form. ------ 198089/23649483. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(a (^y.(y (^z.z))))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(a (^y.(y (^z.z))))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(a (^x.(x (^y.y))))) REDUCED to normal form. ------ 198090/23649564. ------ 1. ==[ start ]==> (((^a.b)(a a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(a a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (b ((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 198091/23649591. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.y)(a (a a)))) 3. ==[ beta ]==> ((a (^x.(a a)))(a (a a))) REDUCED to normal form. ------ 198092/23649609. ------ 1. ==[ start ]==> (((a a)(a b))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(a b))((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 198093/23649636. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((b a)(^y.a))) REDUCED to normal form. ------ 198094/23649663. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(^z.b))) REDUCED to normal form. ------ 198095/23649690. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x)(a a))(^y.(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(^y.(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)(^x.(a a)))) REDUCED to normal form. ------ 198096/23649717. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((a b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) a)((a b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) a)((a b)(^y.(^z.z)))) 7. ==[ beta ]==> (a ((a b)(^y.(^z.z)))) 8. ==[ alpha ]==> (a ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 198097/23649771. ------ 1. ==[ start ]==> (((a b)(a a))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(a a))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(a a))((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(a a))((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (((a b)(a a))(^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a b)(a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 198098/23649798. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (a a))(^y.y))) 3. ==[ beta ]==> ((a (a a))((a (a a))(^y.y))) 4. ==[ alpha ]==> ((a (a a))((a (a a))(^x.x))) REDUCED to normal form. ------ 198099/23649807. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(z z))((^x1.x1) b))) 3. ==[ beta ]==> ((^y.(a a))((^z.(z z))((^x1.x1) b))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198100/23649834. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.a)((a a)(a a))) 6. ==[ alpha ]==> ((^x.a)((a a)(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198101/23649888. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.(^x2.x2)) a))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.(^x2.x2)) a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) a)) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) a)) 9. ==[ beta ]==> ((^y.(^z.z)) a) 10. ==[ alpha ]==> ((^x.(^y.y)) a) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198102/23649969. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 198103/23650023. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 198104/23650104. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(^z.z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> ((((^y.y)(^z.z))((^y.y)(^z.z)))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(^z1.(a a)))) 5. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(a a))(^z1.(a a)))) 6. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(a a))(^y1.(a a)))) 7. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(a a))(^y1.(a a)))) 8. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(^x1.(a a)))) 9. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.(a a)))) 10. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(a a)))) 11. ==[ beta ]==> ((^y.(a a))(^z.(a a))) 12. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 13. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198105/23650185. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198106/23650410. ------ 1. ==[ start ]==> (((^a.b) c)((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.b) c)((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (b ((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (b ((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 198107/23650644. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(c (^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(c (^z.(a a)))) 3. ==[ beta ]==> (b (c (^z.(a a)))) 4. ==[ alpha ]==> (b (c (^x.(a a)))) REDUCED to normal form. ------ 198108/23650653. ------ 1. ==[ start ]==> (((a b) c)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a b) c)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 198109/23650680. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a a)(b (^y.y)))) 3. ==[ beta ]==> (((a a) b)((a a)(b (^y.y)))) 4. ==[ alpha ]==> (((a a) b)((a a)(b (^x.x)))) REDUCED to normal form. ------ 198110/23650806. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.(^z.(^x1.x1)))(a (a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.(^y.(^z.z)))(a (a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 198111/23650887. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(a a))(a b))) 3. ==[ beta ]==> (b ((^z.(a a))(a b))) 4. ==[ alpha ]==> (b ((^x.(a a))(a b))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 198112/23650986. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 198113/23651013. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.x))(a a))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))(a a))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a a))(a (^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(a a))(a (^y.y))) REDUCED to normal form. ------ 198114/23651040. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (^y.y))(^z.(a a)))) 3. ==[ beta ]==> ((a (a b))((a (^y.y))(^z.(a a)))) 4. ==[ alpha ]==> ((a (a b))((a (^x.x))(^y.(a a)))) REDUCED to normal form. ------ 198115/23651094. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((b (^y1.y1)) a)) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((b (^y1.y1)) a)) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b (^x1.x1)) a)) 5. ==[ beta ]==> (((^y.y)(^z.z))((b (^x1.x1)) a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))((b (^z.z)) a)) 7. ==[ beta ]==> ((^y.y)((b (^z.z)) a)) 8. ==[ alpha ]==> ((^x.x)((b (^y.y)) a)) 9. ==[ beta ]==> ((b (^y.y)) a) 10. ==[ alpha ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 198116/23651121. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(((a a)(a a)) b)) REDUCED to normal form. ------ 198117/23651148. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((^a.a) b) c)) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((^y.y) b) c)) 3. ==[ beta ]==> (((a b) a)(((^y.y) b) c)) 4. ==[ alpha ]==> (((a b) a)(((^x.x) b) c)) 5. ==[ beta ]==> (((a b) a)(b c)) REDUCED to normal form. ------ 198118/23651319. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^c.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b ((^z.a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.a)(^y.(^z.z)))) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198119/23651400. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^b.a)(^b.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.a)(^x1.x1))) 3. ==[ beta ]==> (b ((^z.a)(^x1.x1))) 4. ==[ alpha ]==> (b ((^x.a)(^y.y))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198120/23651463. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(a (b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(a (b (^y.y)))) REDUCED to normal form. ------ 198121/23651571. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((b a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((b a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.(a a)))((b a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.(a a)))((b a)(a (a a)))) REDUCED to normal form. ------ 198122/23651598. ------ 1. ==[ start ]==> (((a (a a))(^a.b))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.b))(((a a)(^y.y))(^x1.x1))) 4. ==[ alpha ]==> (((a (a a))(^x.b))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 198123/23651652. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))((a b)(a b))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((a b)(a b))) REDUCED to normal form. ------ 198124/23651679. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((a a) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(^x.(x x)))(((a a) a)(a a))) REDUCED to normal form. ------ 198125/23651706. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.a))(((^z.z)(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((^y.y)(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.a))((^z.z)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.a))((^y.y)((a a)(^z.z)))) 7. ==[ beta ]==> (((a a)(^x.a))((a a)(^z.z))) 8. ==[ alpha ]==> (((a a)(^x.a))((a a)(^y.y))) REDUCED to normal form. ------ 198126/23651733. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))((a (a a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a (a a))(b a))) REDUCED to normal form. ------ 198127/23651850. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(((a a)(a a))(^y.y))) 5. ==[ beta ]==> ((a (a a))(((a a)(a a))(^y.y))) 6. ==[ alpha ]==> ((a (a a))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 198128/23651877. ------ 1. ==[ start ]==> (((a (a a))(a b))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))(a b))(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a b))(b (^x.(^y.y)))) REDUCED to normal form. ------ 198129/23651904. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> (((^y.y)((a a) a))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((a (^y.(^z.z)))(^x1.a))) 5. ==[ beta ]==> (((a a) a)((a (^y.(^z.z)))(^x1.a))) 6. ==[ alpha ]==> (((a a) a)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 198130/23651931. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((b a)(^z.(z z)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((b a)(^z.(z z)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((b a)(^y.(y y)))) REDUCED to normal form. ------ 198131/23651958. ------ 1. ==[ start ]==> (((a b)(a (a a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 198132/23652012. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((a b)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((a b)(^z.b))) REDUCED to normal form. ------ 198133/23652075. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^b.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))((a a)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))((a a)(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198134/23652156. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.z) b))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 198135/23652237. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^b.b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 198136/23652345. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198137/23652372. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.b)(^y1.b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)(^y1.b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.b))) 5. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 198138/23652399. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.(a a)))) 5. ==[ beta ]==> ((^y.a)(^z.(a a))) 6. ==[ alpha ]==> ((^x.a)(^y.(a a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198139/23652489. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))(c (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.b))(c (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))(c (a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((^y.b)(c (a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((^x.b)(c (a (^y.(^z.z))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 198140/23652534. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.x1)(^y1.(a a)))) 3. ==[ beta ]==> (b ((^x1.x1)(^y1.(a a)))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 5. ==[ beta ]==> (b (^y.(a a))) 6. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 198141/23652543. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 198142/23652570. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(((^z.z) b)(a a))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(((^z.z) b)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y) b)(a a))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(b (a a))) REDUCED to normal form. ------ 198143/23652597. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((a (^z.(^x1.x1)))(a (^y1.y1)))) REDUCED to normal form. ------ 198144/23652651. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(((a a)(^x1.x1))(a (a a)))) REDUCED to normal form. ------ 198145/23652903. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(((^z.z) b)(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(((^y.y) b)(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)(b (^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.y))) REDUCED to normal form. ------ 198146/23652957. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((b a)(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((b a)(^z.a))) REDUCED to normal form. ------ 198147/23652984. ------ 1. ==[ start ]==> ((a ((^a.a) b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))(((a a)(^y.y))(^z.(z z)))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))(^z.(z z)))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))(^y.(y y)))) REDUCED to normal form. ------ 198148/23652993. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^c.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198149/23653020. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((^b.(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(a a))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)((^z1.(a a))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))((^y.y)(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198150/23653155. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.a)(b a))) 3. ==[ beta ]==> (b ((^z.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198151/23653263. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.(^y2.y2)))(^z2.(^x3.x3)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198152/23653317. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198153/23653344. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198154/23653488. ------ 1. ==[ start ]==> (((a b)(^c.a))(c (b a))) 2. ==[ alpha ]==> (((a b)(^x.a))(c (b a))) REDUCED to normal form. ------ 198155/23653515. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(b (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(b (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 198156/23653542. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(a ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(a ((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(a b)) REDUCED to normal form. ------ 198157/23653596. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((b a)(a (^y1.y1)))) REDUCED to normal form. ------ 198158/23653623. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(((a a)(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))(((a a)(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))(((a a)(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 198159/23653875. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a (^y.(^z.z)))(^x1.x1))) REDUCED to normal form. ------ 198160/23653929. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(((a a)(^x1.x1))(^y1.a))) REDUCED to normal form. ------ 198161/23653956. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> ((b (a a))(((^y.y)(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b (a a))(((^x.x)(a a))(^y.(y y)))) 5. ==[ beta ]==> ((b (a a))((a a)(^y.(y y)))) 6. ==[ alpha ]==> ((b (a a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 198162/23653983. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 198163/23654019. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^c.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.a)((a a) a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)((a a) a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)((a a) a))) 5. ==[ beta ]==> ((^y.a)((a a) a)) 6. ==[ alpha ]==> ((^x.a)((a a) a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198164/23654154. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.z)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 198165/23654262. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(a a))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(a a))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198166/23654343. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.b))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.b))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 198167/23654370. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(x1 x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(a a)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(a a))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(a a))) 7. ==[ beta ]==> ((^y.(a a))(^y.(a a))) 8. ==[ alpha ]==> ((^x.(a a))(^y.(a a))) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198168/23654487. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((b a)(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((b a)(a a))) REDUCED to normal form. ------ 198169/23654514. ------ 1. ==[ start ]==> (((a b)(^a.b))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.b))(((a a)(^y.y))(a (^z.z)))) REDUCED to normal form. ------ 198170/23654568. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((a b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a b)(a (a a)))) REDUCED to normal form. ------ 198171/23654622. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((^y1.y1)((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((^x1.x1)((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))((a a) a)) REDUCED to normal form. ------ 198172/23654649. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))((a (a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a))(a b))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a))(a b))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a))(a b))) REDUCED to normal form. ------ 198173/23654676. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y) a)((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))(a ((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))(a ((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.x))(a (a a))) REDUCED to normal form. ------ 198174/23654766. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((b a)(^x1.x1))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((b a)(^x1.x1))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((b a)(^z.z))) REDUCED to normal form. ------ 198175/23654793. ------ 1. ==[ start ]==> (((a (a a))(b a))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(b a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 198176/23654820. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((^x1.x1)(a a))(^y1.a))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((^x1.x1)(a a))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((^z.z)(a a))(^x1.a))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(a a))(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(a a))(^z.a))) 7. ==[ beta ]==> (((a a)(^x.x))((a a)(^z.a))) 8. ==[ alpha ]==> (((a a)(^x.x))((a a)(^y.a))) REDUCED to normal form. ------ 198177/23654847. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((a b)(^y.(y y)))) 3. ==[ beta ]==> ((((a a) a)(a a))((a b)(^y.(y y)))) 4. ==[ alpha ]==> ((((a a) a)(a a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 198178/23654874. ------ 1. ==[ start ]==> (((a b)(a b))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 198179/23654928. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((a (a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((a (a a))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((a (a a))(^x1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a (a a))(^z.b))) REDUCED to normal form. ------ 198180/23655036. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((b a) a)) REDUCED to normal form. ------ 198181/23655063. ------ 1. ==[ start ]==> ((a (b (^a.a)))(((a a)(^a.a)) b)) 2. ==[ alpha ]==> ((a (b (^x.x)))(((a a)(^y.y)) b)) REDUCED to normal form. ------ 198182/23655234. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.a)(^x1.(a a)))) 3. ==[ beta ]==> (b ((^z.a)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198183/23655378. ------ 1. ==[ start ]==> ((((^a.a) b) c)((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b) c)((a b)((^y.y) a))) 3. ==[ beta ]==> ((b c)((a b)((^y.y) a))) 4. ==[ alpha ]==> ((b c)((a b)((^x.x) a))) 5. ==[ beta ]==> ((b c)((a b) a)) REDUCED to normal form. ------ 198184/23655405. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((a a) a)(a (a a)))) REDUCED to normal form. ------ 198185/23655513. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.y))(a a))) REDUCED to normal form. ------ 198186/23655531. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(b (^y1.(^z1.z1)))) REDUCED to normal form. ------ 198187/23655540. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a a)((a a)(^x1.x1)))) REDUCED to normal form. ------ 198188/23655612. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (b ((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(a (^y.y)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 198189/23655720. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198190/23655846. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a a) b)) REDUCED to normal form. ------ 198191/23655873. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((a b) c)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a b) c)) REDUCED to normal form. ------ 198192/23656116. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^a.b) c)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.b) c)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a))) b) REDUCED to normal form. ------ 198193/23656143. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^c.a) d)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.a) d)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.a) d)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.a) d)) 5. ==[ beta ]==> ((b a)((^y.a) d)) 6. ==[ alpha ]==> ((b a)((^x.a) d)) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 198194/23656314. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((^b.(a a))(a a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((^z.(a a))(a a))) 3. ==[ beta ]==> (((^y.y)(^y.y))((^z.(a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(a a))(a a))) 5. ==[ beta ]==> ((^y.y)((^z.(a a))(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.(a a))(a a))) 7. ==[ beta ]==> ((^y.(a a))(a a)) 8. ==[ alpha ]==> ((^x.(a a))(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198195/23656395. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^b.(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(^y1.y1))(a (a a)))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a (a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198196/23656503. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)((^x2.x2)(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)((^x2.x2)(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198197/23656638. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(z z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 9. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 10. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198198/23656665. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198199/23656719. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.z)(^x1.(a a)))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.z)(^x1.(a a)))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.z)(^x1.(a a)))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.y)(^z.(a a)))) 7. ==[ beta ]==> ((b b)((^y.y)(^z.(a a)))) 8. ==[ alpha ]==> ((b b)((^x.x)(^y.(a a)))) 9. ==[ beta ]==> ((b b)(^y.(a a))) 10. ==[ alpha ]==> ((b b)(^x.(a a))) REDUCED to normal form. ------ 198200/23656728. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(a ((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(a (a a))) REDUCED to normal form. ------ 198201/23656755. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((a b)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((a b)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((a b)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a b)(a a))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a b)(a a))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(a a))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198202/23656809. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> (((a b)(^x.(^y.y)))((^x1.x1) a)) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 198203/23656836. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((a (a a))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))((a (a a))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 198204/23656863. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))(a (^x1.x1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(a (^z.z))) REDUCED to normal form. ------ 198205/23656908. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(b (^z1.b))) 3. ==[ beta ]==> ((^y.(^z.z))(b (^z1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198206/23656917. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a a)(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a a)(a b))) REDUCED to normal form. ------ 198207/23657043. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((a (a a))(a (a a)))) REDUCED to normal form. ------ 198208/23657061. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 198209/23657088. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 198210/23657115. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((a a)(^y.b))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a)(^y.b))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a a)(^x.b))) REDUCED to normal form. ------ 198211/23657142. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a b) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a b) a)) 3. ==[ beta ]==> (((a (a a)) b)((a b) a)) REDUCED to normal form. ------ 198212/23657169. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(((a a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(((a a) a) b)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))(((a a) a) b)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))(((a a) a) b)) 5. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a) b)) REDUCED to normal form. ------ 198213/23657196. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> ((((a a) a)(b a))(((^x.x)(^y.y)) c)) 3. ==[ beta ]==> ((((a a) a)(b a))((^y.y) c)) 4. ==[ alpha ]==> ((((a a) a)(b a))((^x.x) c)) 5. ==[ beta ]==> ((((a a) a)(b a)) c) REDUCED to normal form. ------ 198214/23657331. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.b) a)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.b) a)) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 198215/23657358. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^c.a) b)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.a) b)) 3. ==[ beta ]==> ((b (a (a a)))((^y.a) b)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.a) b)) 5. ==[ beta ]==> ((b (a (a a))) a) REDUCED to normal form. ------ 198216/23657385. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.(^z.z)) c)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.(^z.z)) c)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(^y.y)) c)) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.y)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.x)) REDUCED to normal form. ------ 198217/23657457. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.y))((a (^z.z))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (^y.y))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 198218/23657475. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(b (^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(b (^x1.a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(b (^x1.a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(b (^z.a))) 5. ==[ beta ]==> ((b (^z.a))(^y.y)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 198219/23657862. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((^y.y) b)(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> (((^x.x) b)(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> (b (((^y.y)(^z.z))(a a))) 6. ==[ alpha ]==> (b (((^x.x)(^y.y))(a a))) 7. ==[ beta ]==> (b ((^y.y)(a a))) 8. ==[ alpha ]==> (b ((^x.x)(a a))) 9. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 198220/23657889. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 198221/23657916. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z) a)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a ((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(a ((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 198222/23658069. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.a)((^z.z) a))) 3. ==[ beta ]==> (b ((^y.a)((^z.z) a))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198223/23658177. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198224/23658213. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(c ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(c ((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(c ((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(c ((^z.z) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(c a)) REDUCED to normal form. ------ 198225/23658240. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))(b (a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(b (a (a a)))) REDUCED to normal form. ------ 198226/23658294. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((a (a a))(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((a (a a))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (a a))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a a))(a a))) 5. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198227/23658321. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(((^z.z) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a (a (^x1.x1)))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (a (^z.z)))) REDUCED to normal form. ------ 198228/23658339. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(c (^b.a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(c (^x1.a))) REDUCED to normal form. ------ 198229/23658411. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (a a))(^z.z))) 3. ==[ beta ]==> ((a (b (^y.y)))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (a a))(^y.y))) REDUCED to normal form. ------ 198230/23658438. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(((^x.x) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))(a (^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 198231/23658465. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.z))(^x1.a))) 5. ==[ beta ]==> (((^y.y) b)((a (^z.z))(^x1.a))) 6. ==[ alpha ]==> (((^x.x) b)((a (^y.y))(^z.a))) 7. ==[ beta ]==> (b ((a (^y.y))(^z.a))) 8. ==[ alpha ]==> (b ((a (^x.x))(^y.a))) REDUCED to normal form. ------ 198232/23658492. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a a)(^z.(z z)))) REDUCED to normal form. ------ 198233/23658519. ------ 1. ==[ start ]==> (((a b)(b a))((a (a a)) a)) REDUCED to normal form. ------ 198234/23658546. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(((^z.z) a) b)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(((^z.z) a) b)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(((^y.y) a) b)) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a b)) REDUCED to normal form. ------ 198235/23658627. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.(a a)) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.(z z)) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(a a)) REDUCED to normal form. ------ 198236/23658654. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^b.a) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.a) b)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.a) b)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.a) b)) 5. ==[ beta ]==> ((b (^y.y))((^z.a) b)) 6. ==[ alpha ]==> ((b (^x.x))((^y.a) b)) 7. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 198237/23658735. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(^z.z))) 7. ==[ beta ]==> ((a (^x.x))(a (^z.z))) 8. ==[ alpha ]==> ((a (^x.x))(a (^y.y))) REDUCED to normal form. ------ 198238/23658753. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(c b)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(c b)) 3. ==[ beta ]==> ((b (^y.y))(c b)) 4. ==[ alpha ]==> ((b (^x.x))(c b)) REDUCED to normal form. ------ 198239/23658762. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 198240/23658789. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a a)(^x1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.a))) REDUCED to normal form. ------ 198241/23658798. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198242/23658825. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^b.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.a)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^y1.a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198243/23658960. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a (^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a (^y1.a))) 3. ==[ beta ]==> (b (a (^y1.a))) 4. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 198244/23659068. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((^a.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198245/23659203. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(a (^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(a (^y1.y1))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(a (^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (^x1.x1))) 5. ==[ beta ]==> ((^y.y)(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(a (^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 198246/23659212. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(a a)) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(a a)) REDUCED to normal form. ------ 198247/23671125. ------ 1. ==[ start ]==> (((a (a (^a.a))) b) b) 2. ==[ alpha ]==> (((a (a (^x.x))) b) b) REDUCED to normal form. ------ 198248/23671149. ------ 1. ==[ start ]==> ((^a.(^a.a))((a (a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.y))((a (a (^z.z))) b)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198249/23671566. ------ 1. ==[ start ]==> (((a a)(^b.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 198250/23671734. ------ 1. ==[ start ]==> ((^a.(a (a a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((^x.(x (x x)))((a (^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))((a a) a))(((a (^y.(^z.z)))((a a) a))((a (^y.(^z.z)))((a a) a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(((a (^z.(^x1.x1)))((a a) a))((a (^y1.(^z1.z1)))((a a) a)))) REDUCED to normal form. ------ 198251/23672898. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(^x1.(x1 (x1 (^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(x1 (x1 (^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z (z (^x1.x1))))) REDUCED to normal form. ------ 198252/23673030. ------ 1. ==[ start ]==> ((^a.(a b))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x b))((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))((^x1.x1)(^y1.y1))) b) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1))) b) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1)) b) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 198253/23673321. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(^y.(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 198254/23673417. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((^z.z) b)(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.((((^z.z) b)(^x1.(x1 x1)))(((^z.z) b)(^x1.(x1 x1))))) 4. ==[ alpha ]==> (^x.((((^y.y) b)(^z.(z z)))(((^x1.x1) b)(^y1.(y1 y1))))) 5. ==[ beta ]==> (^x.((b (^z.(z z)))(((^x1.x1) b)(^y1.(y1 y1))))) 6. ==[ alpha ]==> (^x.((b (^y.(y y)))(((^z.z) b)(^x1.(x1 x1))))) 7. ==[ beta ]==> (^x.((b (^y.(y y)))(b (^x1.(x1 x1))))) 8. ==[ alpha ]==> (^x.((b (^y.(y y)))(b (^z.(z z))))) REDUCED to normal form. ------ 198255/23674140. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.((^z.(^x1.x1)) y))) 3. ==[ eta ]==> ((((^x.x) a)((a a) a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((^x.x) a)((a a) a))(^y.(^z.z))) 5. ==[ beta ]==> ((a ((a a) a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a ((a a) a))(^x.(^y.y))) REDUCED to normal form. ------ 198256/23674299. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))(((a a)(^z.z))((a a) a))) 3. ==[ beta ]==> (((((a a)(^z.z))((a a) a))(((a a)(^z.z))((a a) a)))(^y.y)) 4. ==[ alpha ]==> (((((a a)(^x.x))((a a) a))(((a a)(^y.y))((a a) a)))(^z.z)) REDUCED to normal form. ------ 198257/23676372. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 198258/23677371. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(^b.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 198259/23677983. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(^c.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 198260/23678568. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(^c.(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(^z.(b a))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.(b a))) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.(b a))) REDUCED to normal form. ------ 198261/23679891. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.((y y)(^z.z)))) REDUCED to normal form. ------ 198262/23680050. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1) a)((a a) a))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1) a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198263/23680332. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(^c.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.(^x2.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(^z1.(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198264/23680557. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.(a a)))) REDUCED to normal form. ------ 198265/23680773. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(^x1.(z z)))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(^x1.(z z)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(^z.(y y)))) REDUCED to normal form. ------ 198266/23680869. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((a (a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 198267/23681160. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^a.(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.(y1 b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(y1 b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(x1 b))) REDUCED to normal form. ------ 198268/23681292. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^z.z))((^x1.x1)(^y1.y1)))(((a (^z.z))((^x1.x1)(^y1.y1)))(^y.y))) 4. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(((a (^x1.x1))((^y1.y1)(^z1.z1)))(^x2.x2))) 5. ==[ beta ]==> (((a (^x.x))(^z.z))(((a (^x1.x1))((^y1.y1)(^z1.z1)))(^x2.x2))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a (^z.z))((^x1.x1)(^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> (((a (^x.x))(^y.y))(((a (^z.z))(^y1.y1))(^z1.z1))) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(((a (^z.z))(^x1.x1))(^y1.y1))) REDUCED to normal form. ------ 198269/23681961. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.x1))) REDUCED to normal form. ------ 198270/23682165. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.a) c)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198271/23682456. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^a.(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(z (z z)))) REDUCED to normal form. ------ 198272/23682615. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(b c)) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(b c)) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198273/23682627. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^c.(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198274/23682789. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^b.c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.c)) 3. ==[ beta ]==> (b (^y1.c)) 4. ==[ alpha ]==> (b (^x.c)) REDUCED to normal form. ------ 198275/23682897. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^c.b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.b)) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.b)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198276/23683032. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(^b.a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(^y1.a)) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(^y1.a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.a)) 5. ==[ beta ]==> ((^y.y)(^x1.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 198277/23683041. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^a.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.(^z.z))) REDUCED to normal form. ------ 198278/23683071. ------ 1. ==[ start ]==> ((a (^a.a))((a (a (^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y))) b)) REDUCED to normal form. ------ 198279/23683080. ------ 1. ==[ start ]==> (((^a.a) a)((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(y (^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (a ((^y.(y (^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (a ((^x.(x (^y.y)))(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^z.(^x1.x1))(^y.y))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 198280/23683161. ------ 1. ==[ start ]==> (((^a.a) b)((^c.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x) b)((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 198281/23683188. ------ 1. ==[ start ]==> (((^a.(^a.a)) a)((^b.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.a))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 198282/23683215. ------ 1. ==[ start ]==> (((a a) b)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((a a) b)((^x.(^y.(^z.z)))(^x1.b))) 3. ==[ beta ]==> (((a a) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) b)(^x.(^y.y))) REDUCED to normal form. ------ 198283/23683350. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^c.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.z))) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198284/23683458. ------ 1. ==[ start ]==> ((((^a.a) a) a)((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a) a)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 198285/23683485. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 198286/23683503. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1))) a)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1))) a) 6. ==[ alpha ]==> ((^x.(^y.(^z.z))) a) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198287/23683575. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a) a)((b (^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a a) a)((b (^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a a) a)((b (^x.x)) a)) REDUCED to normal form. ------ 198288/23683602. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 198289/23683629. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))(((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x) b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (a a))(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a (a a))(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a (a a))(b (^y.y))) 8. ==[ alpha ]==> ((a (a a))(b (^x.x))) REDUCED to normal form. ------ 198290/23683656. ------ 1. ==[ start ]==> ((a (a (a a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((a (a (a a)))((a (^x.(^y.y)))((a a) a))) REDUCED to normal form. ------ 198291/23683899. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.x))((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (^x.x))(^z.z))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.x))(^y.y))) REDUCED to normal form. ------ 198292/23683926. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> (((a (^x.x)) a)((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 198293/23683971. ------ 1. ==[ start ]==> (((^a.(a a)) b)((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((^y.(y (^z.z)))(a a))) 3. ==[ beta ]==> ((b b)((^y.(y (^z.z)))(a a))) 4. ==[ alpha ]==> ((b b)((^x.(x (^y.y)))(a a))) 5. ==[ beta ]==> ((b b)((a a)(^y.y))) 6. ==[ alpha ]==> ((b b)((a a)(^x.x))) REDUCED to normal form. ------ 198294/23684016. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((b (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b (^z.z))(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198295/23684043. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 198296/23684106. ------ 1. ==[ start ]==> (((a (a a)) b)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.(^z.z)))((a a) a))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.y))) REDUCED to normal form. ------ 198297/23684151. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(((a a)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 7. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 198298/23684160. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 198299/23684187. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(y y)))(a a)) REDUCED to normal form. ------ 198300/23684214. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.b)(b a))) 3. ==[ beta ]==> ((a (^y.a))((^z.b)(b a))) 4. ==[ alpha ]==> ((a (^x.a))((^y.b)(b a))) 5. ==[ beta ]==> ((a (^x.a)) b) REDUCED to normal form. ------ 198301/23684232. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 198302/23684268. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) b))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) b))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198303/23684700. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a (a a))(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.a))(^y.y)) REDUCED to normal form. ------ 198304/23684790. ------ 1. ==[ start ]==> (((a a)((a a) a))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)((a a) a))(b ((^x.(^y.y)) a))) 3. ==[ beta ]==> (((a a)((a a) a))(b (^y.y))) 4. ==[ alpha ]==> (((a a)((a a) a))(b (^x.x))) REDUCED to normal form. ------ 198305/23684817. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(a (a (a (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(a (a (a (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a (a (^z.z))))) REDUCED to normal form. ------ 198306/23684844. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> ((a (a (a a)))(((^y.(^z.z)) a)(a a))) 4. ==[ alpha ]==> ((a (a (a a)))(((^x.(^y.y)) a)(a a))) 5. ==[ beta ]==> ((a (a (a a)))((^y.y)(a a))) 6. ==[ alpha ]==> ((a (a (a a)))((^x.x)(a a))) 7. ==[ beta ]==> ((a (a (a a)))(a a)) REDUCED to normal form. ------ 198307/23684871. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((b (^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a (a a)) a)((b (^y.y))(a (^z.z)))) 4. ==[ alpha ]==> (((a (a a)) a)((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 198308/23684898. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((a a)(a a))((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((a a)(a a))((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((a a)(a a))((^z.z) a))) 5. ==[ beta ]==> ((a (^y.y))(((a a)(a a))((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.x))(((a a)(a a))((^y.y) a))) 7. ==[ beta ]==> ((a (^x.x))(((a a)(a a)) a)) REDUCED to normal form. ------ 198309/23684925. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(a a))(b (a (a a)))) REDUCED to normal form. ------ 198310/23684952. ------ 1. ==[ start ]==> ((a (a b))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a b))((a (^x.(^y.y)))(^x1.x1))) 4. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(^z.z))) REDUCED to normal form. ------ 198311/23685240. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))(a (^y.(y (^z.z))))) REDUCED to normal form. ------ 198312/23685312. ------ 1. ==[ start ]==> (((^a.b)(a a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.b)(a a))(((a a)(a a))(^y.a))) 3. ==[ beta ]==> (b (((a a)(a a))(^y.a))) 4. ==[ alpha ]==> (b (((a a)(a a))(^x.a))) REDUCED to normal form. ------ 198313/23685321. ------ 1. ==[ start ]==> (((a b)(^a.a))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(^x.x))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a b)(^x.x))(a a)) REDUCED to normal form. ------ 198314/23685339. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> ((a (^x.(a a)))(b (^z.(z z)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(b (^y.(y y)))) REDUCED to normal form. ------ 198315/23685510. ------ 1. ==[ start ]==> (((^a.b) b)((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.b) b)((^y.a)(b a))) 3. ==[ beta ]==> (b ((^y.a)(b a))) 4. ==[ alpha ]==> (b ((^x.a)(b a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198316/23685555. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((a (a a))(^z.z))) 3. ==[ beta ]==> ((^y.(a a))((a (a a))(^z.z))) 4. ==[ alpha ]==> ((^x.(a a))((a (a a))(^y.y))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198317/23685582. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> (((^y.y) a)(^z.(a a))) 6. ==[ alpha ]==> (((^x.x) a)(^y.(a a))) 7. ==[ beta ]==> (a (^y.(a a))) 8. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 198318/23685717. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(a a)) c)) 3. ==[ beta ]==> (b (((a a)(a a)) c)) REDUCED to normal form. ------ 198319/23685726. ------ 1. ==[ start ]==> (((a b) b)((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a b) b)((^x.(a a))(^y.a))) 3. ==[ beta ]==> (((a b) b)(a a)) REDUCED to normal form. ------ 198320/23685753. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a a) a)((^y.y)(^z.(z z)))) 4. ==[ alpha ]==> (((a a) a)((^x.x)(^y.(y y)))) 5. ==[ beta ]==> (((a a) a)(^y.(y y))) 6. ==[ alpha ]==> (((a a) a)(^x.(x x))) REDUCED to normal form. ------ 198321/23685780. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 198322/23685861. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a))(^x1.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 198323/23685888. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.b)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y y))((^z.b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.b)(^z.(^x1.x1)))((^y.b)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(^y1.(^z1.z1)))) 9. ==[ beta ]==> (b ((^x1.b)(^y1.(^z1.z1)))) 10. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 198324/23685915. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^c.a)(^d.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) a) REDUCED to normal form. ------ 198325/23685942. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 198326/23685969. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(^z.z))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 198327/23686032. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(b (b (^y.y)))) REDUCED to normal form. ------ 198328/23686059. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(a ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a ((a a) a))(a ((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((a ((a a) a))(a ((^x.(^y.y)) a))) 5. ==[ beta ]==> ((a ((a a) a))(a (^y.y))) 6. ==[ alpha ]==> ((a ((a a) a))(a (^x.x))) REDUCED to normal form. ------ 198329/23686086. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))((b (^z.z))(a a))) 3. ==[ beta ]==> (((a (a a))(^y.y))((b (^z.z))(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((b (^y.y))(a a))) REDUCED to normal form. ------ 198330/23686113. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(((a a)(a a))(a (^z.z)))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(((a a)(a a))(a (^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(a a))(a (^y.y)))) 5. ==[ beta ]==> ((a (a a))(((a a)(a a))(a (^y.y)))) 6. ==[ alpha ]==> ((a (a a))(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 198331/23686140. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a) a)(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a) a)(((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a) a)(b ((^y.y) a))) 6. ==[ alpha ]==> ((((a a) a) a)(b ((^x.x) a))) 7. ==[ beta ]==> ((((a a) a) a)(b a)) REDUCED to normal form. ------ 198332/23686167. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 198333/23686194. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a a)(a a))((b a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> (((a a)(a a))((b a)((^x.x)(^y.y)))) 5. ==[ beta ]==> (((a a)(a a))((b a)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))((b a)(^x.x))) REDUCED to normal form. ------ 198334/23686221. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a)(^y.y))((a a) a))) REDUCED to normal form. ------ 198335/23686401. ------ 1. ==[ start ]==> (((a b) c)(c (^c.(a a)))) 2. ==[ alpha ]==> (((a b) c)(c (^x.(a a)))) REDUCED to normal form. ------ 198336/23686473. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.y))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 198337/23686500. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))(((a a)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a))(^y.(^z.z))) 6. ==[ alpha ]==> (((a a)(a a))(^x.(^y.y))) REDUCED to normal form. ------ 198338/23686509. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(a a)))(a a)) REDUCED to normal form. ------ 198339/23686536. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.z)((^x1.x1) a))) 3. ==[ beta ]==> ((a (^y.b))((^z.z)((^x1.x1) a))) 4. ==[ alpha ]==> ((a (^x.b))((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((a (^x.b))((^z.z) a)) 6. ==[ alpha ]==> ((a (^x.b))((^y.y) a)) 7. ==[ beta ]==> ((a (^x.b)) a) REDUCED to normal form. ------ 198340/23686554. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((a (^y.(^z.z)))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((a (^x.(^y.y)))(^z.(z z)))) REDUCED to normal form. ------ 198341/23686635. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.b))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.b))) 5. ==[ beta ]==> (b ((a a)(^y.b))) 6. ==[ alpha ]==> (b ((a a)(^x.b))) REDUCED to normal form. ------ 198342/23686644. ------ 1. ==[ start ]==> (((a b)(^b.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(a a))(a b))) 3. ==[ beta ]==> (((a b)(^x.a))(a a)) REDUCED to normal form. ------ 198343/23686671. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.b)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.b)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y))) b) REDUCED to normal form. ------ 198344/23687256. ------ 1. ==[ start ]==> (((^a.a)(b a))((^c.(a a)) b)) 2. ==[ alpha ]==> (((^x.x)(b a))((^y.(a a)) b)) 3. ==[ beta ]==> ((b a)((^y.(a a)) b)) 4. ==[ alpha ]==> ((b a)((^x.(a a)) b)) 5. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 198345/23687283. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))((^x1.x1) c)) 3. ==[ beta ]==> ((^y.y)((^x1.x1) c)) 4. ==[ alpha ]==> ((^x.x)((^y.y) c)) 5. ==[ beta ]==> ((^y.y) c) 6. ==[ alpha ]==> ((^x.x) c) 7. ==[ beta ]==> c REDUCED to normal form. ------ 198346/23687544. ------ 1. ==[ start ]==> (((a a)(b a))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(b a))((a (^x.x))((^y.y) b))) 3. ==[ beta ]==> (((a a)(b a))((a (^x.x)) b)) REDUCED to normal form. ------ 198347/23687571. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a a)((a a)(a a)))) REDUCED to normal form. ------ 198348/23687904. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((a (^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((a (^z.z))(^x1.x1))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((a (^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((a (^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a a)((a (^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a a)((a (^x.x))(^y.y))) REDUCED to normal form. ------ 198349/23687985. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((^a.a) b) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1) b) b)) 3. ==[ beta ]==> (b (((^x1.x1) b) b)) 4. ==[ alpha ]==> (b (((^x.x) b) b)) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 198350/23688102. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) a)((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(a a))(^x1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(a a)) REDUCED to normal form. ------ 198351/23688129. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.b)(^y1.b))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 198352/23688237. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((^y.b)((^z.a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((^x.b)((^y.a)(^z.(^x1.(^y1.y1))))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 198353/23688291. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.(a a))) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.(a a))) REDUCED to normal form. ------ 198354/23688435. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((a a)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((a a)(^z.z))) REDUCED to normal form. ------ 198355/23688462. ------ 1. ==[ start ]==> (((a (^a.a))(b a))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b a))((a b)((a a) a))) REDUCED to normal form. ------ 198356/23688489. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((a a) a)(a b))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((a a) a)(a b))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((a a) a)(a b))) REDUCED to normal form. ------ 198357/23688516. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((^y.y)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (a a))(a a))(((^y.y)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a a))(((^x.x)(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (((a (a a))(a a))((^y.y)((^z.z)(a a)))) 6. ==[ alpha ]==> (((a (a a))(a a))((^x.x)((^y.y)(a a)))) 7. ==[ beta ]==> (((a (a a))(a a))((^y.y)(a a))) 8. ==[ alpha ]==> (((a (a a))(a a))((^x.x)(a a))) 9. ==[ beta ]==> (((a (a a))(a a))(a a)) REDUCED to normal form. ------ 198358/23688543. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((^y.y)(a b))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((^x.x)(a b))((a (a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a b)((a (a a))((a a)(^y.y)))) 6. ==[ alpha ]==> ((a b)((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 198359/23688570. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) a)(b a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(a (b a))) REDUCED to normal form. ------ 198360/23688597. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^y.y))((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 198361/23688624. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a a)((^y.y) b))) 3. ==[ beta ]==> (((a a)(a (a a)))((a a)((^y.y) b))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a a)((^x.x) b))) 5. ==[ beta ]==> (((a a)(a (a a)))((a a) b)) REDUCED to normal form. ------ 198362/23688696. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198363/23688741. ------ 1. ==[ start ]==> (((^a.a)(^b.b))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 198364/23688768. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((^a.a)(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(a a))(^x2.(^y2.y2)))) 3. ==[ beta ]==> ((^y.y)(((^z1.z1)(a a))(^x2.(^y2.y2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(^z.z))) 7. ==[ beta ]==> ((a a)(^y.(^z.z))) 8. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 198365/23688903. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a) a)(^d.a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.a))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 198366/23689011. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.(^x2.x2))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.(^x2.x2))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198367/23689020. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 198368/23689074. ------ 1. ==[ start ]==> (((a a)(^b.b))((^c.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 198369/23689101. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))(a a)) REDUCED to normal form. ------ 198370/23689182. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.(^y1.y1))(^z1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(^y1.(a a)))) 5. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(^y1.(a a)))) 6. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(^x1.(a a)))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198371/23689209. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 6. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 198372/23689236. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.a)(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a b)(^x.a)) a) REDUCED to normal form. ------ 198373/23689263. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 198374/23689290. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.z)(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 198375/23689335. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.(^z1.(^x2.x2))) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2))) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198376/23689407. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> (((a a) b)(((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> (((a a) b)(((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> (((a a) b)((a a)(a (a a)))) REDUCED to normal form. ------ 198377/23689434. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a b)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))((a b)(^x1.x1))) REDUCED to normal form. ------ 198378/23689461. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((a a) a)((a a) a))) 3. ==[ beta ]==> ((a (b a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 198379/23689488. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((^y.y)(^z.z))(a b))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((^z.z)(a b))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((^y.y)(a b))) 5. ==[ beta ]==> (((a (a a))((a a)(^x.x)))(a b)) REDUCED to normal form. ------ 198380/23689515. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))((a (a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))((a (a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((a (a a))((^z.z)(a a)))) 5. ==[ beta ]==> (((^y.y)(a a))((a (a a))((^z.z)(a a)))) 6. ==[ alpha ]==> (((^x.x)(a a))((a (a a))((^y.y)(a a)))) 7. ==[ beta ]==> ((a a)((a (a a))((^y.y)(a a)))) 8. ==[ alpha ]==> ((a a)((a (a a))((^x.x)(a a)))) 9. ==[ beta ]==> ((a a)((a (a a))(a a))) REDUCED to normal form. ------ 198381/23689542. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x) a)((a a)(^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a b))(a ((a a)(^y.y)))) 4. ==[ alpha ]==> ((((a a) a)(a b))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 198382/23689569. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (^a.a))(b a))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (^x.x))(b a))) REDUCED to normal form. ------ 198383/23689596. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a a)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^y.y))((a a)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a a)(^x.x))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 198384/23689767. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((a a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((a a) a)(^x1.a))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(^x1.a))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.a))) 5. ==[ beta ]==> (((a a) a)(^y.a)) 6. ==[ alpha ]==> (((a a) a)(^x.a)) REDUCED to normal form. ------ 198385/23689902. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((a a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((a a)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 198386/23690046. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((b b)((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((b b)((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 198387/23690127. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))((^x1.(a a))(^x1.(a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 198388/23690154. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 198389/23690460. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))((a (^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 198390/23690487. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a a)(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a a)(b a))) 3. ==[ beta ]==> (((a (^x.x)) b)((a a)(b a))) REDUCED to normal form. ------ 198391/23691261. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(c (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(c (^z.(a a)))) 3. ==[ beta ]==> ((a (^y.y))(c (^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.x))(c (^y.(a a)))) REDUCED to normal form. ------ 198392/23691288. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(b (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(b (^x1.(^y1.y1)))) REDUCED to normal form. ------ 198393/23691360. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((a a)(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((a a)(^x.(^y.y)))) REDUCED to normal form. ------ 198394/23691369. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(a a))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(a a)) REDUCED to normal form. ------ 198395/23691396. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^a.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.b)((^x1.x1) a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.b)((^x1.x1) a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.b)((^z.z) a))) 5. ==[ beta ]==> (((a a)(^x.b)) b) REDUCED to normal form. ------ 198396/23691477. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(x1 x1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 198397/23691504. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.a)(a b))) 3. ==[ beta ]==> ((b (^y.a))((^z.a)(a b))) 4. ==[ alpha ]==> ((b (^x.a))((^y.a)(a b))) 5. ==[ beta ]==> ((b (^x.a)) a) REDUCED to normal form. ------ 198398/23691531. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 198399/23691756. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))(c (a b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))(c (a b))) 3. ==[ beta ]==> (((a b)(a a))(c (a b))) REDUCED to normal form. ------ 198400/23691783. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(b ((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)(a b))(b ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)(a b))(b ((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)(a b))(b (a a))) REDUCED to normal form. ------ 198401/23691810. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 198402/23691864. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((a b)(a (^z.z)))) REDUCED to normal form. ------ 198403/23691891. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((a a) a)((^z.z) a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((a a) a)((^z.z) a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((a a) a)((^y.y) a))) 5. ==[ beta ]==> ((b a)(((a a) a)((^y.y) a))) 6. ==[ alpha ]==> ((b a)(((a a) a)((^x.x) a))) 7. ==[ beta ]==> ((b a)(((a a) a) a)) REDUCED to normal form. ------ 198404/23691918. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((^y.y)(^z.z))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(a (a a))) REDUCED to normal form. ------ 198405/23691972. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a) a)((a a) a))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z) a)((a a) a))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)((a a) a))) 5. ==[ beta ]==> ((a (^x.x))(a ((a a) a))) REDUCED to normal form. ------ 198406/23692062. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(((^a.a)(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.z))) 7. ==[ beta ]==> (((^y.y)(a a))(^z.z)) 8. ==[ alpha ]==> (((^x.x)(a a))(^y.y)) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 198407/23692143. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((^a.a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (b (((^x1.x1)(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(y y)))) 7. ==[ beta ]==> (b (^y.(y y))) 8. ==[ alpha ]==> (b (^x.(x x))) REDUCED to normal form. ------ 198408/23692251. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(^z1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198409/23692368. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.(^x1.x1))(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(z z)))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 198410/23692476. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.(a a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(a a))) REDUCED to normal form. ------ 198411/23692548. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^c.a) c)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.a) c)) 3. ==[ beta ]==> (b ((^z.a) c)) 4. ==[ alpha ]==> (b ((^x.a) c)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198412/23692665. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(b (^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(b (^y1.b))) REDUCED to normal form. ------ 198413/23692692. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(a (^z.(a a)))) 3. ==[ beta ]==> ((b (^y.(y y)))(a (^z.(a a)))) 4. ==[ alpha ]==> ((b (^x.(x x)))(a (^y.(a a)))) REDUCED to normal form. ------ 198414/23692719. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((^y.b)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.a)) b) REDUCED to normal form. ------ 198415/23692773. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((^x1.x1) a))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198416/23692791. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 198417/23693025. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))(c ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c ((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(c (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(c (^y.y))) REDUCED to normal form. ------ 198418/23693079. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(a (a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(a (a b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(a (a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(a (a b))) REDUCED to normal form. ------ 198419/23693106. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(((a a) a)(a a))) 3. ==[ beta ]==> ((b (a (a a)))(((a a) a)(a a))) REDUCED to normal form. ------ 198420/23693133. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((^y.y)(^z.z))(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((^y.y)(^z.z))(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(((^x.x)(^y.y))(a (^z.z)))) 5. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> ((((a a)(a a)) a)(a (^y.y))) 8. ==[ alpha ]==> ((((a a)(a a)) a)(a (^x.x))) REDUCED to normal form. ------ 198421/23693187. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> ((a a)(((^y.y) a)(a (a a)))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(a (a a)))) 7. ==[ beta ]==> ((a a)(a (a (a a)))) REDUCED to normal form. ------ 198422/23693214. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a (^y.y))(^x1.x1))) 4. ==[ alpha ]==> ((a (a (a (^x.x))))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 198423/23693628. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(^y1.y1)) b)) 3. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(^y1.y1)) b)) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1)) b)) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1)) b)) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b)) 7. ==[ beta ]==> ((^y.(^z.z)) b) 8. ==[ alpha ]==> ((^x.(^y.y)) b) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198424/23693772. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a a))) 7. ==[ beta ]==> ((^y.(^z.z))(a a)) 8. ==[ alpha ]==> ((^x.(^y.y))(a a)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198425/23693799. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(x1 x1))(a (^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^y1.y1))(a (^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 198426/23693817. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y) a)(^z.a))) 3. ==[ beta ]==> (b (((^y.y) a)(^z.a))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.a))) 5. ==[ beta ]==> (b (a (^y.a))) 6. ==[ alpha ]==> (b (a (^x.a))) REDUCED to normal form. ------ 198427/23693880. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 198428/23693925. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a (a a)) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a (a a)) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a)) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a)) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198429/23693961. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 198430/23693988. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 198431/23694060. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(z z)) b)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z)) b)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y)) b)) 5. ==[ beta ]==> (((a a)(^x.x))(b b)) REDUCED to normal form. ------ 198432/23694087. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^b.a) c)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.a) c)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 198433/23694105. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))((a (^y.y)) a)) REDUCED to normal form. ------ 198434/23694132. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a a)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a a)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a a)(a (a a)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a a)(a (a a)))) REDUCED to normal form. ------ 198435/23694213. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(c c)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(c c)) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(c c)) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(c c)) 5. ==[ beta ]==> (((^y.y) b)(c c)) 6. ==[ alpha ]==> (((^x.x) b)(c c)) 7. ==[ beta ]==> (b (c c)) REDUCED to normal form. ------ 198436/23694375. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(a (a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(a (a (a a)))) REDUCED to normal form. ------ 198437/23694402. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(((^x1.x1) a)(a a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(((^x1.x1) a)(a a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(((^z.z) a)(a a))) 5. ==[ beta ]==> ((b (^y.y))(((^z.z) a)(a a))) 6. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)(a a))) 7. ==[ beta ]==> ((b (^x.x))(a (a a))) REDUCED to normal form. ------ 198438/23694429. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 198439/23694501. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.a)(a a))) 3. ==[ beta ]==> ((b (^y.y))((^z.a)(a a))) 4. ==[ alpha ]==> ((b (^x.x))((^y.a)(a a))) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 198440/23694537. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(b c)) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(b c)) 3. ==[ beta ]==> ((a (^y.(^z.z)))(b c)) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(b c)) REDUCED to normal form. ------ 198441/23694546. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a a)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a)(^x1.a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198442/23694573. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(((^a.a) a) a)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(((^y1.y1) a) a)) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a) a)) 5. ==[ beta ]==> (((^y.y) a) a) 6. ==[ alpha ]==> (((^x.x) a) a) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198443/23694708. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.a) c)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.y1) c)) 3. ==[ beta ]==> (b ((^y1.y1) c)) 4. ==[ alpha ]==> (b ((^x.x) c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 198444/23694816. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((a a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((a a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((a a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((a a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198445/23694951. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))((^a.a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))((^y1.y1) a)) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))((^y1.y1) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1) a)) 5. ==[ beta ]==> ((^y.y)((^x1.x1) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 198446/23694960. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(a (^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(a (^y.y))) REDUCED to normal form. ------ 198447/23694977. ------ 1. ==[ start ]==> (^a.((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (^x.((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (^x.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198448/23694978. ------ 1. ==[ start ]==> (a ((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> (a (^y.(^z.z))) 4. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 198449/23706882. ------ 1. ==[ start ]==> (((a (a (^a.a))) b) c) 2. ==[ alpha ]==> (((a (a (^x.x))) b) c) REDUCED to normal form. ------ 198450/23706906. ------ 1. ==[ start ]==> ((^a.a)((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198451/23706933. ------ 1. ==[ start ]==> ((^a.(a a))((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(y (^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.(y (^z.z)))(^x1.(^y1.y1)))((^y.(y (^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))((^y1.(y1 (^z1.z1)))(^x2.(^y2.y2)))) 5. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))((^y1.(y1 (^z1.z1)))(^x2.(^y2.y2)))) 6. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(x1 (^y1.y1)))(^z1.(^x2.x2)))) 7. ==[ beta ]==> ((^y.y)((^x1.(x1 (^y1.y1)))(^z1.(^x2.x2)))) 8. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.(^y1.y1)))) 9. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.(^y1.y1))) 10. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.x1))) 11. ==[ beta ]==> ((^z.(^x1.x1))(^y.y)) 12. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198452/23707041. ------ 1. ==[ start ]==> ((^a.(a (^a.a)))((^b.b)(^c.a))) 2. ==[ alpha ]==> ((^x.(x (^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((^z.z)(^x1.a))(^y.y)) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.z)) 5. ==[ beta ]==> ((^y.a)(^z.z)) 6. ==[ alpha ]==> ((^x.a)(^y.y)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198453/23707230. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ eta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198454/23707350. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.((^y1.y1)(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.((^y1.y1)(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198455/23707401. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 198456/23707725. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(b (^y1.y1)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198457/23707800. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 198458/23708232. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 198459/23708616. ------ 1. ==[ start ]==> ((^a.(^a.b))(c (b (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.b))(c (b (^z.z)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 198460/23708664. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 198461/23709390. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1))(a (^y1.(^z1.z1))))((^z.(^x1.x1))(a (^y1.(^z1.z1)))))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z))(a (^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.(^z2.z2)))))) 5. ==[ beta ]==> (((^y.(^z.z))(a (^x1.(^y1.y1))))((^z1.(^x2.x2))(a (^y2.(^z2.z2))))) 6. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 7. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.(^y2.y2))))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 9. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 10. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198462/23710689. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))(^y1.(y1 (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))(^y1.(y1 (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))(^x1.(x1 (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(^z.(z (^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(y (^z.z)))) 9. ==[ beta ]==> (^y.(y (^z.z))) 10. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 198463/23711370. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198464/23712261. ------ 1. ==[ start ]==> ((^a.(^b.b))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a (a a)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198465/23713470. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(^a.(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(^y.(^z.z))) REDUCED to normal form. ------ 198466/23713575. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((^y.(a a))(a (a a)))) 3. ==[ beta ]==> ((((^y.(a a))(a (a a)))((^y.(a a))(a (a a))))(((^y.(a a))(a (a a)))((^y.(a a))(a (a a))))) 4. ==[ alpha ]==> ((((^x.(a a))(a (a a)))((^y.(a a))(a (a a))))(((^z.(a a))(a (a a)))((^x1.(a a))(a (a a))))) 5. ==[ beta ]==> (((a a)((^y.(a a))(a (a a))))(((^z.(a a))(a (a a)))((^x1.(a a))(a (a a))))) 6. ==[ alpha ]==> (((a a)((^x.(a a))(a (a a))))(((^y.(a a))(a (a a)))((^z.(a a))(a (a a))))) 7. ==[ beta ]==> (((a a)(a a))(((^y.(a a))(a (a a)))((^z.(a a))(a (a a))))) 8. ==[ alpha ]==> (((a a)(a a))(((^x.(a a))(a (a a)))((^y.(a a))(a (a a))))) 9. ==[ beta ]==> (((a a)(a a))((a a)((^y.(a a))(a (a a))))) 10. ==[ alpha ]==> (((a a)(a a))((a a)((^x.(a a))(a (a a))))) 11. ==[ beta ]==> (((a a)(a a))((a a)(a a))) REDUCED to normal form. ------ 198467/23714361. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(^z.(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 198468/23714631. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))(^b.(b a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.(x a))) REDUCED to normal form. ------ 198469/23715657. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 198470/23716737. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^b.(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(a y))) 3. ==[ eta ]==> (((a (a a))((^x.x) b)) a) 4. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 198471/23716926. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(^b.(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(^y1.(^z1.y1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(^y1.(^z1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.(^y1.x1))) REDUCED to normal form. ------ 198472/23717727. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(^c.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 198473/23717931. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1) a)(a (^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198474/23718006. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 198475/23718114. ------ 1. ==[ start ]==> (((a b)(b a))(^b.(a (a a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(a (a a)))) REDUCED to normal form. ------ 198476/23718222. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(^b.(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 198477/23718330. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 198478/23718381. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198479/23718555. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^c.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> (b (^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> (b (^x.(a (^y.y)))) REDUCED to normal form. ------ 198480/23718798. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(^a.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(^y1.(y1 y1))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(^y1.(y1 y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(x1 x1))) 5. ==[ beta ]==> ((^y.y)(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(y y))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 198481/23718807. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^b.a)) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.a)) REDUCED to normal form. ------ 198482/23718837. ------ 1. ==[ start ]==> ((a a)((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a a)((^x.(^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a a)(^y.(^z.z))) 4. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 198483/23718855. ------ 1. ==[ start ]==> (((^a.a) a)((a (a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x) a)((a (a (^y.y))) b)) 3. ==[ beta ]==> (a ((a (a (^y.y))) b)) 4. ==[ alpha ]==> (a ((a (a (^x.x))) b)) REDUCED to normal form. ------ 198484/23718864. ------ 1. ==[ start ]==> ((a (a a))((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (a a))((^x.(x (^y.y)))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (a a))((^z.(^x1.x1))(^y.y))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 198485/23718972. ------ 1. ==[ start ]==> ((a (a (^a.a)))((^b.b)(^c.a))) 2. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(^z.a))) 3. ==[ beta ]==> ((a (a (^x.x)))(^z.a)) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.a)) REDUCED to normal form. ------ 198486/23719107. ------ 1. ==[ start ]==> (((a a)(a (^a.a)))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(a (^x.x))) b) REDUCED to normal form. ------ 198487/23719161. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a a)((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 198488/23719251. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))(b (a (a (^z.z))))) 3. ==[ beta ]==> (((^y.y) a)(b (a (a (^z.z))))) 4. ==[ alpha ]==> (((^x.x) a)(b (a (a (^y.y))))) 5. ==[ beta ]==> (a (b (a (a (^y.y))))) 6. ==[ alpha ]==> (a (b (a (a (^x.x))))) REDUCED to normal form. ------ 198489/23719278. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(a ((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(a ((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 198490/23719287. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.(^z1.z1))) a)) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 198491/23719314. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1))) b)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z))) b)) 5. ==[ beta ]==> ((a (^x.x))(b (^z.z))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.y))) REDUCED to normal form. ------ 198492/23719332. ------ 1. ==[ start ]==> ((a (^a.(a a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x x)))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(x x)))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.(x x)))(a (^z.z))) 6. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.y))) REDUCED to normal form. ------ 198493/23719440. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))((a (^z.(^x1.x1)))((a a) a))) 3. ==[ beta ]==> ((^y.(y y))((a (^z.(^x1.x1)))((a a) a))) 4. ==[ alpha ]==> ((^x.(x x))((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> (((a (^y.(^z.z)))((a a) a))((a (^y.(^z.z)))((a a) a))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((a (^z.(^x1.x1)))((a a) a))) REDUCED to normal form. ------ 198494/23719467. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((b a)(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((b a)(a b))) 3. ==[ beta ]==> ((^y.y)((b a)(a b))) 4. ==[ alpha ]==> ((^x.x)((b a)(a b))) 5. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 198495/23719521. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(a a))((a a)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 7. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 8. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 9. ==[ beta ]==> ((a a)((a a)(^y.y))) 10. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 198496/23719548. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))((a b)(b a))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))((a b)(b a))) 3. ==[ beta ]==> ((a (a a))((a b)(b a))) REDUCED to normal form. ------ 198497/23719575. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((a a) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a a) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a a) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 198498/23719629. ------ 1. ==[ start ]==> (((^a.(a a))(a a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a a))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(a a))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 198499/23719656. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a (^x.(^y.y)))(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (b (^z.z)))) REDUCED to normal form. ------ 198500/23719701. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (^x.x)) a)(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (^x.x)) a)(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 198501/23719728. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 198502/23719746. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a (a (^y.y)))(^z.z))) 3. ==[ beta ]==> ((b b)((a (a (^y.y)))(^z.z))) 4. ==[ alpha ]==> ((b b)((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 198503/23719755. ------ 1. ==[ start ]==> (((a (a a))(a a))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a (a a))(a a))((^x.(x (^y.y)))(a a))) 3. ==[ beta ]==> (((a (a a))(a a))((a a)(^y.y))) 4. ==[ alpha ]==> (((a (a a))(a a))((a a)(^x.x))) REDUCED to normal form. ------ 198504/23719881. ------ 1. ==[ start ]==> (((a (a a)) b)((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a (a a)) b)((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 198505/23719908. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((b a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((b a)(^z.b))) 3. ==[ beta ]==> (((^y.y) a)((b a)(^z.b))) 4. ==[ alpha ]==> (((^x.x) a)((b a)(^y.b))) 5. ==[ beta ]==> (a ((b a)(^y.b))) 6. ==[ alpha ]==> (a ((b a)(^x.b))) REDUCED to normal form. ------ 198506/23719935. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 198507/23720016. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(((a a) a)(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 198508/23720043. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198509/23720079. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> (((a a)(^x.x))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 198510/23720106. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a))) a) REDUCED to normal form. ------ 198511/23720133. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 198512/23720160. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(a (a (^y.y)))) REDUCED to normal form. ------ 198513/23720187. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(z (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(z (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(y (^z.z)))(^x1.x1))) 5. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(^x1.x1))) 6. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(^z.z))) 7. ==[ beta ]==> ((a a)((^z.z)(^y.y))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 198514/23720547. ------ 1. ==[ start ]==> ((a (^a.b))(c (b (^a.a)))) 2. ==[ alpha ]==> ((a (^x.b))(c (b (^y.y)))) REDUCED to normal form. ------ 198515/23720592. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.x1)(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.z)(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.(z (^x1.x1)))) REDUCED to normal form. ------ 198516/23720736. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((a (^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.b)((a (^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.b)((a (^y.(^z.z)))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 198517/23720817. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((^a.a)(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((^z.z)(a a))((^x1.x1)(a a)))) IRREDUCIBLE: cycle. ------ 198518/23720898. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 198519/23720925. ------ 1. ==[ start ]==> (((^a.a)(a b))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.x)(a b))((a (a a))((^y.y) b))) 3. ==[ beta ]==> ((a b)((a (a a))((^y.y) b))) 4. ==[ alpha ]==> ((a b)((a (a a))((^x.x) b))) 5. ==[ beta ]==> ((a b)((a (a a)) b)) REDUCED to normal form. ------ 198520/23720952. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z) a)((a a)(a a)))) 3. ==[ beta ]==> ((^y.y)(((^z.z) a)((a a)(a a)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((a a)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((a a)(a a))) 6. ==[ alpha ]==> (((^x.x) a)((a a)(a a))) 7. ==[ beta ]==> (a ((a a)(a a))) REDUCED to normal form. ------ 198521/23721006. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a a)((^y.(^z.z)) a))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)((^x.(^y.y)) a))) 5. ==[ beta ]==> (((a (a a))(a (a a)))((a a)(^y.y))) 6. ==[ alpha ]==> (((a (a a))(a (a a)))((a a)(^x.x))) REDUCED to normal form. ------ 198522/23721042. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(((^x1.(^y1.y1)) a)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.a))(((^x1.(^y1.y1)) a)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(((^z.(^x1.x1)) a)(^y1.y1))) 5. ==[ beta ]==> ((^y.a)(((^z.(^x1.x1)) a)(^y1.y1))) 6. ==[ alpha ]==> ((^x.a)(((^y.(^z.z)) a)(^x1.x1))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198523/23721069. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((b (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 198524/23721096. ------ 1. ==[ start ]==> (((a b)(^a.a))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 198525/23721132. ------ 1. ==[ start ]==> (((a a)(a b))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a a)(a b))((^x.x)(a (a a)))) 3. ==[ beta ]==> (((a a)(a b))(a (a a))) REDUCED to normal form. ------ 198526/23721159. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(^y.(^z.z))) REDUCED to normal form. ------ 198527/23721240. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))((^x1.(a a))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))((^x1.(a a))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(a a))((^x1.x1)(a a)))) 5. ==[ beta ]==> (((^y.y) a)((^z.(a a))((^x1.x1)(a a)))) 6. ==[ alpha ]==> (((^x.x) a)((^y.(a a))((^z.z)(a a)))) 7. ==[ beta ]==> (a ((^y.(a a))((^z.z)(a a)))) 8. ==[ alpha ]==> (a ((^x.(a a))((^y.y)(a a)))) 9. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 198528/23721267. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x))) b) REDUCED to normal form. ------ 198529/23721294. ------ 1. ==[ start ]==> (((a b)(a a))((^c.a)(b a))) 2. ==[ alpha ]==> (((a b)(a a))((^x.a)(b a))) 3. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 198530/23721321. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 198531/23721501. ------ 1. ==[ start ]==> (((a b) b)(((a a)(a a)) c)) REDUCED to normal form. ------ 198532/23721780. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a a)(a a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> (((a a)(a a)) a) REDUCED to normal form. ------ 198533/23721933. ------ 1. ==[ start ]==> (((^a.b) c)((^b.b) d)) 2. ==[ alpha ]==> (((^x.b) c)((^y.y) d)) 3. ==[ beta ]==> (b ((^y.y) d)) 4. ==[ alpha ]==> (b ((^x.x) d)) 5. ==[ beta ]==> (b d) REDUCED to normal form. ------ 198534/23722032. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((^a.a)(a a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((^x1.x1)(a a))(a b))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(a b))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(a b))) 5. ==[ beta ]==> (((^y.y)(a a))(a b)) 6. ==[ alpha ]==> (((^x.x)(a a))(a b)) 7. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 198535/23722167. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z) a)((^x1.x1) b))) 3. ==[ beta ]==> (b (((^z.z) a)((^x1.x1) b))) 4. ==[ alpha ]==> (b (((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (b (a ((^y.y) b))) 6. ==[ alpha ]==> (b (a ((^x.x) b))) 7. ==[ beta ]==> (b (a b)) REDUCED to normal form. ------ 198536/23722284. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(((a a)(a a))(^z.(^x1.x1)))) REDUCED to normal form. ------ 198537/23722311. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((^z.z) b)(^x1.a))) 3. ==[ beta ]==> ((a (^y.b))(((^z.z) b)(^x1.a))) 4. ==[ alpha ]==> ((a (^x.b))(((^y.y) b)(^z.a))) 5. ==[ beta ]==> ((a (^x.b))(b (^z.a))) 6. ==[ alpha ]==> ((a (^x.b))(b (^y.a))) REDUCED to normal form. ------ 198538/23722365. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((b a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((b a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((b a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))((b a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((b a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198539/23722419. ------ 1. ==[ start ]==> (((a b)(^b.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> (((a b)(^x.a))(((^y.y)(a a))(^z.b))) 3. ==[ beta ]==> (((a b)(^x.a))((a a)(^z.b))) 4. ==[ alpha ]==> (((a b)(^x.a))((a a)(^y.b))) REDUCED to normal form. ------ 198540/23722446. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((a b)(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((a b)(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a b)(^z.(a a)))) REDUCED to normal form. ------ 198541/23722509. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))(b a))) 3. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 198542/23722536. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(z z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(z z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(y y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a (^x.x))(a a))((a (^z.(^x1.x1)))(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> (((a (^x.x))(a a))((a (^y.(^z.z)))(a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 198543/23722563. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.a)((^z.z) b))) 3. ==[ beta ]==> ((a (a b))((^y.a)((^z.z) b))) 4. ==[ alpha ]==> ((a (a b))((^x.a)((^y.y) b))) 5. ==[ beta ]==> ((a (a b)) a) REDUCED to normal form. ------ 198544/23722590. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))((a a) a))(^y.y)) 4. ==[ alpha ]==> (((a (a a))((a a) a))(^x.x)) REDUCED to normal form. ------ 198545/23722617. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.y1)(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.y1)(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.x1)(b (^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(b (^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(b (^x1.x1)))) 7. ==[ beta ]==> ((^y.y)((^z.z)(b (^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(b (^z.z)))) 9. ==[ beta ]==> ((^y.y)(b (^z.z))) 10. ==[ alpha ]==> ((^x.x)(b (^y.y))) 11. ==[ beta ]==> (b (^y.y)) 12. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198546/23722671. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^c.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)((^y.(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)((^x.(a a))(^y.(^z.z)))) 5. ==[ beta ]==> (((a b) a)(a a)) REDUCED to normal form. ------ 198547/23722698. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))((^z.z)(^x1.a))) 3. ==[ beta ]==> (((a a)(a (^y.y)))((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((a a)(a (^x.x)))((^y.y)(^z.a))) 5. ==[ beta ]==> (((a a)(a (^x.x)))(^z.a)) 6. ==[ alpha ]==> (((a a)(a (^x.x)))(^y.a)) REDUCED to normal form. ------ 198548/23722725. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(^z.z))) REDUCED to normal form. ------ 198549/23723031. ------ 1. ==[ start ]==> (((^a.a)(b a))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.x)(b a))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((b a)(((a a)(a a))(a a))) REDUCED to normal form. ------ 198550/23723058. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((^x1.x1) b)(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> (((^y.y) b)(a (^z.z))) 6. ==[ alpha ]==> (((^x.x) b)(a (^y.y))) 7. ==[ beta ]==> (b (a (^y.y))) 8. ==[ alpha ]==> (b (a (^x.x))) REDUCED to normal form. ------ 198551/23723112. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((b a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((b a)(a (a a)))) 3. ==[ beta ]==> (((a b)(a b))((b a)(a (a a)))) REDUCED to normal form. ------ 198552/23723193. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))((a b)(a b))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))((a b)(a b))) 3. ==[ beta ]==> (b ((a b)(a b))) REDUCED to normal form. ------ 198553/23723301. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (a (^x1.(^y1.y1))))) REDUCED to normal form. ------ 198554/23723319. ------ 1. ==[ start ]==> (((a a)(b a))(c (^b.b))) 2. ==[ alpha ]==> (((a a)(b a))(c (^x.x))) REDUCED to normal form. ------ 198555/23723346. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(b (^z.(a a)))) REDUCED to normal form. ------ 198556/23723400. ------ 1. ==[ start ]==> (((a (a a))(a b))((^c.(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))(a b))((^x.(a a))(a a))) 3. ==[ beta ]==> (((a (a a))(a b))(a a)) REDUCED to normal form. ------ 198557/23723427. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (((a a) a)(a (^y.y))) 8. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 198558/23723454. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 198559/23723535. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 198560/23723580. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)(((a a) a)(^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198561/23724057. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(b ((^x1.x1) b))) 3. ==[ beta ]==> (b (b ((^x1.x1) b))) 4. ==[ alpha ]==> (b (b ((^x.x) b))) 5. ==[ beta ]==> (b (b b)) REDUCED to normal form. ------ 198562/23724120. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^b.b) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a)) b) REDUCED to normal form. ------ 198563/23724165. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((b a)((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(^z.z))((b a)((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((b a)((^z.z) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198564/23724192. ------ 1. ==[ start ]==> ((a (^b.b))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a (^x.x))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 198565/23724372. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(c (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(c (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^y.y))(c (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a b)(^x.x))(c (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 198566/23724399. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(b (^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(b (^y.y))) 3. ==[ beta ]==> (((a a)(a (a a)))(b (^y.y))) 4. ==[ alpha ]==> (((a a)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 198567/23724471. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198568/23724480. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(^z.(^x1.x1))) REDUCED to normal form. ------ 198569/23724795. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a (^z.(^x1.x1))) b)) REDUCED to normal form. ------ 198570/23724822. ------ 1. ==[ start ]==> ((((^a.a) b) a)((b a) c)) 2. ==[ alpha ]==> ((((^x.x) b) a)((b a) c)) 3. ==[ beta ]==> ((b a)((b a) c)) REDUCED to normal form. ------ 198571/23725110. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((a (^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.(^z1.z1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198572/23725119. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2))) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.(^x2.x2))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 198573/23725344. ------ 1. ==[ start ]==> (((a b)((a a) a))(c (^d.a))) 2. ==[ alpha ]==> (((a b)((a a) a))(c (^x.a))) REDUCED to normal form. ------ 198574/23725371. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(b (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(b (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(b (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^y.y))(b (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 198575/23725398. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(a (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(a (^y.y))) REDUCED to normal form. ------ 198576/23725479. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^c.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.y))((^z.z) a))) 5. ==[ beta ]==> ((b (a a))(^y.y)) 6. ==[ alpha ]==> ((b (a a))(^x.x)) REDUCED to normal form. ------ 198577/23725506. ------ 1. ==[ start ]==> ((a ((a a)(a a)))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(a a))(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(a a)) REDUCED to normal form. ------ 198578/23725947. ------ 1. ==[ start ]==> (((^a.(a a))(b a))(c ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))(c ((a a)(^y.y)))) 3. ==[ beta ]==> (((b a)(b a))(c ((a a)(^y.y)))) 4. ==[ alpha ]==> (((b a)(b a))(c ((a a)(^x.x)))) REDUCED to normal form. ------ 198579/23726010. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 198580/23726028. ------ 1. ==[ start ]==> (((^a.b)(a b))((b a)(a a))) 2. ==[ alpha ]==> (((^x.b)(a b))((b a)(a a))) 3. ==[ beta ]==> (b ((b a)(a a))) REDUCED to normal form. ------ 198581/23726136. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((a a) a)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198582/23726289. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))(a (^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 198583/23726370. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)(a a))((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)(a a))((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)(a a))(a a)) REDUCED to normal form. ------ 198584/23726397. ------ 1. ==[ start ]==> (((a b)(a b))((^a.b)(a (a a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.b)(a (a a)))) 3. ==[ beta ]==> (((a b)(a b)) b) REDUCED to normal form. ------ 198585/23726451. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(^x1.x1)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 198586/23726505. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.a)((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.a)((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.a)((^x1.x1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a) a) REDUCED to normal form. ------ 198587/23726532. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(^z.z))((a a)(^x1.x1)))) 5. ==[ beta ]==> ((b (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((b (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 198588/23726559. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.a)(b a))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.x)(b a))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(b a)) REDUCED to normal form. ------ 198589/23726865. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(((a a)(^y1.y1))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198590/23726901. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^b.(a a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(a a)) c)) 3. ==[ beta ]==> ((b c)((^y.(a a)) c)) 4. ==[ alpha ]==> ((b c)((^x.(a a)) c)) 5. ==[ beta ]==> ((b c)(a a)) REDUCED to normal form. ------ 198591/23726973. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.x))((^z.z)((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((b (^x.x))((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.z))) 9. ==[ beta ]==> ((b (^x.x))(^z.z)) 10. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 198592/23727000. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))((a (a a))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (a a))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((a a) a))) 5. ==[ beta ]==> ((a (a a))((a a) a)) REDUCED to normal form. ------ 198593/23727054. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))((^z1.z1)(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (^y1.y1))(a a))) REDUCED to normal form. ------ 198594/23727144. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((^y.y)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.(a a)))((a a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.(a a)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 198595/23727171. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((a b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((a b)(^z.a))) 3. ==[ beta ]==> (((a a)(^y.b))((a b)(^z.a))) 4. ==[ alpha ]==> (((a a)(^x.b))((a b)(^y.a))) REDUCED to normal form. ------ 198596/23727279. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z) a)(^x1.b))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y) a)(^z.b))) 5. ==[ beta ]==> ((b (^x.a))(a (^z.b))) 6. ==[ alpha ]==> ((b (^x.a))(a (^y.b))) REDUCED to normal form. ------ 198597/23727306. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((a (^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((a (^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 198598/23727369. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 198599/23727396. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))(a a)) REDUCED to normal form. ------ 198600/23727423. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.b)(^z.a))) 5. ==[ beta ]==> ((a b)((^y.b)(^z.a))) 6. ==[ alpha ]==> ((a b)((^x.b)(^y.a))) 7. ==[ beta ]==> ((a b) b) REDUCED to normal form. ------ 198601/23727477. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b a)((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b a)((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 198602/23727531. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.a)(^a.b))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a b)(a a))((^y.a)(^z.b))) 4. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.b))) 5. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 198603/23727558. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(a b))((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(a b))(^y.y)) 6. ==[ alpha ]==> (((a a)(a b))(^x.x)) REDUCED to normal form. ------ 198604/23728242. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(b (a b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(b (a b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(b (a b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(b (a b))) 5. ==[ beta ]==> ((b ((^y.y) b))(b (a b))) 6. ==[ alpha ]==> ((b ((^x.x) b))(b (a b))) 7. ==[ beta ]==> ((b b)(b (a b))) REDUCED to normal form. ------ 198605/23728278. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^b.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(a a)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(a a)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(a a)) a)) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(a a)) a)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(a a)) a)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198606/23728323. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> (b (((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> (b (((a a) a)(a (^x.x)))) REDUCED to normal form. ------ 198607/23728332. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^c.a) c)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a) c)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 198608/23728431. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (^z1.z1))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198609/23728494. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a b)(^a.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a b)(^y.y))) REDUCED to normal form. ------ 198610/23728548. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.a)) 9. ==[ beta ]==> ((^y.y)(^z.a)) 10. ==[ alpha ]==> ((^x.x)(^y.a)) 11. ==[ beta ]==> (^y.a) 12. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 198611/23728584. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(z z))(a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(y y))(a (a a)))) 5. ==[ beta ]==> (((a a)(^x.x))((a (a a))(a (a a)))) REDUCED to normal form. ------ 198612/23728611. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y))) a) REDUCED to normal form. ------ 198613/23728638. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> ((a ((a a)(a a)))(^y.y)) 6. ==[ alpha ]==> ((a ((a a)(a a)))(^x.x)) REDUCED to normal form. ------ 198614/23728665. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.a)(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.y)(a b))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(a b))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(a b))) 5. ==[ beta ]==> (((a (a a)) b)(a b)) REDUCED to normal form. ------ 198615/23728692. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.b)(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.b)(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.b)(^y1.y1))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.b)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.b)(^x1.x1))) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 198616/23728719. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 198617/23728746. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 198618/23728773. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(z z))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(z z))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.(z z)))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.(y y)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^y.(y y)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.(y y)))) IRREDUCIBLE: cycle. ------ 198619/23728800. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b)) a) REDUCED to normal form. ------ 198620/23728854. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.y1)(^z1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.y1)(^z1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1)(^y1.b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))(^y1.b)) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(^x1.b)) REDUCED to normal form. ------ 198621/23728998. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((a (^z.z))((^x1.x1)(^y1.y1)))(^y.y)) 6. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (((a (^x.x))(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 198622/23729385. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^c.a) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.a) a)) 3. ==[ beta ]==> (((^y.y) b)((^z.a) a)) 4. ==[ alpha ]==> (((^x.x) b)((^y.a) a)) 5. ==[ beta ]==> (b ((^y.a) a)) 6. ==[ alpha ]==> (b ((^x.a) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198623/23729403. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(((^x1.x1)(^y1.y1))(a a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(((^x1.x1)(^y1.y1))(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(a a))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a a))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a a))) 7. ==[ beta ]==> (((^y.y)(^z.z))(a a)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(a a)) 9. ==[ beta ]==> ((^y.y)(a a)) 10. ==[ alpha ]==> ((^x.x)(a a)) 11. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198624/23729412. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.(^z.z)) b)) 3. ==[ beta ]==> (((a (a (^x.x))) a)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.y)) REDUCED to normal form. ------ 198625/23729430. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((a (a a))(a (^z.z)))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (a a))(a (^z.z)))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (a a))(a (^y.y)))) REDUCED to normal form. ------ 198626/23729457. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1) a)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1) a)((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) a)((^z.z) a))) 5. ==[ beta ]==> (((^y.y) a)((^z.z) a)) 6. ==[ alpha ]==> (((^x.x) a)((^y.y) a)) 7. ==[ beta ]==> (a ((^y.y) a)) 8. ==[ alpha ]==> (a ((^x.x) a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198627/23729511. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a a)(^y.y))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a a)(^x.x))) REDUCED to normal form. ------ 198628/23729547. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((^x1.x1)(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.x1))) 7. ==[ beta ]==> (((^y.y)(^z.z))(^x1.x1)) 8. ==[ alpha ]==> (((^x.x)(^y.y))(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198629/23729574. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((a (a a))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 198630/23729655. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 198631/23729736. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(((^a.a) a) c)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1) a) c)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1) a) c)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z) a) c)) 5. ==[ beta ]==> ((b (^x.(^y.y)))(a c)) REDUCED to normal form. ------ 198632/23729817. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1)) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1)) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1)) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1)) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198633/23729835. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((a (a a))(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((a (a a))(a a))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(a a))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(a a))) REDUCED to normal form. ------ 198634/23729844. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(z z)) b)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(b b)) REDUCED to normal form. ------ 198635/23729862. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (a (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (a (^x1.x1)))) REDUCED to normal form. ------ 198636/23729907. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(b (^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.(z z)))) REDUCED to normal form. ------ 198637/23729934. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^y.y)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 198638/23729961. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((^a.(a a))(a a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((^x.(x x))(a a))) 3. ==[ beta ]==> (((a (a a))((a a)(a a)))((a a)(a a))) REDUCED to normal form. ------ 198639/23729988. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.a)(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.a)(a (^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.a)(a (^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)((^y.a)(a (^z.z)))) 7. ==[ beta ]==> (b ((^y.a)(a (^z.z)))) 8. ==[ alpha ]==> (b ((^x.a)(a (^y.y)))) 9. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198640/23730015. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(^z.z)) REDUCED to normal form. ------ 198641/23730042. ------ 1. ==[ start ]==> (((a b)(b a))((^a.a)(a (a a)))) 2. ==[ alpha ]==> (((a b)(b a))((^x.x)(a (a a)))) 3. ==[ beta ]==> (((a b)(b a))(a (a a))) REDUCED to normal form. ------ 198642/23730069. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(y y))(^z.z))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))((^z.z)(^z.z))) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 8. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 198643/23730096. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a)) a) REDUCED to normal form. ------ 198644/23730150. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.(z z))) REDUCED to normal form. ------ 198645/23730258. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(a (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(a (^z.(z z)))) 5. ==[ beta ]==> ((a (^y.y))(a (^z.(z z)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 198646/23730276. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(((^z.z) a)(^x1.x1))) 3. ==[ beta ]==> ((b (^y.y))(((^z.z) a)(^x1.x1))) 4. ==[ alpha ]==> ((b (^x.x))(((^y.y) a)(^z.z))) 5. ==[ beta ]==> ((b (^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((b (^x.x))(a (^y.y))) REDUCED to normal form. ------ 198647/23730285. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((^b.a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((^y.a)(a a))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a)) a) REDUCED to normal form. ------ 198648/23730312. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.(^y1.y1))(a (^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))(a (^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 198649/23730321. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(b c)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b c)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b c)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b c)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198650/23730483. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a a)(a (^y1.y1)))) 3. ==[ beta ]==> (b ((a a)(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((a a)(a (^x.x)))) REDUCED to normal form. ------ 198651/23730591. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(b (a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(b (a a))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198652/23730726. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(a (a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(a (a a))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(a (a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a (a a))) 5. ==[ beta ]==> ((^y.y)(a (a a))) 6. ==[ alpha ]==> ((^x.x)(a (a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 198653/23730735. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)((^a.a) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) b)((^y.y) a)) 3. ==[ beta ]==> (((a (a (^x.x))) b) a) REDUCED to normal form. ------ 198654/23730761. ------ 1. ==[ start ]==> (^a.(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> (^x.(((^y.y)(^z.(^x1.x1))) x)) 3. ==[ eta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198655/23730762. ------ 1. ==[ start ]==> (a (((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> (a (((^x.x)(^y.(^z.z))) a)) 3. ==[ beta ]==> (a ((^y.(^z.z)) a)) 4. ==[ alpha ]==> (a ((^x.(^y.y)) a)) 5. ==[ beta ]==> (a (^y.y)) 6. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 198656/23742693. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a) a) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a) a) 3. ==[ beta ]==> (((^y.(^z.z)) a) a) 4. ==[ alpha ]==> (((^x.(^y.y)) a) a) 5. ==[ beta ]==> ((^y.y) a) 6. ==[ alpha ]==> ((^x.x) a) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198657/23742699. ------ 1. ==[ start ]==> ((^a.a)(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1))) a) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) a) 5. ==[ beta ]==> ((^y.(^z.z)) a) 6. ==[ alpha ]==> ((^x.(^y.y)) a) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198658/23742708. ------ 1. ==[ start ]==> ((^a.(^a.a))((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198659/23742726. ------ 1. ==[ start ]==> ((^a.(a a))((a (a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.(x x))((a (a (^y.y))) b)) 3. ==[ beta ]==> (((a (a (^y.y))) b)((a (a (^y.y))) b)) 4. ==[ alpha ]==> (((a (a (^x.x))) b)((a (a (^y.y))) b)) REDUCED to normal form. ------ 198660/23742753. ------ 1. ==[ start ]==> ((^a.b)(((^a.(^a.a)) a) c)) 2. ==[ alpha ]==> ((^x.b)(((^y.(^z.z)) a) c)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 198661/23743143. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 198662/23743152. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.((^y1.y1)(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 198663/23743644. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198664/23744076. ------ 1. ==[ start ]==> ((^a.((a a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((^x.((x x) x))(((^y.(^z.z)) a) b)) 3. ==[ beta ]==> (((((^y.(^z.z)) a) b)(((^y.(^z.z)) a) b))(((^y.(^z.z)) a) b)) 4. ==[ alpha ]==> (((((^x.(^y.y)) a) b)(((^z.(^x1.x1)) a) b))(((^y1.(^z1.z1)) a) b)) 5. ==[ beta ]==> ((((^y.y) b)(((^z.(^x1.x1)) a) b))(((^y1.(^z1.z1)) a) b)) 6. ==[ alpha ]==> ((((^x.x) b)(((^y.(^z.z)) a) b))(((^x1.(^y1.y1)) a) b)) 7. ==[ beta ]==> ((b (((^y.(^z.z)) a) b))(((^x1.(^y1.y1)) a) b)) 8. ==[ alpha ]==> ((b (((^x.(^y.y)) a) b))(((^z.(^x1.x1)) a) b)) 9. ==[ beta ]==> ((b ((^y.y) b))(((^z.(^x1.x1)) a) b)) 10. ==[ alpha ]==> ((b ((^x.x) b))(((^y.(^z.z)) a) b)) 11. ==[ beta ]==> ((b b)(((^y.(^z.z)) a) b)) 12. ==[ alpha ]==> ((b b)(((^x.(^y.y)) a) b)) 13. ==[ beta ]==> ((b b)((^y.y) b)) 14. ==[ alpha ]==> ((b b)((^x.x) b)) 15. ==[ beta ]==> ((b b) b) REDUCED to normal form. ------ 198665/23744976. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((^z.(a a))((^x1.x1) a))) 3. ==[ beta ]==> (^y.(((^z.(a a))((^x1.x1) a))((^z.(a a))((^x1.x1) a)))) 4. ==[ alpha ]==> (^x.(((^y.(a a))((^z.z) a))((^x1.(a a))((^y1.y1) a)))) 5. ==[ beta ]==> (^x.((a a)((^x1.(a a))((^y1.y1) a)))) 6. ==[ alpha ]==> (^x.((a a)((^y.(a a))((^z.z) a)))) 7. ==[ beta ]==> (^x.((a a)(a a))) REDUCED to normal form. ------ 198666/23745183. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2)))))) 4. ==[ alpha ]==> ((^x.x)((((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(^z2.(^x3.(^y3.y3)))))) 5. ==[ beta ]==> ((((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))(((^x2.x2)(^y2.y2))(^z2.(^x3.(^y3.y3))))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.(^z2.(^x3.x3))))) 7. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(((^z1.z1)(^x2.x2))(^y2.(^z2.(^x3.x3))))) 8. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 9. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1)(^z1.z1))(^x2.(^y2.(^z2.z2))))) 10. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 11. ==[ beta ]==> (^y.(^z.z)) 12. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198667/23747451. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))(((a a) a)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x1.(a a)))(^y.(^z.z))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.z))) REDUCED to normal form. ------ 198668/23747958. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.((z z)(z z)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.((z z)(z z)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.((y y)(y y)))) REDUCED to normal form. ------ 198669/23748369. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((b a)(^b.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 198670/23749368. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((^y.y)(a a))(^z.(z z)))) 3. ==[ beta ]==> (((((^y.y)(a a))(^z.(z z)))(((^y.y)(a a))(^z.(z z))))((((^y.y)(a a))(^z.(z z)))(((^y.y)(a a))(^z.(z z))))) 4. ==[ alpha ]==> (((((^x.x)(a a))(^y.(y y)))(((^z.z)(a a))(^x1.(x1 x1))))((((^y1.y1)(a a))(^z1.(z1 z1)))(((^x2.x2)(a a))(^y2.(y2 y2))))) 5. ==[ beta ]==> ((((a a)(^y.(y y)))(((^z.z)(a a))(^x1.(x1 x1))))((((^y1.y1)(a a))(^z1.(z1 z1)))(((^x2.x2)(a a))(^y2.(y2 y2))))) 6. ==[ alpha ]==> ((((a a)(^x.(x x)))(((^y.y)(a a))(^z.(z z))))((((^x1.x1)(a a))(^y1.(y1 y1)))(((^z1.z1)(a a))(^x2.(x2 x2))))) 7. ==[ beta ]==> ((((a a)(^x.(x x)))((a a)(^z.(z z))))((((^x1.x1)(a a))(^y1.(y1 y1)))(((^z1.z1)(a a))(^x2.(x2 x2))))) 8. ==[ alpha ]==> ((((a a)(^x.(x x)))((a a)(^y.(y y))))((((^z.z)(a a))(^x1.(x1 x1)))(((^y1.y1)(a a))(^z1.(z1 z1))))) 9. ==[ beta ]==> ((((a a)(^x.(x x)))((a a)(^y.(y y))))(((a a)(^x1.(x1 x1)))(((^y1.y1)(a a))(^z1.(z1 z1))))) 10. ==[ alpha ]==> ((((a a)(^x.(x x)))((a a)(^y.(y y))))(((a a)(^z.(z z)))(((^x1.x1)(a a))(^y1.(y1 y1))))) 11. ==[ beta ]==> ((((a a)(^x.(x x)))((a a)(^y.(y y))))(((a a)(^z.(z z)))((a a)(^y1.(y1 y1))))) 12. ==[ alpha ]==> ((((a a)(^x.(x x)))((a a)(^y.(y y))))(((a a)(^z.(z z)))((a a)(^x1.(x1 x1))))) REDUCED to normal form. ------ 198671/23749875. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 198672/23750448. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((b a) a)) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((b a) a)) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198673/23751702. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^a.(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198674/23752143. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.((^x2.x2)(z1 z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.((^x2.x2)(z1 z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(y1 y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.((^z1.z1)(y1 y1)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.((^y1.y1)(x1 x1)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198675/23752332. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(^c.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(^z.(a b))) 3. ==[ beta ]==> ((b (^y.(y y)))(^z.(a b))) 4. ==[ alpha ]==> ((b (^x.(x x)))(^y.(a b))) REDUCED to normal form. ------ 198676/23752428. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.(^y1.y1))((^z1.z1) a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 198677/23752530. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))(^c.(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))(^y.(^z.b))) 3. ==[ beta ]==> (((a (a a)) b)(^y.(^z.b))) 4. ==[ alpha ]==> (((a (a a)) b)(^x.(^y.b))) REDUCED to normal form. ------ 198678/23753250. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^a.((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.((z z) z))) 3. ==[ beta ]==> (((^y.y) b)(^z.((z z) z))) 4. ==[ alpha ]==> (((^x.x) b)(^y.((y y) y))) 5. ==[ beta ]==> (b (^y.((y y) y))) 6. ==[ alpha ]==> (b (^x.((x x) x))) REDUCED to normal form. ------ 198679/23753682. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198680/23753907. ------ 1. ==[ start ]==> (((a b)(b a))(^c.(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(b a))(^x.(^y.(y y)))) REDUCED to normal form. ------ 198681/23754174. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198682/23754213. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(^b.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(^y1.((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)(^y1.((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z) a))) 5. ==[ beta ]==> (^y.((^z.z) a)) 6. ==[ alpha ]==> (^x.((^y.y) a)) 7. ==[ beta ]==> (^x.a) REDUCED to normal form. ------ 198683/23754591. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(^b.(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198684/23754600. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^a.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.(y y))) REDUCED to normal form. ------ 198685/23754627. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)(^a.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(^x1.x1)) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.x1)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.z)) 5. ==[ beta ]==> ((^y.y)(^z.z)) 6. ==[ alpha ]==> ((^x.x)(^y.y)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198686/23754639. ------ 1. ==[ start ]==> ((a a)(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a a)(((^x.x)(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a a)((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((a a)((^x.(^y.y)) a)) 5. ==[ beta ]==> ((a a)(^y.y)) 6. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 198687/23754648. ------ 1. ==[ start ]==> ((a (^a.a))((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 198688/23754666. ------ 1. ==[ start ]==> ((a (a a))((a (a (^a.a))) b)) 2. ==[ alpha ]==> ((a (a a))((a (a (^x.x))) b)) REDUCED to normal form. ------ 198689/23754675. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.(^x1.x1))) 7. ==[ beta ]==> ((^z.(^x1.x1))(^y.y)) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198690/23754693. ------ 1. ==[ start ]==> ((a b)(((^a.(^a.a)) a) c)) 2. ==[ alpha ]==> ((a b)(((^x.(^y.y)) a) c)) 3. ==[ beta ]==> ((a b)((^y.y) c)) 4. ==[ alpha ]==> ((a b)((^x.x) c)) 5. ==[ beta ]==> ((a b) c) REDUCED to normal form. ------ 198691/23754783. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.a)))((^b.b)(^c.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198692/23754810. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(^y1.(^z1.z1)))(^x2.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.(^z1.z1)))(^x2.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.b)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.b)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198693/23754972. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> ((^y.a)((^z.(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.a)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 198694/23755053. ------ 1. ==[ start ]==> (((^a.a)((^a.a) a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.x)((^y.y) a))((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.x1))(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> (a ((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> (a ((^x.(^y.y))(^z.(z (^x1.x1))))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 198695/23755062. ------ 1. ==[ start ]==> (((a a)(^b.a))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))(b (a (a (^y.y))))) REDUCED to normal form. ------ 198696/23755080. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198697/23755089. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a ((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(a (^x1.(^y1.y1)))) REDUCED to normal form. ------ 198698/23755116. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> ((a (^y.y))((a (a (^z.z)))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 198699/23755224. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a a)(((^y.y) b)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(((^x.x) b)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a a)(b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> ((a a)(b ((^x.x)(^y.y)))) 7. ==[ beta ]==> ((a a)(b (^y.y))) 8. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 198700/23755305. ------ 1. ==[ start ]==> ((((^a.a) a) b)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a) b)(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a b)(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a b)(((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a b)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 198701/23755332. ------ 1. ==[ start ]==> (((a (a a)) a)(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) a)(((^x.x)(a a))((a a)(^y.y)))) 3. ==[ beta ]==> (((a (a a)) a)((a a)((a a)(^y.y)))) 4. ==[ alpha ]==> (((a (a a)) a)((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 198702/23755359. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))((a b)(b a))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))((a b)(b a))) REDUCED to normal form. ------ 198703/23755386. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))(((a a) a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 198704/23755413. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)((^y1.y1) b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1) b))) 7. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) b)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 9. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 198705/23755440. ------ 1. ==[ start ]==> (((a (a a))(^a.a))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 198706/23755557. ------ 1. ==[ start ]==> (((a (a a))(a a))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a a))((a (a (^x.x)))(^y.y))) REDUCED to normal form. ------ 198707/23755584. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 198708/23755674. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198709/23755809. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.b)(b a))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.b)(b a))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y))) b) REDUCED to normal form. ------ 198710/23755962. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((a a)(^y.(y (^z.z))))) REDUCED to normal form. ------ 198711/23755989. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a (a (^z.z))) a)) 3. ==[ beta ]==> (((^y.y)(a a))((a (a (^z.z))) a)) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a (^y.y))) a)) 5. ==[ beta ]==> ((a a)((a (a (^y.y))) a)) 6. ==[ alpha ]==> ((a a)((a (a (^x.x))) a)) REDUCED to normal form. ------ 198712/23756016. ------ 1. ==[ start ]==> ((a ((a a) a))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> ((a ((a a) a))(((^x.(^y.y)) a) b)) 3. ==[ beta ]==> ((a ((a a) a))((^y.y) b)) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x) b)) 5. ==[ beta ]==> ((a ((a a) a)) b) REDUCED to normal form. ------ 198713/23756106. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.z)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (a ((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 198714/23756214. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(^x1.x1)))((^y1.(a a))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(a a))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(a a))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(a a))(^y.(^z.z))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198715/23756421. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> ((a (a (a a)))((^y.(y (^z.z))) a)) 4. ==[ alpha ]==> ((a (a (a a)))((^x.(x (^y.y))) a)) 5. ==[ beta ]==> ((a (a (a a)))(a (^y.y))) 6. ==[ alpha ]==> ((a (a (a a)))(a (^x.x))) REDUCED to normal form. ------ 198716/23756520. ------ 1. ==[ start ]==> (((^a.b) a)(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.b) a)(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> (b (((^y.y) b)(a (a a)))) 4. ==[ alpha ]==> (b (((^x.x) b)(a (a a)))) 5. ==[ beta ]==> (b (b (a (a a)))) REDUCED to normal form. ------ 198717/23756682. ------ 1. ==[ start ]==> ((((a a) a) b)(((a a) a)(b a))) REDUCED to normal form. ------ 198718/23756709. ------ 1. ==[ start ]==> (((a b) a)(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) a)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a b) a)((^y.y)(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(a (^y.(^z.z))))) 5. ==[ beta ]==> (((a b) a)(a (^y.(^z.z)))) 6. ==[ alpha ]==> (((a b) a)(a (^x.(^y.y)))) REDUCED to normal form. ------ 198719/23756736. ------ 1. ==[ start ]==> (((a a)(^a.b))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)(^x.b))((a (a a))((^y.y) b))) 3. ==[ beta ]==> (((a a)(^x.b))((a (a a)) b)) REDUCED to normal form. ------ 198720/23756790. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))((a (^x1.x1))(b (^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(b (^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(b (^x1.x1)))) REDUCED to normal form. ------ 198721/23756817. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a a)((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a (a a))(^x.(x x)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a a)(^y.y))) REDUCED to normal form. ------ 198722/23756916. ------ 1. ==[ start ]==> ((a (^b.(a a)))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 198723/23756934. ------ 1. ==[ start ]==> (((a a)(a b))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(a b))(((^x.x) b)(^y.(y y)))) 3. ==[ beta ]==> (((a a)(a b))(b (^y.(y y)))) 4. ==[ alpha ]==> (((a a)(a b))(b (^x.(x x)))) REDUCED to normal form. ------ 198724/23756961. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 198725/23756988. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((b a)(^c.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((b a)(^x1.a))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((b a)(^x1.a))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((b a)(^z.a))) 5. ==[ beta ]==> ((a (^y.y))((b a)(^z.a))) 6. ==[ alpha ]==> ((a (^x.x))((b a)(^y.a))) REDUCED to normal form. ------ 198726/23757015. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))(((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 198727/23757042. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((^x1.x1)(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((^x1.x1)(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((^z.z)(a a))(^x1.(a a)))) 5. ==[ beta ]==> (((^y.y) a)(((^z.z)(a a))(^x1.(a a)))) 6. ==[ alpha ]==> (((^x.x) a)(((^y.y)(a a))(^z.(a a)))) 7. ==[ beta ]==> (a (((^y.y)(a a))(^z.(a a)))) 8. ==[ alpha ]==> (a (((^x.x)(a a))(^y.(a a)))) 9. ==[ beta ]==> (a ((a a)(^y.(a a)))) 10. ==[ alpha ]==> (a ((a a)(^x.(a a)))) REDUCED to normal form. ------ 198728/23757069. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a b)(^y.(^z.z)))) REDUCED to normal form. ------ 198729/23757123. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 198730/23757132. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(a a))((^z.(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(a a))((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198731/23757159. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^a.(a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(x1 x1))((^y1.y1) b))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))((^z.z) b))) 5. ==[ beta ]==> ((^y.(y y))((^z.z) b)) 6. ==[ alpha ]==> ((^x.(x x))((^y.y) b)) 7. ==[ beta ]==> (((^y.y) b)((^y.y) b)) 8. ==[ alpha ]==> (((^x.x) b)((^y.y) b)) 9. ==[ beta ]==> (b ((^y.y) b)) 10. ==[ alpha ]==> (b ((^x.x) b)) 11. ==[ beta ]==> (b b) REDUCED to normal form. ------ 198732/23757213. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^a.(^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.(^y1.y1))(b (^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(b (^x2.x2)))) 5. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(b (^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(b (^x1.x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(b (^x1.x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(b (^z.z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198733/23757348. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((a a)((^y.y)(^z.(z z)))) 6. ==[ alpha ]==> ((a a)((^x.x)(^y.(y y)))) 7. ==[ beta ]==> ((a a)(^y.(y y))) 8. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 198734/23757375. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.y1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198735/23757510. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (b ((^z.a)(^x1.a))) 4. ==[ alpha ]==> (b ((^x.a)(^y.a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198736/23757735. ------ 1. ==[ start ]==> (((^a.b) c)(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) c)(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (b (((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (b (((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (b (b ((^y.y) a))) 6. ==[ alpha ]==> (b (b ((^x.x) a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 198737/23757978. ------ 1. ==[ start ]==> (((a b) c)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> (((a b) c)(((^x.x) a)((^y.y) b))) 3. ==[ beta ]==> (((a b) c)(a ((^y.y) b))) 4. ==[ alpha ]==> (((a b) c)(a ((^x.x) b))) 5. ==[ beta ]==> (((a b) c)(a b)) REDUCED to normal form. ------ 198738/23758005. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)((a (^y.y))((a a)(a a)))) 3. ==[ beta ]==> (((a a) b)((a (^y.y))((a a)(a a)))) 4. ==[ alpha ]==> (((a a) b)((a (^x.x))((a a)(a a)))) REDUCED to normal form. ------ 198739/23758032. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)(b (^y.y)))) REDUCED to normal form. ------ 198740/23758131. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))((^y.y)((^z.z) a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)((^z.z) a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)((^y.y) a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y) a)) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x) a)) 7. ==[ beta ]==> ((((a a) a)((a a) a)) a) REDUCED to normal form. ------ 198741/23758212. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((^z.(^x1.x1))((a a) a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((a a) a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198742/23758338. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((a (a a))(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a))((a (a a))(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((a (a a))(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 198743/23758365. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> ((a (a b))(((^y.y) a)(^z.z))) 4. ==[ alpha ]==> ((a (a b))(((^x.x) a)(^y.y))) 5. ==[ beta ]==> ((a (a b))(a (^y.y))) 6. ==[ alpha ]==> ((a (a b))(a (^x.x))) REDUCED to normal form. ------ 198744/23758446. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((b (^a.a)) a)) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((b (^x.x)) a)) REDUCED to normal form. ------ 198745/23758473. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(((a a)(a a)) b)) 2. ==[ alpha ]==> (((a b)((^x.x) a))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a b) a)(((a a)(a a)) b)) REDUCED to normal form. ------ 198746/23758500. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((^z.z) b) c)) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((^z.z) b) c)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((^y.y) b) c)) 5. ==[ beta ]==> (((a a)(a (^x.x)))(b c)) REDUCED to normal form. ------ 198747/23758644. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^a.b)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.b)(^x1.(a a)))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.b)(^x1.(a a)))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.b)(^x1.(a a)))) 5. ==[ beta ]==> (b ((^z.b)(^x1.(a a)))) 6. ==[ alpha ]==> (b ((^x.b)(^y.(a a)))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 198748/23758725. ------ 1. ==[ start ]==> (((^a.b)(^a.(a a)))((^a.(a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.(y y)))((^z.(z z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 198749/23758788. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(b ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(b ((a a)(a a)))) REDUCED to normal form. ------ 198750/23758896. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((a (^z.(^x1.x1)))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^y.(a a)))((a (^z.(^x1.x1)))((^y1.y1) a))) 4. ==[ alpha ]==> ((a (^x.(a a)))((a (^y.(^z.z)))((^x1.x1) a))) 5. ==[ beta ]==> ((a (^x.(a a)))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 198751/23758923. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((b a)(a (a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((b a)(a (a a)))) REDUCED to normal form. ------ 198752/23758977. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.z)(a a))((a a) a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((a a)((a a) a))) REDUCED to normal form. ------ 198753/23759004. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))((a b)(a b))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))((a b)(a b))) REDUCED to normal form. ------ 198754/23759031. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))(((a a) a)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)(^y.a))(((a a) a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.a))(((a a) a)((^y.y)(a a)))) 5. ==[ beta ]==> (((a a)(^x.a))(((a a) a)(a a))) REDUCED to normal form. ------ 198755/23759058. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((^y1.y1)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.x1)((a a)(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^y1.y1))) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)(^x1.x1))) REDUCED to normal form. ------ 198756/23759202. ------ 1. ==[ start ]==> (((a (a a))(a b))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))(a b))(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 198757/23759229. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(((^y.y) b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(((^x.x) b)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a) a)(b (^y.(^z.z)))) 8. ==[ alpha ]==> (((a a) a)(b (^x.(^y.y)))) REDUCED to normal form. ------ 198758/23759256. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((a (^z.(^x1.x1)))(^y1.a))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((a (^y.(^z.z)))(^x1.a))) REDUCED to normal form. ------ 198759/23759283. ------ 1. ==[ start ]==> (((a b)(a (a a)))((b a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((b a)(^x.(x x)))) REDUCED to normal form. ------ 198760/23759310. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))(((a a)(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y) a))(((a a)(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))(((a a)(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a) a)(((a a)(^y.y))(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a) a)(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 198761/23759391. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))(((a a) a)(^z.(a a)))) REDUCED to normal form. ------ 198762/23759481. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^b.a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.a)(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a a)((^z.a)(a (^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((a a)((^x.a)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 198763/23759562. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^c.(a a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.(a a))(^y1.y1))) 3. ==[ beta ]==> (b ((^x1.(a a))(^y1.y1))) 4. ==[ alpha ]==> (b ((^x.(a a))(^y.y))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 198764/23759697. ------ 1. ==[ start ]==> (((^a.a)(a (^a.(^a.a))))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(a a))(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(a a))(^x1.a))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a a)) REDUCED to normal form. ------ 198765/23759724. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^a.b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.b)(^x1.b))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.b))) 5. ==[ beta ]==> ((^y.b)(^z.b)) 6. ==[ alpha ]==> ((^x.b)(^y.b)) 7. ==[ beta ]==> b REDUCED to normal form. ------ 198766/23759778. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a)(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((((^y.y)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 8. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(^x1.x1)))) 9. ==[ beta ]==> (((a a)(a a))(^y.y)) 10. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 198767/23759859. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> (b ((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198768/23759868. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(b ((^a.a) b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(b ((^z.z) b))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(b b)) REDUCED to normal form. ------ 198769/23759895. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(a ((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(a ((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(a ((a a)(a a)))) REDUCED to normal form. ------ 198770/23759922. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(((^z.z) b)(a a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(b (a a))) REDUCED to normal form. ------ 198771/23759976. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((b a)((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z))((b a) a)) REDUCED to normal form. ------ 198772/23760282. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) REDUCED to normal form. ------ 198773/23760309. ------ 1. ==[ start ]==> ((a ((^a.a) b))((b a)(^b.a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((b a)(^y.a))) 3. ==[ beta ]==> ((a b)((b a)(^y.a))) 4. ==[ alpha ]==> ((a b)((b a)(^x.a))) REDUCED to normal form. ------ 198774/23760480. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^a.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(z z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.(z z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(x x))((a a)(^y.y)))) 5. ==[ beta ]==> (b (((a a)(^y.y))((a a)(^y.y)))) 6. ==[ alpha ]==> (b (((a a)(^x.x))((a a)(^y.y)))) REDUCED to normal form. ------ 198775/23760588. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^b.b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198776/23760723. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.b)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.b)(^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y))) b) REDUCED to normal form. ------ 198777/23760804. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((^y.(y y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.(^z.z)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^y.(^z.z)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198778/23760813. ------ 1. ==[ start ]==> (((a b)(^c.a))(d ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))(d ((a a)(^y.y)))) REDUCED to normal form. ------ 198779/23760840. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))(c (b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(c (b a))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(c (b a))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(c (b a))) REDUCED to normal form. ------ 198780/23760867. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(b (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 198781/23760921. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(a a))) REDUCED to normal form. ------ 198782/23760948. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((b a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((b a)(a (^z.z)))) 3. ==[ beta ]==> ((b (^y.y))((b a)(a (^z.z)))) 4. ==[ alpha ]==> ((b (^x.x))((b a)(a (^y.y)))) REDUCED to normal form. ------ 198783/23760984. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((^c.(^a.a)) d)) 2. ==[ alpha ]==> (((a a)((^x.x) b))((^y.(^z.z)) d)) 3. ==[ beta ]==> (((a a) b)((^y.(^z.z)) d)) 4. ==[ alpha ]==> (((a a) b)((^x.(^y.y)) d)) 5. ==[ beta ]==> (((a a) b)(^y.y)) 6. ==[ alpha ]==> (((a a) b)(^x.x)) REDUCED to normal form. ------ 198784/23761254. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((b a)(^x1.(^y1.y1)))) REDUCED to normal form. ------ 198785/23761281. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> ((b (a a))(((a a)(^y.y))(^z.a))) 4. ==[ alpha ]==> ((b (a a))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 198786/23761308. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x)(a a))(^y.(y y)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((a a)(^y.(y y)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((a a)(^x.(x x)))) REDUCED to normal form. ------ 198787/23761344. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^a.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.b)((^y.y)(^z.z))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 198788/23761479. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^a.(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(b a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198789/23761587. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((^y1.(^z1.z1))(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198790/23761695. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.(^y1.y1))(^z1.b))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.b))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.b))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.b)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.b)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198791/23761749. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^b.a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((b a)(b a))((^y.a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.a)(^y.(^z.z)))) 5. ==[ beta ]==> (((b a)(b a)) a) REDUCED to normal form. ------ 198792/23761812. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 198793/23761839. ------ 1. ==[ start ]==> (((a b)(^a.b))((b a)(a a))) 2. ==[ alpha ]==> (((a b)(^x.b))((b a)(a a))) REDUCED to normal form. ------ 198794/23761893. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((^x1.x1)(a a))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)((^y1.y1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a)((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))((a a) a)) REDUCED to normal form. ------ 198795/23761947. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a)(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))(((a a) a)(^x1.x1))) REDUCED to normal form. ------ 198796/23761974. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a) a))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(^y1.y1))((a a) a))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(^x1.x1))((a a) a))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1)((a a) a))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z)((a a) a))) 7. ==[ beta ]==> ((b (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 198797/23762001. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))((a (a a))(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))((a (a a))(a b))) REDUCED to normal form. ------ 198798/23762118. ------ 1. ==[ start ]==> (((a (a a))(b a))((b a)(^a.a))) 2. ==[ alpha ]==> (((a (a a))(b a))((b a)(^x.x))) REDUCED to normal form. ------ 198799/23762145. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(((a a)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((a a)(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((a a)(^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 198800/23762172. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((^y.y)(a a))(^z.a))) 3. ==[ beta ]==> ((((a a) a)(a a))(((^y.y)(a a))(^z.a))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((^x.x)(a a))(^y.a))) 5. ==[ beta ]==> ((((a a) a)(a a))((a a)(^y.a))) 6. ==[ alpha ]==> ((((a a) a)(a a))((a a)(^x.a))) REDUCED to normal form. ------ 198801/23762199. ------ 1. ==[ start ]==> (((a b)(a b))((a b)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(a b))((a b)(^x.(x x)))) REDUCED to normal form. ------ 198802/23762226. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))(((a a) a)(^y.(^z.z)))) 3. ==[ beta ]==> (((a a)((a a) a))(((a a) a)(^y.(^z.z)))) 4. ==[ alpha ]==> (((a a)((a a) a))(((a a) a)(^x.(^y.y)))) REDUCED to normal form. ------ 198803/23762307. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)(((^z.z) a)(^x1.(a a)))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(a (^x1.(a a)))) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(a (^z.(a a)))) REDUCED to normal form. ------ 198804/23762334. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((b (a (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((a (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 198805/23762388. ------ 1. ==[ start ]==> ((a (b (^a.a)))((b a) a)) 2. ==[ alpha ]==> ((a (b (^x.x)))((b a) a)) REDUCED to normal form. ------ 198806/23762478. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^a.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.b)(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.b)(^y2.(y2 y2)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.b)(^y2.(y2 y2)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(^x1.(x1 x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198807/23762559. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^a.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(z z))(^x1.b))) 3. ==[ beta ]==> (b ((^z.(z z))(^x1.b))) 4. ==[ alpha ]==> (b ((^x.(x x))(^y.b))) 5. ==[ beta ]==> (b ((^y.b)(^y.b))) 6. ==[ alpha ]==> (b ((^x.b)(^y.b))) 7. ==[ beta ]==> (b b) REDUCED to normal form. ------ 198808/23762703. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((^y.y)(a a))(a (^z.z)))) 3. ==[ beta ]==> ((b c)(((^y.y)(a a))(a (^z.z)))) 4. ==[ alpha ]==> ((b c)(((^x.x)(a a))(a (^y.y)))) 5. ==[ beta ]==> ((b c)((a a)(a (^y.y)))) 6. ==[ alpha ]==> ((b c)((a a)(a (^x.x)))) REDUCED to normal form. ------ 198809/23762730. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((a b)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a)) b)((a b)((^x.x) a))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a b) a)) REDUCED to normal form. ------ 198810/23762838. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))(((^a.a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(((^z.z) a)(a b))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(a b))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(a b))) 5. ==[ beta ]==> ((a (^x.x))(a (a b))) REDUCED to normal form. ------ 198811/23762865. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))((a (^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))((a (^x1.x1))(a a))) REDUCED to normal form. ------ 198812/23762937. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 198813/23763045. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198814/23763171. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 198815/23763198. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((^y.y)(a a)) b)) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a a) b)) REDUCED to normal form. ------ 198816/23763225. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((a b) c)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((a b) c)) 3. ==[ beta ]==> ((a ((^y.y) b))((a b) c)) 4. ==[ alpha ]==> ((a ((^x.x) b))((a b) c)) 5. ==[ beta ]==> ((a b)((a b) c)) REDUCED to normal form. ------ 198817/23763441. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))((^b.(a a)) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))((^z.(a a)) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))(a a)) REDUCED to normal form. ------ 198818/23763468. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^a.b) c)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.b) c)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.b) c)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.b) c)) 5. ==[ beta ]==> ((b a)((^y.b) c)) 6. ==[ alpha ]==> ((b a)((^x.b) c)) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 198819/23763639. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(a (^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(a (^z.(^x1.x1)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 198820/23763720. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^c.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.a)((^y1.y1) a))) 3. ==[ beta ]==> (b ((^x1.a)((^y1.y1) a))) 4. ==[ alpha ]==> (b ((^x.a)((^y.y) a))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 198821/23763828. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^a.(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.(^x2.x2))(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.(^x2.x2))(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198822/23763963. ------ 1. ==[ start ]==> (((^a.a)((^a.(^a.a)) a))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)((^y.(^z.z)) a))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.(^x1.x1))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 7. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198823/23763990. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^a.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(y y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.(y y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.(x x))(^y.(^z.z))) 7. ==[ beta ]==> ((^y.(^z.z))(^y.(^z.z))) 8. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198824/23764044. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.(^x1.x1))(^y1.b))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.(^x1.x1))(^y1.b))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.(^z.z))(^x1.b))) 7. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.b))) 8. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.b))) 9. ==[ beta ]==> ((b b)(^y.y)) 10. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 198825/23764053. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(b (a b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(b (a b))) REDUCED to normal form. ------ 198826/23764080. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(a ((^z1.z1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(a ((^z1.z1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(a ((^y1.y1)(a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a ((^y1.y1)(a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a ((^x1.x1)(a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198827/23764134. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(((a a) a)(a (^z.z)))) REDUCED to normal form. ------ 198828/23764161. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((^z.z)(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((^y.y)(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z)((^x1.x1) a))) 6. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)((^z.z) a))) 7. ==[ beta ]==> (((a a)(^x.(a a)))((^z.z) a)) 8. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y) a)) 9. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 198829/23764188. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((a (a a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((a (a a))(a (a a)))) REDUCED to normal form. ------ 198830/23764242. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((a (^y1.y1))((a a) a))) REDUCED to normal form. ------ 198831/23764269. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a a)(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a a)(a b))) 3. ==[ beta ]==> ((b (^y.(y y)))((a a)(a b))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a a)(a b))) REDUCED to normal form. ------ 198832/23764368. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 198833/23764386. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((a (a a))(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (a a))(^z.(z z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (a a))(^y.(y y)))) REDUCED to normal form. ------ 198834/23764413. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 198835/23764467. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a a)(^a.b))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a a)(^y.b))) 3. ==[ beta ]==> (((a (a a)) b)((a a)(^y.b))) 4. ==[ alpha ]==> (((a (a a)) b)((a a)(^x.b))) REDUCED to normal form. ------ 198836/23764494. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a b) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a b) a)) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a b) a)) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a b) a)) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a b) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a b) a)) REDUCED to normal form. ------ 198837/23764521. ------ 1. ==[ start ]==> ((((a a) a)(b a))(((a a) a) b)) REDUCED to normal form. ------ 198838/23764548. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((^a.a)(^a.a)) c)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((^y.y)(^z.z)) c)) 3. ==[ beta ]==> (((a b)((a a)(^x.x)))((^z.z) c)) 4. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.y) c)) 5. ==[ beta ]==> (((a b)((a a)(^x.x))) c) REDUCED to normal form. ------ 198839/23764683. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.b) a)) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.b) a)) 3. ==[ beta ]==> ((b (a (a a)))((^y.b) a)) 4. ==[ alpha ]==> ((b (a (a a)))((^x.b) a)) 5. ==[ beta ]==> ((b (a (a a))) b) REDUCED to normal form. ------ 198840/23764782. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z) a)(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y) a)(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))(a (a (a a)))) REDUCED to normal form. ------ 198841/23765187. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(a ((a a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(a ((a a) a))) 3. ==[ beta ]==> (((^y.y) b)(a ((a a) a))) 4. ==[ alpha ]==> (((^x.x) b)(a ((a a) a))) 5. ==[ beta ]==> (b (a ((a a) a))) REDUCED to normal form. ------ 198842/23765214. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(((^y.y)(^z.z))(a a))) 3. ==[ beta ]==> (((a (a (^x.x))) a)((^z.z)(a a))) 4. ==[ alpha ]==> (((a (a (^x.x))) a)((^y.y)(a a))) 5. ==[ beta ]==> (((a (a (^x.x))) a)(a a)) REDUCED to normal form. ------ 198843/23765241. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((a (a a))(a (^z.z)))) REDUCED to normal form. ------ 198844/23765313. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(b (^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(b (^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(b (^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(b (^x.(^y.y)))) REDUCED to normal form. ------ 198845/23765394. ------ 1. ==[ start ]==> (((^a.b)(b a))((^a.(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(y y))(a (^z.z)))) 3. ==[ beta ]==> (b ((^y.(y y))(a (^z.z)))) 4. ==[ alpha ]==> (b ((^x.(x x))(a (^y.y)))) 5. ==[ beta ]==> (b ((a (^y.y))(a (^y.y)))) 6. ==[ alpha ]==> (b ((a (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 198846/23765502. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198847/23765619. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(a ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a ((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a ((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a ((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198848/23765646. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((a (a a))(a a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((a (a a))(a a))) REDUCED to normal form. ------ 198849/23765682. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^b.a) c)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.a) c)) 3. ==[ beta ]==> (((a a)(a (a (^x.x)))) a) REDUCED to normal form. ------ 198850/23765763. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a (a a))(^a.a))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))((a (a a))(^x.x))) REDUCED to normal form. ------ 198851/23765790. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(((^x1.x1) a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(((^x1.x1) a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(((^z.z) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)(((^z.z) a)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)(((^y.y) a)(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (((^y.y) a)(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 9. ==[ beta ]==> (b (a (^y.(^z.z)))) 10. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 198852/23765817. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((a (^z.z))(^x1.a))) REDUCED to normal form. ------ 198853/23765844. ------ 1. ==[ start ]==> (((a b)(b a))((a a)(^a.(a a)))) 2. ==[ alpha ]==> (((a b)(b a))((a a)(^x.(x x)))) REDUCED to normal form. ------ 198854/23765871. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a (a a)) a)) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a (a a)) a)) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a (a a)) a)) REDUCED to normal form. ------ 198855/23765898. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(((^a.a) a) b)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(((^z.z) a) b)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(((^z.z) a) b)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) a) b)) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a b)) REDUCED to normal form. ------ 198856/23765979. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(x1 x1)) a)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(x1 x1)) a)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(z z)) a)) 5. ==[ beta ]==> ((b (^y.y))((^z.(z z)) a)) 6. ==[ alpha ]==> ((b (^x.x))((^y.(y y)) a)) 7. ==[ beta ]==> ((b (^x.x))(a a)) REDUCED to normal form. ------ 198857/23766006. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^b.a) b)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.a) b)) 3. ==[ beta ]==> ((((a a)(a a))(a (a a))) a) REDUCED to normal form. ------ 198858/23766087. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(((^y.y) a)(^z.z))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))(a (^z.z))) 4. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a (^y.y))) REDUCED to normal form. ------ 198859/23766114. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((a (^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((a (^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 198860/23766123. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(a (^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198861/23766150. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.y1)((^z1.z1) a))) 3. ==[ beta ]==> ((^y.y)((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z) a))) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 198862/23766285. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(b (^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(b (^y1.(^z1.z1)))) 3. ==[ beta ]==> (b (b (^y1.(^z1.z1)))) 4. ==[ alpha ]==> (b (b (^x.(^y.y)))) REDUCED to normal form. ------ 198863/23766393. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((^a.(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198864/23766528. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))((^a.a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198865/23766537. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(a (a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(a (a a))) REDUCED to normal form. ------ 198866/23766564. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)(a a)) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(a a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a a)) 5. ==[ beta ]==> ((^y.y)(a a)) 6. ==[ alpha ]==> ((^x.x)(a a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198867/23778504. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a) b) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a) b) 3. ==[ beta ]==> (((^y.(^z.z)) a) b) 4. ==[ alpha ]==> (((^x.(^y.y)) a) b) 5. ==[ beta ]==> ((^y.y) b) 6. ==[ alpha ]==> ((^x.x) b) 7. ==[ beta ]==> b REDUCED to normal form. ------ 198868/23778528. ------ 1. ==[ start ]==> ((^a.(^a.a))(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198869/23778972. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) REDUCED to normal form. ------ 198870/23779014. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(z (^x1.x1))) b)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 198871/23779113. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((^y.y) b)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((^y.y) b)((^z.z)(^x1.x1)))((((^y.y) b)((^z.z)(^x1.x1)))(((^y.y) b)((^z.z)(^x1.x1))))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((((^x1.x1) b)((^y1.y1)(^z1.z1)))(((^x2.x2) b)((^y2.y2)(^z2.z2))))) 5. ==[ beta ]==> ((b ((^y.y)(^z.z)))((((^x1.x1) b)((^y1.y1)(^z1.z1)))(((^x2.x2) b)((^y2.y2)(^z2.z2))))) 6. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((((^z.z) b)((^x1.x1)(^y1.y1)))(((^z1.z1) b)((^x2.x2)(^y2.y2))))) 7. ==[ beta ]==> ((b (^y.y))((((^z.z) b)((^x1.x1)(^y1.y1)))(((^z1.z1) b)((^x2.x2)(^y2.y2))))) 8. ==[ alpha ]==> ((b (^x.x))((((^y.y) b)((^z.z)(^x1.x1)))(((^y1.y1) b)((^z1.z1)(^x2.x2))))) 9. ==[ beta ]==> ((b (^x.x))((b ((^z.z)(^x1.x1)))(((^y1.y1) b)((^z1.z1)(^x2.x2))))) 10. ==[ alpha ]==> ((b (^x.x))((b ((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1))))) 11. ==[ beta ]==> ((b (^x.x))((b (^z.z))(((^x1.x1) b)((^y1.y1)(^z1.z1))))) 12. ==[ alpha ]==> ((b (^x.x))((b (^y.y))(((^z.z) b)((^x1.x1)(^y1.y1))))) 13. ==[ beta ]==> ((b (^x.x))((b (^y.y))(b ((^x1.x1)(^y1.y1))))) 14. ==[ alpha ]==> ((b (^x.x))((b (^y.y))(b ((^z.z)(^x1.x1))))) 15. ==[ beta ]==> ((b (^x.x))((b (^y.y))(b (^x1.x1)))) 16. ==[ alpha ]==> ((b (^x.x))((b (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 198872/23779431. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((b b)(^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((b b)(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 198873/23780304. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> ((a (a (a a)))(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 198874/23780409. ------ 1. ==[ start ]==> ((^a.(a b))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x b))(((^y.y) b)(a (a a)))) 3. ==[ beta ]==> ((((^y.y) b)(a (a a))) b) 4. ==[ alpha ]==> ((((^x.x) b)(a (a a))) b) 5. ==[ beta ]==> ((b (a (a a))) b) REDUCED to normal form. ------ 198875/23780727. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.(^y1.(y1 (^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.(^y1.(y1 (^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.a)(^z.(^x1.(x1 (^y1.y1))))) 6. ==[ alpha ]==> ((^x.a)(^y.(^z.(z (^x1.x1))))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198876/23780796. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))(((a a)(a a))(^z.a))) 3. ==[ beta ]==> (^y.((((a a)(a a))(^z.a))(((a a)(a a))(^z.a)))) 4. ==[ alpha ]==> (^x.((((a a)(a a))(^y.a))(((a a)(a a))(^z.a)))) REDUCED to normal form. ------ 198877/23781546. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> (((a (a a))((^x.x)(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(^z.(^x1.x1))) 5. ==[ beta ]==> (((a (a a))(^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 198878/23781678. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((b a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((((b a)((^z.z)(^x1.x1)))((b a)((^z.z)(^x1.x1))))(^y.y)) 4. ==[ alpha ]==> ((((b a)((^x.x)(^y.y)))((b a)((^z.z)(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> ((((b a)(^y.y))((b a)((^z.z)(^x1.x1))))(^y1.y1)) 6. ==[ alpha ]==> ((((b a)(^x.x))((b a)((^y.y)(^z.z))))(^x1.x1)) 7. ==[ beta ]==> ((((b a)(^x.x))((b a)(^z.z)))(^x1.x1)) 8. ==[ alpha ]==> ((((b a)(^x.x))((b a)(^y.y)))(^z.z)) REDUCED to normal form. ------ 198879/23783778. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(^z.(^x1.(a a)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.(^z.(a a)))) REDUCED to normal form. ------ 198880/23785695. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 198881/23787429. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))((a (a a))((^x1.x1)(^y1.y1)))) 3. ==[ eta ]==> ((^y.(^z.z))((a (a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198882/23787963. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(^b.(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(^z1.(^x2.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(^z1.(^x2.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198883/23788179. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^a.(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(^z.(y y)))) REDUCED to normal form. ------ 198884/23788248. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((^x1.x1)(^y1.y1))(^z1.a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 198885/23788566. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^a.(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(y b))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(y b))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(x b))) REDUCED to normal form. ------ 198886/23788671. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))(((^z.z) a)(a (a a)))) 3. ==[ beta ]==> ((((^z.z) a)(a (a a)))((((^z.z) a)(a (a a)))(^y.y))) 4. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((((^y.y) a)(a (a a)))(^z.z))) 5. ==[ beta ]==> ((a (a (a a)))((((^y.y) a)(a (a a)))(^z.z))) 6. ==[ alpha ]==> ((a (a (a a)))((((^x.x) a)(a (a a)))(^y.y))) 7. ==[ beta ]==> ((a (a (a a)))((a (a (a a)))(^y.y))) 8. ==[ alpha ]==> ((a (a (a a)))((a (a (a a)))(^x.x))) REDUCED to normal form. ------ 198887/23789070. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(^b.(^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(^z.(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)(^z.(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)(^y.(^z.a))) 5. ==[ beta ]==> (b (^y.(^z.a))) 6. ==[ alpha ]==> (b (^x.(^y.a))) REDUCED to normal form. ------ 198888/23789232. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^a.(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.(^y1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.z))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.z))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.y))) 7. ==[ beta ]==> (^y.(^z.y)) 8. ==[ alpha ]==> (^x.(^y.x)) REDUCED to normal form. ------ 198889/23789502. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198890/23789544. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(y1 y1)) b)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 198891/23789619. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(^c.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(^z.(a (a a)))) 3. ==[ beta ]==> ((a (b (^y.y)))(^z.(a (a a)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.(a (a a)))) REDUCED to normal form. ------ 198892/23789862. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(x1 (x1 x1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(x1 (x1 x1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(z (z z)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(z (z z)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(y (y y)))) REDUCED to normal form. ------ 198893/23789961. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.(^x1.(x1 x1)))) 3. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 198894/23790420. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^b.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.(^z.z))) REDUCED to normal form. ------ 198895/23790447. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)(^a.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198896/23790461. ------ 1. ==[ start ]==> (^a.(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^x.(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 198897/23790462. ------ 1. ==[ start ]==> (a (^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (a (^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (a (^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 198898/23790477. ------ 1. ==[ start ]==> ((a (^a.a))(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a (^x.x))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 198899/23790486. ------ 1. ==[ start ]==> (((^a.a) a)((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))(^x1.x1))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 198900/23790504. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((a (a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (a (^z.z))) b)) 3. ==[ beta ]==> ((^y.y)((a (a (^z.z))) b)) 4. ==[ alpha ]==> ((^x.x)((a (a (^y.y))) b)) 5. ==[ beta ]==> ((a (a (^y.y))) b) 6. ==[ alpha ]==> ((a (a (^x.x))) b) REDUCED to normal form. ------ 198901/23790513. ------ 1. ==[ start ]==> (((a a) a)((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y)))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a) a)((^z.(^x1.x1))(^y.y))) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 198902/23790621. ------ 1. ==[ start ]==> (((a a) b)((^b.b)(^c.a))) 2. ==[ alpha ]==> (((a a) b)((^x.x)(^y.a))) 3. ==[ beta ]==> (((a a) b)(^y.a)) 4. ==[ alpha ]==> (((a a) b)(^x.a)) REDUCED to normal form. ------ 198903/23790648. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.(^z.(^x1.x1)))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.(^z.z))) REDUCED to normal form. ------ 198904/23790756. ------ 1. ==[ start ]==> (((^a.(^a.a)) b)((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y)) b)((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)((^z.b)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 198905/23790891. ------ 1. ==[ start ]==> (((a a)(^b.a))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.a))((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a a)(^x.a))(^y.y)) REDUCED to normal form. ------ 198906/23790918. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.x1)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 198907/23790963. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> ((a (^x.(x x)))(b (^z.z))) 4. ==[ alpha ]==> ((a (^x.(x x)))(b (^y.y))) REDUCED to normal form. ------ 198908/23790981. ------ 1. ==[ start ]==> (((a a)((^a.a) a))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) a))(((^y.(^z.z)) a)(a (^x1.x1)))) 3. ==[ beta ]==> (((a a) a)(((^y.(^z.z)) a)(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a) a)(((^x.(^y.y)) a)(a (^z.z)))) 5. ==[ beta ]==> (((a a) a)((^y.y)(a (^z.z)))) 6. ==[ alpha ]==> (((a a) a)((^x.x)(a (^y.y)))) 7. ==[ beta ]==> (((a a) a)(a (^y.y))) 8. ==[ alpha ]==> (((a a) a)(a (^x.x))) REDUCED to normal form. ------ 198909/23791008. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((b (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((b (^z.z)) a)) REDUCED to normal form. ------ 198910/23791035. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((a (a a))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 198911/23791062. ------ 1. ==[ start ]==> ((a (a (a a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (a (a a)))(((^x.x) b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (a (a a)))(b ((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a (a (a a)))(b ((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a (a (a a)))(b (^y.y))) 6. ==[ alpha ]==> ((a (a (a a)))(b (^x.x))) REDUCED to normal form. ------ 198912/23791305. ------ 1. ==[ start ]==> (((a a)(a (a a)))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x) a)(b (^y.y)))) 3. ==[ beta ]==> (((a a)(a (a a)))(a (b (^y.y)))) 4. ==[ alpha ]==> (((a a)(a (a a)))(a (b (^x.x)))) REDUCED to normal form. ------ 198913/23791332. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x)) a)((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a (^x.x)) a)((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x)) a)((a (^y.y))(^z.z))) REDUCED to normal form. ------ 198914/23791359. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a a)(a (a (^z.z))))) 3. ==[ beta ]==> ((a (a (^y.y)))((a a)(a (a (^z.z))))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a a)(a (a (^y.y))))) REDUCED to normal form. ------ 198915/23791377. ------ 1. ==[ start ]==> (((^a.(a a)) b)(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(a (^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((b b)(a (^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((b b)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 198916/23791422. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.(^x1.x1)) a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198917/23791449. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))((b (^a.a))(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))((b (^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.a))) 5. ==[ beta ]==> ((b (^y.y))(^z.a)) 6. ==[ alpha ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 198918/23791503. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) b)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.(^x2.x2)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) b)(^z1.(^x2.x2)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) b)(^z.(^x1.x1)))) 7. ==[ beta ]==> (((^y.y) b)(^z.(^x1.x1))) 8. ==[ alpha ]==> (((^x.x) b)(^y.(^z.z))) 9. ==[ beta ]==> (b (^y.(^z.z))) 10. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 198919/23791512. ------ 1. ==[ start ]==> (((a (a a)) b)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.x)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.y)(^z.z))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.x)(^y.y))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 198920/23791539. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((^y.y) a)((^z.(^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> (((^x.x) a)((^y.(^z.(^x1.x1)))((a a) a))) 5. ==[ beta ]==> (a ((^y.(^z.(^x1.x1)))((a a) a))) 6. ==[ alpha ]==> (a ((^x.(^y.(^z.z)))((a a) a))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 198921/23791557. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((b a)(^x1.b))) 3. ==[ beta ]==> (((^y.y)(^z.z))((b a)(^x1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.b))) 5. ==[ beta ]==> ((^y.y)((b a)(^z.b))) 6. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 7. ==[ beta ]==> ((b a)(^y.b)) 8. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 198922/23791584. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(a a))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(a a))) REDUCED to normal form. ------ 198923/23791620. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(a a))((a a)(^z.z)))) 5. ==[ beta ]==> ((a (^x.a))(a a)) REDUCED to normal form. ------ 198924/23791647. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^a.b)(b a))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.b)(b a))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y))) b) REDUCED to normal form. ------ 198925/23791881. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))((b (^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((b (^y1.y1)) c)) 3. ==[ beta ]==> ((^y.y)((b (^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.x)((b (^y.y)) c)) 5. ==[ beta ]==> ((b (^y.y)) c) 6. ==[ alpha ]==> ((b (^x.x)) c) REDUCED to normal form. ------ 198926/23791971. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^a.(^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.(^x1.(^y1.y1)))(^z1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1)))(^z1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))(^y1.a))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.a))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.a))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 198927/23792052. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(a a))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(a a)) REDUCED to normal form. ------ 198928/23792106. ------ 1. ==[ start ]==> (((a (a a))(^b.a))((^c.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(^x.a))((^y.a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (a a))(^x.a)) a) REDUCED to normal form. ------ 198929/23792133. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.a)))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.x2))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.z1))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.y1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198930/23792223. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(^a.a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(^z.z)))(b ((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(b ((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(b ((^z.(^x1.x1)) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(b (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(b (^z.z))) REDUCED to normal form. ------ 198931/23792250. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(a (a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(a (a (a (^y.y))))) 3. ==[ beta ]==> ((a (a (a a)))(a (a (a (^y.y))))) 4. ==[ alpha ]==> ((a (a (a a)))(a (a (a (^x.x))))) REDUCED to normal form. ------ 198932/23792277. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(((^y.(^z.z)) a)(a a))) 3. ==[ beta ]==> (((a (a a)) a)(((^y.(^z.z)) a)(a a))) 4. ==[ alpha ]==> (((a (a a)) a)(((^x.(^y.y)) a)(a a))) 5. ==[ beta ]==> (((a (a a)) a)((^y.y)(a a))) 6. ==[ alpha ]==> (((a (a a)) a)((^x.x)(a a))) 7. ==[ beta ]==> (((a (a a)) a)(a a)) REDUCED to normal form. ------ 198933/23792304. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))((b (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((b (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((b (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((b (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((b (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 198934/23792331. ------ 1. ==[ start ]==> ((((a a) a)(a a))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> ((((a a) a)(a a))(((a a)(a a)) a)) REDUCED to normal form. ------ 198935/23792358. ------ 1. ==[ start ]==> ((a (a b))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> ((a (a b))(((^x.x) b)(a (a a)))) 3. ==[ beta ]==> ((a (a b))(b (a (a a)))) REDUCED to normal form. ------ 198936/23792619. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(c (^d.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(c (^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(c (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(c (^z.(^x1.x1)))) REDUCED to normal form. ------ 198937/23792673. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(a (^x1.(x1 (^y1.y1))))) 3. ==[ beta ]==> (((^y.y)(^z.a))(a (^x1.(x1 (^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(a (^z.(z (^x1.x1))))) 5. ==[ beta ]==> ((^y.a)(a (^z.(z (^x1.x1))))) 6. ==[ alpha ]==> ((^x.a)(a (^y.(y (^z.z))))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 198938/23792718. ------ 1. ==[ start ]==> (((^a.b)(a a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a a))((b (^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((b (^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((b (^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 198939/23792745. ------ 1. ==[ start ]==> ((a (^b.(a a)))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(a a)))(((a a)(a a))(^y.a))) REDUCED to normal form. ------ 198940/23792916. ------ 1. ==[ start ]==> (((^a.b) b)((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> (b ((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 198941/23792961. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(a a))(((^z.z)(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(a a))(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198942/23792988. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((a (a a))(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((a (a a))(^x1.x1))) 3. ==[ beta ]==> ((^y.y)((a (a a))(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(^y.y))) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 198943/23793123. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))((b (^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((b (^x1.x1)) b)) 3. ==[ beta ]==> (b ((b (^x1.x1)) b)) 4. ==[ alpha ]==> (b ((b (^x.x)) b)) REDUCED to normal form. ------ 198944/23793186. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.y)(^z.(z z)))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(^z.(z z))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(^y.(y y))) REDUCED to normal form. ------ 198945/23793213. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^a.(^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(^x1.x1))) REDUCED to normal form. ------ 198946/23793267. ------ 1. ==[ start ]==> (((a (a a))(^b.(^a.a)))((^c.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 198947/23793294. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(a a)))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(z z)))((^x1.(a a))(^y1.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(z z)))((^x1.(a a))(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(y y)))((^z.(a a))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(y y))((^z.(a a))(^x1.(a a)))) 6. ==[ alpha ]==> ((^x.(x x))((^y.(a a))(^z.(a a)))) 7. ==[ beta ]==> (((^y.(a a))(^z.(a a)))((^y.(a a))(^z.(a a)))) 8. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(a a))(^x1.(a a)))) 9. ==[ beta ]==> ((a a)((^z.(a a))(^x1.(a a)))) 10. ==[ alpha ]==> ((a a)((^x.(a a))(^y.(a a)))) 11. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 198948/23793321. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^x.a)) b) REDUCED to normal form. ------ 198949/23793348. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^c.a)(^d.a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 198950/23793375. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.a))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 198951/23793438. ------ 1. ==[ start ]==> (((a (^a.a))(a b))(c ((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))(c ((a a)(a a)))) REDUCED to normal form. ------ 198952/23793465. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))(b (b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))(b (b (^y.y)))) 3. ==[ beta ]==> ((a ((a a) a))(b (b (^y.y)))) 4. ==[ alpha ]==> ((a ((a a) a))(b (b (^x.x)))) REDUCED to normal form. ------ 198953/23793492. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((a (a a))(^y.y))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> (((a (a a))(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a (a a))(^x.x))(a (^y.y))) REDUCED to normal form. ------ 198954/23793519. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))((b (^z.z))(a a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))((b (^z.z))(a a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))((b (^y.y))(a a))) 5. ==[ beta ]==> ((a (a a))((b (^y.y))(a a))) 6. ==[ alpha ]==> ((a (a a))((b (^x.x))(a a))) REDUCED to normal form. ------ 198955/23793546. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> ((((a a) a) a)(((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> ((((a a) a) a)(((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 198956/23793573. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a b)(a (^x.x)))(b ((^z.z) a))) 4. ==[ alpha ]==> (((a b)(a (^x.x)))(b ((^y.y) a))) 5. ==[ beta ]==> (((a b)(a (^x.x)))(b a)) REDUCED to normal form. ------ 198957/23793600. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))((a (^y.(^z.z)))(a (a a)))) 3. ==[ beta ]==> (((a a)(a a))((a (^y.(^z.z)))(a (a a)))) 4. ==[ alpha ]==> (((a a)(a a))((a (^x.(^y.y)))(a (a a)))) REDUCED to normal form. ------ 198958/23793627. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a ((a a)(^x.x)))((b a)(^z.z))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((b a)(^y.y))) REDUCED to normal form. ------ 198959/23793807. ------ 1. ==[ start ]==> (((a b) c)(d (^b.b))) 2. ==[ alpha ]==> (((a b) c)(d (^x.x))) REDUCED to normal form. ------ 198960/23793834. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(c (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(c (^y.(a a)))) 3. ==[ beta ]==> (((a a) b)(c (^y.(a a)))) 4. ==[ alpha ]==> (((a a) b)(c (^x.(a a)))) REDUCED to normal form. ------ 198961/23793906. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((b (^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)((b (^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((^x.x)((b (^y.y))(^z.z))) 5. ==[ beta ]==> ((b (^y.y))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 198962/23793942. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((^c.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 198963/23793960. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((^y.y) b)(^z.a))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((^y.y) b)(^z.a))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x) b)(^y.a))) 5. ==[ beta ]==> ((((a a) a)((a a) a))(b (^y.a))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))(b (^x.a))) REDUCED to normal form. ------ 198964/23793996. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.(^x2.x2)))(a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.(^z1.z1)))(a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.(^z1.z1)))(a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198965/23794041. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))(((a a)(^z.z))(^x1.a))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.a))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 198966/23794050. ------ 1. ==[ start ]==> (((a b)(^b.a))((^c.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 198967/23794077. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(a a))(a b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(a a))(a b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(a a))(a b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 198968/23794104. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 198969/23794617. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^a.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x)) b)(^y.y)) REDUCED to normal form. ------ 198970/23794950. ------ 1. ==[ start ]==> (((a a)(b a))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(b a))(((^x.x) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(b a))(a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a)(b a))(a (a (^x.(^y.y))))) REDUCED to normal form. ------ 198971/23794977. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))((a (^z.z)) b)) REDUCED to normal form. ------ 198972/23795004. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a a)((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a a)((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a a)((a a)(a a)))) 5. ==[ beta ]==> ((a (a a))((a a)((a a)(a a)))) REDUCED to normal form. ------ 198973/23795211. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.b)(a b))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.b)(a b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.b)(a b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198974/23795229. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))(((a a) a)(^b.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((a a) a)(^y1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((a a) a)(^y1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((a a) a)(^x1.(a a)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 198975/23795310. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))(((^a.a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> ((a a)(((^z.z) a)(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> ((a a)(((^x.x) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> ((a a)(a (^y.(^z.(^x1.x1))))) 8. ==[ alpha ]==> ((a a)(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 198976/23795391. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(((a a)(a a)) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a)(a a)) a)) 3. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 198977/23795535. ------ 1. ==[ start ]==> (((a a)(^a.(^a.(^a.a))))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.(a a))(^y1.a))) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 198978/23795616. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 198979/23795697. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 198980/23795841. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))(((a a)(^z.z))(a (a a)))) REDUCED to normal form. ------ 198981/23795868. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((^y.y)(a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x))(b a))((a a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(b a))((a a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (^x.x))(b a))((a a)(^z.z))) 6. ==[ alpha ]==> (((a (^x.x))(b a))((a a)(^y.y))) REDUCED to normal form. ------ 198982/23795895. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))((a b)((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))((a b)((a a) a))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))((a b)((a a) a))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))((a b)((a a) a))) REDUCED to normal form. ------ 198983/23795922. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))(((a a) a)(a b))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))(((a a) a)(a b))) 3. ==[ beta ]==> (((a (a a))(a a))(((a a) a)(a b))) REDUCED to normal form. ------ 198984/23795949. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (((^y.y)(a b))(((^z.z)(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a b)(((^y.y)(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> ((a b)((^y.y)((^z.z)(a a)))) 8. ==[ alpha ]==> ((a b)((^x.x)((^y.y)(a a)))) 9. ==[ beta ]==> ((a b)((^y.y)(a a))) 10. ==[ alpha ]==> ((a b)((^x.x)(a a))) 11. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 198985/23795976. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))((a (a a))((a a)(^x.x)))) REDUCED to normal form. ------ 198986/23796003. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))(((^z.z) a)(b a))) 3. ==[ beta ]==> (((a b)(^y.y))(((^z.z) a)(b a))) 4. ==[ alpha ]==> (((a b)(^x.x))(((^y.y) a)(b a))) 5. ==[ beta ]==> (((a b)(^x.x))(a (b a))) REDUCED to normal form. ------ 198987/23796030. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))((a (^y.y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(a (a a)))((a (^y.y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(a (a a)))((a (^x.x))(a (^y.(^z.z))))) REDUCED to normal form. ------ 198988/23796057. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a a)((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a a)((^z.z) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a a)((^z.z) b))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a a)((^y.y) b))) 5. ==[ beta ]==> ((((a a)(^x.x)) a)((a a) b)) REDUCED to normal form. ------ 198989/23796102. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)((^b.b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)((^x1.x1)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198990/23796147. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(^z.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.a))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 198991/23796174. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))(((a a)(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))(((a a)(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> ((^y.y)(((a a)(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))(^z.(z z)))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(z z))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(y y))) REDUCED to normal form. ------ 198992/23796309. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((a (a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((a (a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 198993/23796417. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(((^a.a) b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) b) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) b) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 198994/23796426. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^b.b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 198995/23796453. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b a)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b a)((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b a)(^y.(^z.z))) 6. ==[ alpha ]==> ((b a)(^x.(^y.y))) REDUCED to normal form. ------ 198996/23796471. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((b a) c)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((b a) c)) 3. ==[ beta ]==> (((^y.y) b)((b a) c)) 4. ==[ alpha ]==> (((^x.x) b)((b a) c)) 5. ==[ beta ]==> (b ((b a) c)) REDUCED to normal form. ------ 198997/23796588. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.a)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(^x1.b))) 5. ==[ beta ]==> ((^y.(a a))((^z.a)(^x1.b))) 6. ==[ alpha ]==> ((^x.(a a))((^y.a)(^z.b))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 198998/23796615. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.b))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.b))(^y.y)) REDUCED to normal form. ------ 198999/23796642. ------ 1. ==[ start ]==> (((a b)(^c.a))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)(^x.a))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 199000/23796696. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(a a)))((^a.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))((^z.(^x1.x1))(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(y y)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(y y)))(^z.z)) REDUCED to normal form. ------ 199001/23796741. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.y1) a)) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199002/23796813. ------ 1. ==[ start ]==> (((a a)((^a.a) b))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.x) b))(((a a)(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a a) b)(((a a)(^y.y))((^z.z) a))) 4. ==[ alpha ]==> (((a a) b)(((a a)(^x.x))((^y.y) a))) 5. ==[ beta ]==> (((a a) b)(((a a)(^x.x)) a)) REDUCED to normal form. ------ 199003/23796840. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((^x1.x1)(a a))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))((a a)(a (a a)))) REDUCED to normal form. ------ 199004/23796867. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> ((a (b a))((a b)((^y.y)(^z.z)))) 4. ==[ alpha ]==> ((a (b a))((a b)((^x.x)(^y.y)))) 5. ==[ beta ]==> ((a (b a))((a b)(^y.y))) 6. ==[ alpha ]==> ((a (b a))((a b)(^x.x))) REDUCED to normal form. ------ 199005/23796894. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 199006/23796921. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((^x1.x1)(^y1.y1))(a b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((^x1.x1)(^y1.y1))(a b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((^z.z)(^x1.x1))(a b))) 5. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(a b))) 6. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(a b))) 7. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(a b))) 8. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a b))) 9. ==[ beta ]==> ((a a)((^y.y)(a b))) 10. ==[ alpha ]==> ((a a)((^x.x)(a b))) 11. ==[ beta ]==> ((a a)(a b)) REDUCED to normal form. ------ 199007/23796948. ------ 1. ==[ start ]==> ((((a a) a)(a b))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a b))((a (a a))((^x.x)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a b))((a (a a))(a a))) REDUCED to normal form. ------ 199008/23796975. ------ 1. ==[ start ]==> (((a b)((a a) a))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a) a))(((^x.x) a)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)((a a) a))(a ((a a)(^y.y)))) 4. ==[ alpha ]==> (((a b)((a a) a))(a ((a a)(^x.x)))) REDUCED to normal form. ------ 199009/23797002. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))((a (^x1.x1))(b a))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))((a (^x1.x1))(b a))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((a (^z.z))(b a))) 5. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))(b a))) 6. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))(b a))) REDUCED to normal form. ------ 199010/23797029. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a a)(a (^y.(^z.z))))) REDUCED to normal form. ------ 199011/23797173. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((a b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a b)(^y.(^z.z)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 199012/23797416. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))(((a a)(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))(((a a)(^y1.y1)) c)) 3. ==[ beta ]==> ((^y.(^z.z))(((a a)(^y1.y1)) c)) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a)(^z.z)) c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199013/23797452. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(a a))(^z.(z z)))) 3. ==[ beta ]==> ((b b)((^y.(a a))(^z.(z z)))) 4. ==[ alpha ]==> ((b b)((^x.(a a))(^y.(y y)))) 5. ==[ beta ]==> ((b b)(a a)) REDUCED to normal form. ------ 199014/23797479. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b)(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 199015/23797533. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((a (^x.x))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(^z.z)) REDUCED to normal form. ------ 199016/23797560. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(y1 y1))(^z1.(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1))(^y1.(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.(a a))(^y1.(a a)))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(a a))(^y1.(a a)))) 7. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 199017/23797641. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a) a)(^x.(a a)))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 199018/23797659. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (b ((^y.(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z))) a)) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 199019/23797866. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(a a)))(((^x.x) a)((^y.y)(a a)))) 3. ==[ beta ]==> (((a a)((a a)(a a)))(a ((^y.y)(a a)))) 4. ==[ alpha ]==> (((a a)((a a)(a a)))(a ((^x.x)(a a)))) 5. ==[ beta ]==> (((a a)((a a)(a a)))(a (a a))) REDUCED to normal form. ------ 199020/23797893. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))((a (^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)((a (^z.z))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)((a (^y.y))((a a)(^z.z)))) REDUCED to normal form. ------ 199021/23797920. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a a)(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a a)(b a))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a a)(b a))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a a)(b a))) REDUCED to normal form. ------ 199022/23798766. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (b (((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 199023/23798775. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (((a b)(^x.(a a)))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.y)) REDUCED to normal form. ------ 199024/23798802. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^b.(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(a a))(a (^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(a a))(a (^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(a a))(a (^z.z)))) 5. ==[ beta ]==> (((a a)(^x.b))(a a)) REDUCED to normal form. ------ 199025/23798874. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199026/23798883. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.(^y1.y1))((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.x1)) REDUCED to normal form. ------ 199027/23798910. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((b (^y.a))((^z.(z z))((a a) a))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(y y))((a a) a))) 5. ==[ beta ]==> ((b (^x.a))(((a a) a)((a a) a))) REDUCED to normal form. ------ 199028/23798937. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^b.a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.a)(a b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y))) a) REDUCED to normal form. ------ 199029/23799189. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))(c (a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))(c (a b))) 3. ==[ beta ]==> (((a a)(a b))(c (a b))) REDUCED to normal form. ------ 199030/23799216. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))(b ((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(b ((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(b (a a))) REDUCED to normal form. ------ 199031/23799270. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (a a)))((a a)(a a))) REDUCED to normal form. ------ 199032/23799297. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((a b)(a (^z.z)))) 3. ==[ beta ]==> ((b ((^y.y) a))((a b)(a (^z.z)))) 4. ==[ alpha ]==> ((b ((^x.x) a))((a b)(a (^y.y)))) 5. ==[ beta ]==> ((b a)((a b)(a (^y.y)))) 6. ==[ alpha ]==> ((b a)((a b)(a (^x.x)))) REDUCED to normal form. ------ 199033/23799324. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))(((a a) a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))(((a a) a)((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x)))(((a a) a) a)) REDUCED to normal form. ------ 199034/23799378. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))((a (a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))((a (a a))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a (^x.x))((a (a a))(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a (a a))(^y.y))) REDUCED to normal form. ------ 199035/23799549. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))(((a a) a)(^b.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((a a) a)(^x1.a))) 3. ==[ beta ]==> (b (((a a) a)(^x1.a))) 4. ==[ alpha ]==> (b (((a a) a)(^x.a))) REDUCED to normal form. ------ 199036/23799657. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((a (^a.a))(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a (^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z))(^x1.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199037/23799882. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.(^z.z))(^x1.b))) 3. ==[ beta ]==> (((a (a a))(^x.x))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(^x.x))(^y.y)) REDUCED to normal form. ------ 199038/23799909. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.z1)(^x2.(a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.z1)(^x2.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.x1)(^y1.(a a)))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199039/23799954. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.b) b)) 3. ==[ beta ]==> (b ((^z.b) b)) 4. ==[ alpha ]==> (b ((^x.b) b)) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 199040/23800071. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(c (^c.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(c (^y1.a))) REDUCED to normal form. ------ 199041/23800098. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(b (^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(b (^z.b))) 3. ==[ beta ]==> ((b (^y.(y y)))(b (^z.b))) 4. ==[ alpha ]==> ((b (^x.(x x)))(b (^y.b))) REDUCED to normal form. ------ 199042/23800125. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(a (^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(a (^y.(a a)))) REDUCED to normal form. ------ 199043/23800197. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> ((a (^x.(x (^y.y))))((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((a (^x.(x (^y.y))))((^z.z)(^x1.a))) 5. ==[ beta ]==> ((a (^x.(x (^y.y))))(^x1.a)) 6. ==[ alpha ]==> ((a (^x.(x (^y.y))))(^z.a)) REDUCED to normal form. ------ 199044/23800485. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))(b ((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))(b ((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))(b ((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))(b ((a a) a))) REDUCED to normal form. ------ 199045/23800512. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(a (a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(a (a b))) 3. ==[ beta ]==> ((b (a (a a)))(a (a b))) REDUCED to normal form. ------ 199046/23800539. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(((a a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(((a a) a)(a a))) 3. ==[ beta ]==> ((((a a)(a a)) a)(((a a) a)(a a))) REDUCED to normal form. ------ 199047/23800593. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((^y.y)(a a))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((a (a a))((^y.y) a))) 5. ==[ beta ]==> ((a a)((a (a a))((^y.y) a))) 6. ==[ alpha ]==> ((a a)((a (a a))((^x.x) a))) 7. ==[ beta ]==> ((a a)((a (a a)) a)) REDUCED to normal form. ------ 199048/23800620. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))(((^y.y) a)(a (a a)))) 3. ==[ beta ]==> ((a (a (a (^x.x))))(a (a (a a)))) REDUCED to normal form. ------ 199049/23801016. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.a)(^c.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.z)(^x1.a))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.a))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.a))) 5. ==[ beta ]==> (b ((^y.y)(^z.a))) 6. ==[ alpha ]==> (b ((^x.x)(^y.a))) 7. ==[ beta ]==> (b (^y.a)) 8. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 199050/23801061. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> ((a (a (^y.y)))((^z.(^x1.x1)) b)) 4. ==[ alpha ]==> ((a (a (^x.x)))((^y.(^z.z)) b)) 5. ==[ beta ]==> ((a (a (^x.x)))(^z.z)) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.y)) REDUCED to normal form. ------ 199051/23801178. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(a (^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(a (^x1.a))) 3. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.a))) 5. ==[ beta ]==> ((^y.y)(a (^z.a))) 6. ==[ alpha ]==> ((^x.x)(a (^y.a))) 7. ==[ beta ]==> (a (^y.a)) 8. ==[ alpha ]==> (a (^x.a)) REDUCED to normal form. ------ 199052/23801205. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.(^y1.y1))(a a))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 199053/23801223. ------ 1. ==[ start ]==> (((^a.b)(b a))((a (a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(b a))((a (a a))(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a (a a))(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a (a a))(^x.(^y.y)))) REDUCED to normal form. ------ 199054/23801286. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^a.(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(^x1.x1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(^z.z)) REDUCED to normal form. ------ 199055/23801331. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(((^x1.x1)(^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199056/23801367. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 199057/23801394. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^b.a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.a)(^z.a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x))) a) REDUCED to normal form. ------ 199058/23801448. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.(^y1.y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199059/23801466. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1)) a)) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z)) a)) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 199060/23801493. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(x1 x1)) b)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(b b)) REDUCED to normal form. ------ 199061/23801511. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))(((^y.y) a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(a (a (^z.z)))) 4. ==[ alpha ]==> (((a a)(a (a (^x.x))))(a (a (^y.y)))) REDUCED to normal form. ------ 199062/23801538. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((a (^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((a (^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((a (^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))((a (^z.z)) a)) REDUCED to normal form. ------ 199063/23801565. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a a)(a (a a)))) 3. ==[ beta ]==> ((a (b (^y.y)))((a a)(a (a a)))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a a)(a (a a)))) REDUCED to normal form. ------ 199064/23801781. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))(b ((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(b ((^z.z) a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(b a)) REDUCED to normal form. ------ 199065/23801808. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(a (a (a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(a (a (a a)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(a (a (a a)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(a (a (a a)))) 5. ==[ beta ]==> ((b (^y.y))(a (a (a a)))) 6. ==[ alpha ]==> ((b (^x.x))(a (a (a a)))) REDUCED to normal form. ------ 199066/23801835. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(((^a.a) a)(a a))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(((^x.x) a)(a a))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(a (a a))) REDUCED to normal form. ------ 199067/23801889. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a a)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a a)((^x1.x1) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a a)((^x1.x1) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a a)((^z.z) a))) 5. ==[ beta ]==> ((a (^y.y))((a a)((^z.z) a))) 6. ==[ alpha ]==> ((a (^x.x))((a a)((^y.y) a))) 7. ==[ beta ]==> ((a (^x.x))((a a) a)) REDUCED to normal form. ------ 199068/23801907. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(a (^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(a (^z.(z z)))) 3. ==[ beta ]==> ((b (^y.y))(a (^z.(z z)))) 4. ==[ alpha ]==> ((b (^x.x))(a (^y.(y y)))) REDUCED to normal form. ------ 199069/23801952. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199070/23801979. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((a a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((a a)(^y.a))) 5. ==[ beta ]==> ((a a)(^y.a)) 6. ==[ alpha ]==> ((a a)(^x.a)) REDUCED to normal form. ------ 199071/23802114. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^a.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> (b ((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199072/23802222. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((a (^a.a)) a)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((a (^y1.y1)) a)) 3. ==[ beta ]==> ((^y.(^z.z))((a (^y1.y1)) a)) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.z)) a)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199073/23802357. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))((a a) a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))((a a) a)) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))((a a) a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a) a)) 5. ==[ beta ]==> ((^y.y)((a a) a)) 6. ==[ alpha ]==> ((^x.x)((a a) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 199074/23802366. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)((^a.a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)((^y.y)(^z.z))) 3. ==[ beta ]==> (((a (a (^x.x))) b)(^z.z)) 4. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.y)) REDUCED to normal form. ------ 199075/23802393. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)(a (^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(a (^x1.x1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a (^x1.x1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a (^z.z))) 5. ==[ beta ]==> ((^y.y)(a (^z.z))) 6. ==[ alpha ]==> ((^x.x)(a (^y.y))) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 199076/23802410. ------ 1. ==[ start ]==> (^a.((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.((^y.y)((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^x.((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199077/23802411. ------ 1. ==[ start ]==> (a ((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (a ((^x.x)((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> (a (^y.(^z.z))) 6. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 199078/23802414. ------ 1. ==[ start ]==> ((^a.a)(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^x.(^z.(^x1.x1))) 6. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199079/23810163. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^b.(b a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(z a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199080/23814360. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a)))) a) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1)))) a) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1))) a) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) a) 5. ==[ beta ]==> ((^y.(^z.z)) a) 6. ==[ alpha ]==> ((^x.(^y.y)) a) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199081/23814366. ------ 1. ==[ start ]==> ((^a.a)((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)((^y.y)((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199082/23814369. ------ 1. ==[ start ]==> ((a a)(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)(^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199083/23814393. ------ 1. ==[ start ]==> ((^a.(a a))((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.(x x))((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y1.y1))((^y.(^z.(^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.x1))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 5. ==[ beta ]==> ((^y.(^z.z))((^y1.(^z1.(^x2.x2)))(^y2.y2))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199084/23814420. ------ 1. ==[ start ]==> ((^a.b)((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.b)((^y.(y (^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 199085/23814861. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((a (a (^z.z)))(a a))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 199086/23815185. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a (a a))((a a)(a a)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199087/23815287. ------ 1. ==[ start ]==> (((a (a a))(a a))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 199088/23815311. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199089/23815719. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))(^z.(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a a))(^z.(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a a))(^y.(a (a (^z.z))))) 5. ==[ beta ]==> ((a a)(^y.(a (a (^z.z))))) 6. ==[ alpha ]==> ((a a)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 199090/23815743. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.(y (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((((^y.(y (^z.z)))(^x1.x1))((^y.(y (^z.z)))(^x1.x1)))((^y.(y (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((((^x.(x (^y.y)))(^z.z))((^x1.(x1 (^y1.y1)))(^z1.z1)))((^x2.(x2 (^y2.y2)))(^z2.z2))) 5. ==[ beta ]==> ((((^z.z)(^y.y))((^x1.(x1 (^y1.y1)))(^z1.z1)))((^x2.(x2 (^y2.y2)))(^z2.z2))) 6. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.y1)))((^z1.(z1 (^x2.x2)))(^y2.y2))) 7. ==[ beta ]==> (((^y.y)((^z.(z (^x1.x1)))(^y1.y1)))((^z1.(z1 (^x2.x2)))(^y2.y2))) 8. ==[ alpha ]==> (((^x.x)((^y.(y (^z.z)))(^x1.x1)))((^y1.(y1 (^z1.z1)))(^x2.x2))) 9. ==[ beta ]==> (((^y.(y (^z.z)))(^x1.x1))((^y1.(y1 (^z1.z1)))(^x2.x2))) 10. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))((^x1.(x1 (^y1.y1)))(^z1.z1))) 11. ==[ beta ]==> (((^z.z)(^y.y))((^x1.(x1 (^y1.y1)))(^z1.z1))) 12. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(z (^x1.x1)))(^y1.y1))) 13. ==[ beta ]==> ((^y.y)((^z.(z (^x1.x1)))(^y1.y1))) 14. ==[ alpha ]==> ((^x.x)((^y.(y (^z.z)))(^x1.x1))) 15. ==[ beta ]==> ((^y.(y (^z.z)))(^x1.x1)) 16. ==[ alpha ]==> ((^x.(x (^y.y)))(^z.z)) 17. ==[ beta ]==> ((^z.z)(^y.y)) 18. ==[ alpha ]==> ((^x.x)(^y.y)) 19. ==[ beta ]==> (^y.y) 20. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199091/23816151. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (a (a a)))(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (a a)))(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 199092/23818176. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))(^b.(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 199093/23818281. ------ 1. ==[ start ]==> ((^a.(b a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((^x.(b x))((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 3. ==[ eta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.(y1 y1)))) 4. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 199094/23818563. ------ 1. ==[ start ]==> (((^a.a)(b a))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(^y.(b (^z.z)))) 3. ==[ beta ]==> ((b a)(^y.(b (^z.z)))) 4. ==[ alpha ]==> ((b a)(^x.(b (^y.y)))) REDUCED to normal form. ------ 199095/23818830. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))((a (a a))(b a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (a a))(b a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199096/23819118. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^a.b)(a b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.b)(a b))) 3. ==[ beta ]==> (((^x1.b)(a b))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.z))) 5. ==[ beta ]==> (b (^y.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 199097/23819721. ------ 1. ==[ start ]==> ((^a.(^b.b))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((^x.(^y.y))((b a)((^z.z) a))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199098/23820036. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 199099/23820642. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.((^z1.z1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.((^z1.z1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199100/23821560. ------ 1. ==[ start ]==> (((^a.b)(a b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(y (^z.(^x1.x1))))) 3. ==[ beta ]==> (b (^y.(y (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b (^x.(x (^y.(^z.z))))) REDUCED to normal form. ------ 199101/23821848. ------ 1. ==[ start ]==> (((a (a a))(b a))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 199102/23822115. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.z)(b a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199103/23822118. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^b.(b a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(y a))) REDUCED to normal form. ------ 199104/23822397. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(^a.(b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(^y1.(b y1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1))) b) 4. ==[ beta ]==> ((^y.(^z.z)) b) 5. ==[ alpha ]==> ((^x.(^y.y)) b) 6. ==[ beta ]==> (^y.y) 7. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199105/23822901. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 199106/23823369. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(^c.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(^z.((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(^z.((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(a a)))) 7. ==[ beta ]==> (^y.((^z.z)(a a))) 8. ==[ alpha ]==> (^x.((^y.y)(a a))) 9. ==[ beta ]==> (^x.(a a)) REDUCED to normal form. ------ 199107/23824224. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))(^b.(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))(^y1.(a y1))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1)))) a) 4. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1)))) a) 5. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z)))) a) 6. ==[ beta ]==> ((a (^y.(^z.z))) a) 7. ==[ alpha ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 199108/23824413. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(^b.(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(^y.(^z.y))) 3. ==[ beta ]==> ((b (a (a a)))(^y.(^z.y))) 4. ==[ alpha ]==> ((b (a (a a)))(^x.(^y.x))) REDUCED to normal form. ------ 199109/23824935. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.((x1 x1) x1))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.((x1 x1) x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((z z) z))) 5. ==[ beta ]==> ((^y.y)(^z.((z z) z))) 6. ==[ alpha ]==> ((^x.x)(^y.((y y) y))) 7. ==[ beta ]==> (^y.((y y) y)) 8. ==[ alpha ]==> (^x.((x x) x)) REDUCED to normal form. ------ 199110/23825367. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^y.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199111/23825391. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((a (a a))(a a))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199112/23825493. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199113/23825601. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))(^z.(a (a a)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))(^z.(a (a a)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.(a (a a)))) REDUCED to normal form. ------ 199114/23825709. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^y.y))(^z.(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.(z z)))) REDUCED to normal form. ------ 199115/23825817. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(^y.(^z.(z z)))) REDUCED to normal form. ------ 199116/23825841. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))((^y1.a)(a a))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199117/23826123. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^a.c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.c)) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.c)) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199118/23826258. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(^a.b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(^y1.b)) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(^y1.b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.b)) 5. ==[ beta ]==> ((^y.y)(^x1.b)) 6. ==[ alpha ]==> ((^x.x)(^y.b)) 7. ==[ beta ]==> (^y.b) 8. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 199119/23826267. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^c.a)) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.a)) REDUCED to normal form. ------ 199120/23826294. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)(^b.a)) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(^x1.a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.a)) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 199121/23826312. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))(^y1.y1)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.y1)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.x1)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.x1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199122/23826324. ------ 1. ==[ start ]==> ((a a)((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)((^x.x)((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 199123/23826342. ------ 1. ==[ start ]==> (((^a.a) a)(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x) a)(((^y.y)(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (a (((^y.y)(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> (a (((^x.x)(^y.(^z.z))) a)) 5. ==[ beta ]==> (a ((^y.(^z.z)) a)) 6. ==[ alpha ]==> (a ((^x.(^y.y)) a)) 7. ==[ beta ]==> (a (^y.y)) 8. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 199124/23826351. ------ 1. ==[ start ]==> ((a (a a))((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a (a a))((^x.(^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 199125/23826369. ------ 1. ==[ start ]==> (((a a) a)((a (a (^a.a))) b)) 2. ==[ alpha ]==> (((a a) a)((a (a (^x.x))) b)) REDUCED to normal form. ------ 199126/23826378. ------ 1. ==[ start ]==> ((a b)((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a b)((^x.(x (^y.y)))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a b)((^z.(^x1.x1))(^y.y))) 4. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.z))) 5. ==[ beta ]==> ((a b)(^y.y)) 6. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 199127/23826621. ------ 1. ==[ start ]==> (((a (^a.a))(a a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(a a))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))(a a)) b) REDUCED to normal form. ------ 199128/23826765. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))(b (a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.y)(b (a (a (^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(b (a (a (^y.y))))) 5. ==[ beta ]==> (b (a (a (^y.y)))) 6. ==[ alpha ]==> (b (a (a (^x.x)))) REDUCED to normal form. ------ 199129/23826801. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1))) a)) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199130/23826819. ------ 1. ==[ start ]==> ((a (^a.(a a)))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a (^x.(x x)))((a (a (^y.y)))(a a))) REDUCED to normal form. ------ 199131/23826927. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(y y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(x x))(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((((^y.y) b)((^z.z)(^x1.x1)))(((^y.y) b)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((b ((^y.y)(^z.z)))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 8. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(((^z.z) b)((^x1.x1)(^y1.y1)))) 9. ==[ beta ]==> ((b (^y.y))(((^z.z) b)((^x1.x1)(^y1.y1)))) 10. ==[ alpha ]==> ((b (^x.x))(((^y.y) b)((^z.z)(^x1.x1)))) 11. ==[ beta ]==> ((b (^x.x))(b ((^z.z)(^x1.x1)))) 12. ==[ alpha ]==> ((b (^x.x))(b ((^y.y)(^z.z)))) 13. ==[ beta ]==> ((b (^x.x))(b (^z.z))) 14. ==[ alpha ]==> ((b (^x.x))(b (^y.y))) REDUCED to normal form. ------ 199132/23826954. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))((a (^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))((a (^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> ((^y.y)((a (^x1.(^y1.y1)))((a a) a))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a) a)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a) a)) REDUCED to normal form. ------ 199133/23827008. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a)(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((^y.y)(((a a)(^z.z))((^x1.x1)(a a)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((^z.z)(a a)))) 7. ==[ beta ]==> (((a a)(^y.y))((^z.z)(a a))) 8. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(a a))) 9. ==[ beta ]==> (((a a)(^x.x))(a a)) REDUCED to normal form. ------ 199134/23827035. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> ((a (a a))(((^y.y)(a a))((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (a a))(((^x.x)(a a))((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a))((a a)((a a)(^y.y)))) 6. ==[ alpha ]==> ((a (a a))((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 199135/23827062. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))((a b)(b a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))((a b)(b a))) 3. ==[ beta ]==> ((^y.y)((a b)(b a))) 4. ==[ alpha ]==> ((^x.x)((a b)(b a))) 5. ==[ beta ]==> ((a b)(b a)) REDUCED to normal form. ------ 199136/23827116. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y)(^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x)(^y.y))((^z.z) b))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)((^z.z) b))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)((^y.y) b))) 7. ==[ beta ]==> (((a a)(a a))((^y.y) b)) 8. ==[ alpha ]==> (((a a)(a a))((^x.x) b)) 9. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 199137/23827143. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))((a (a a))((a a)(a a)))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 199138/23827215. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))(b (^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (a (^y.y)))(b (^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (^x.x)))(b (^y.(y (^z.z))))) REDUCED to normal form. ------ 199139/23827242. ------ 1. ==[ start ]==> (((a (a a))(a a))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 199140/23827269. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(z (^x1.x1)))(a a))) 3. ==[ beta ]==> ((a (^y.y))((^z.(z (^x1.x1)))(a a))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(y (^z.z)))(a a))) 5. ==[ beta ]==> ((a (^x.x))((a a)(^z.z))) 6. ==[ alpha ]==> ((a (^x.x))((a a)(^y.y))) REDUCED to normal form. ------ 199141/23827368. ------ 1. ==[ start ]==> (((a (a a)) b)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((^x.x) b)(^y.(^z.z)))) 3. ==[ beta ]==> (((a (a a)) b)(b (^y.(^z.z)))) 4. ==[ alpha ]==> (((a (a a)) b)(b (^x.(^y.y)))) REDUCED to normal form. ------ 199142/23827422. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((b a)(^z.b))) REDUCED to normal form. ------ 199143/23827449. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))(((a a)(^z.z))(^x1.(a a)))) REDUCED to normal form. ------ 199144/23827476. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((^a.a)(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.a))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.a))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.a))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.a))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 199145/23827530. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))(((a a) a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(((a a) a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.(^x1.x1))))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199146/23827566. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))((^z.(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1) b))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1) b))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 199147/23827593. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(y y))((a a)(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 199148/23827620. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.a)(b (^x1.x1)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.a)(b (^z.z)))) 5. ==[ beta ]==> ((a a)((^y.a)(b (^z.z)))) 6. ==[ alpha ]==> ((a a)((^x.a)(b (^y.y)))) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 199149/23827647. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.(^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((a (a a))(a (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a (a a))(a (^x.x)))(^y.y)) REDUCED to normal form. ------ 199150/23827674. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.z)(a (a (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.z)(a (a (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.y)(a (a (^z.z))))) 5. ==[ beta ]==> ((a a)((^y.y)(a (a (^z.z))))) 6. ==[ alpha ]==> ((a a)((^x.x)(a (a (^y.y))))) 7. ==[ beta ]==> ((a a)(a (a (^y.y)))) 8. ==[ alpha ]==> ((a a)(a (a (^x.x)))) REDUCED to normal form. ------ 199151/23827701. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.(a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.(x (^y.y)))(^z.z))) 3. ==[ beta ]==> ((a ((a a) a))((^z.z)(^y.y))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.x)(^y.y))) 5. ==[ beta ]==> ((a ((a a) a))(^y.y)) 6. ==[ alpha ]==> ((a ((a a) a))(^x.x)) REDUCED to normal form. ------ 199152/23828106. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (a (a a)))((^y.y)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> ((a (a (a a)))((^x.x)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a (a (a a)))(^y.(y (^z.z)))) 6. ==[ alpha ]==> ((a (a (a a)))(^x.(x (^y.y)))) REDUCED to normal form. ------ 199153/23828205. ------ 1. ==[ start ]==> (((^a.b) a)((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.b) a)((^y.(a a)) d)) 3. ==[ beta ]==> (b ((^y.(a a)) d)) 4. ==[ alpha ]==> (b ((^x.(a a)) d)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 199154/23828223. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((^a.a) b)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((^z.z) b)(a (a a)))) 3. ==[ beta ]==> ((^y.b)(((^z.z) b)(a (a a)))) 4. ==[ alpha ]==> ((^x.b)(((^y.y) b)(a (a a)))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 199155/23828304. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))(((a a)(^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(^z.z))(a b))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))(((a a)(^z.z))(a b))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))(((a a)(^z.z))(a b))) IRREDUCIBLE: cycle. ------ 199156/23828385. ------ 1. ==[ start ]==> (((^a.b)(^a.a))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.y))(((a a) a)(b a))) 3. ==[ beta ]==> (b (((a a) a)(b a))) REDUCED to normal form. ------ 199157/23828412. ------ 1. ==[ start ]==> (((^a.a)(a b))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(a b))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a b)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a b)(((^x.x)(^y.y))(a (^z.(^x1.x1))))) 5. ==[ beta ]==> ((a b)((^y.y)(a (^z.(^x1.x1))))) 6. ==[ alpha ]==> ((a b)((^x.x)(a (^y.(^z.z))))) 7. ==[ beta ]==> ((a b)(a (^y.(^z.z)))) 8. ==[ alpha ]==> ((a b)(a (^x.(^y.y)))) REDUCED to normal form. ------ 199158/23828439. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))((a (a a))((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))((a (a a))((^z.z) b))) 3. ==[ beta ]==> ((^y.y)((a (a a))((^z.z) b))) 4. ==[ alpha ]==> ((^x.x)((a (a a))((^y.y) b))) 5. ==[ beta ]==> ((a (a a))((^y.y) b)) 6. ==[ alpha ]==> ((a (a a))((^x.x) b)) 7. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 199159/23828493. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))((a (^y.y))(b (^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))((a (^y.y))(b (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))((a (^x.x))(b (^y.y)))) REDUCED to normal form. ------ 199160/23828556. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((^z.(^x1.x1)) a)(^y1.y1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 199161/23828583. ------ 1. ==[ start ]==> (((a b)(^a.a))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.x))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 199162/23828619. ------ 1. ==[ start ]==> (((a a)(a b))((^c.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a b))((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> (((a a)(a b))(a a)) REDUCED to normal form. ------ 199163/23828646. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))((^b.b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))((^y.y)(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(a (a a))) REDUCED to normal form. ------ 199164/23828673. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 5. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))((^z1.z1)(^x2.x2)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))((^y1.y1)(^z1.z1)))) 7. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199165/23828754. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))(a a)) REDUCED to normal form. ------ 199166/23828772. ------ 1. ==[ start ]==> (((^a.b) b)((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b) b)((a b)(^y.(^z.z)))) 3. ==[ beta ]==> (b ((a b)(^y.(^z.z)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 199167/23828781. ------ 1. ==[ start ]==> (((a b)(a a))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.b)((a a)(^y.y)))) 3. ==[ beta ]==> (((a b)(a a)) b) REDUCED to normal form. ------ 199168/23828988. ------ 1. ==[ start ]==> (((a b) b)((b (^a.a)) b)) 2. ==[ alpha ]==> (((a b) b)((b (^x.x)) b)) REDUCED to normal form. ------ 199169/23829267. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a a)(a a))((^y.(y y))(^z.z))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(x x))(^y.y))) 5. ==[ beta ]==> (((a a)(a a))((^y.y)(^y.y))) 6. ==[ alpha ]==> (((a a)(a a))((^x.x)(^y.y))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 199170/23829294. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(a b)) a) REDUCED to normal form. ------ 199171/23829420. ------ 1. ==[ start ]==> (((^a.b) c)((^c.(a a)) c)) 2. ==[ alpha ]==> (((^x.b) c)((^y.(a a)) c)) 3. ==[ beta ]==> (b ((^y.(a a)) c)) 4. ==[ alpha ]==> (b ((^x.(a a)) c)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 199172/23829519. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))(((a a)(^a.a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))(((a a)(^x1.x1))((a a) a))) 3. ==[ beta ]==> ((^y.y)(((a a)(^x1.x1))((a a) a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(^y.y))((a a) a))) 5. ==[ beta ]==> (((a a)(^y.y))((a a) a)) 6. ==[ alpha ]==> (((a a)(^x.x))((a a) a)) REDUCED to normal form. ------ 199173/23829654. ------ 1. ==[ start ]==> (((^a.b)(^b.a))((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((a (a a))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> (b ((a (a a))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> (b ((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 199174/23829735. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a a)(b (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.y))((a a)(b (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a a)(b (^y.y)))) REDUCED to normal form. ------ 199175/23829771. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))((b (^z.z))(^x1.x1))) REDUCED to normal form. ------ 199176/23829798. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))(((a a)(a a))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a (^y.b))(((a a)(a a))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.b))(((a a)(a a))(^y.(^z.z)))) REDUCED to normal form. ------ 199177/23829852. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((a (^y1.(^z1.z1)))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199178/23829879. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 199179/23829906. ------ 1. ==[ start ]==> (((a b)(^b.a))(((a a)(^a.a))(^c.a))) 2. ==[ alpha ]==> (((a b)(^x.a))(((a a)(^y.y))(^z.a))) REDUCED to normal form. ------ 199180/23829933. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(^a.a)))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))(((^x1.x1)(a a))(^y1.b))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(((^z.z)(a a))(^x1.b))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((a a)(^x1.b))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 199181/23829960. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((a b)(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a b)(^z.(a a)))) REDUCED to normal form. ------ 199182/23830023. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a)(a a)))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y)(a a)))((^z.(^x1.x1))(b a))) 3. ==[ beta ]==> (((a (^x.x))(a a))((^z.(^x1.x1))(b a))) 4. ==[ alpha ]==> (((a (^x.x))(a a))((^y.(^z.z))(b a))) 5. ==[ beta ]==> (((a (^x.x))(a a))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 199183/23830050. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(y y))(a (^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))((^y.(y y))(a (^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))((^x.(x x))(a (^y.(^z.z))))) 5. ==[ beta ]==> ((a (a b))((a (^y.(^z.z)))(a (^y.(^z.z))))) 6. ==[ alpha ]==> ((a (a b))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 199184/23830077. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.a)((^y.y) b))) 3. ==[ beta ]==> (((a (a a))((a a) a)) a) REDUCED to normal form. ------ 199185/23830104. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.(^z1.z1))((a a)(a a)))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.y1))((a a)(a a)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.y1))((a a)(a a)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.x1))((a a)(a a)))) 7. ==[ beta ]==> ((^y.y)((^z.(^x1.x1))((a a)(a a)))) 8. ==[ alpha ]==> ((^x.x)((^y.(^z.z))((a a)(a a)))) 9. ==[ beta ]==> ((^y.(^z.z))((a a)(a a))) 10. ==[ alpha ]==> ((^x.(^y.y))((a a)(a a))) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199186/23830131. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.x)(b (^y.y)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(b (^y.y))) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(b (^x.x))) REDUCED to normal form. ------ 199187/23830212. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(^z.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.a)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.a)) REDUCED to normal form. ------ 199188/23830239. ------ 1. ==[ start ]==> ((a (b a))((^a.(^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((a (b a))((^x.(^y.(^z.z)))(^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (b a))(^y.(^z.z))) 4. ==[ alpha ]==> ((a (b a))(^x.(^y.y))) REDUCED to normal form. ------ 199189/23830518. ------ 1. ==[ start ]==> (((^a.a)(b a))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(a (b (^y.y)))) 3. ==[ beta ]==> ((b a)(a (b (^y.y)))) 4. ==[ alpha ]==> ((b a)(a (b (^x.x)))) REDUCED to normal form. ------ 199190/23830545. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(((a a)(a a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(((a a)(a a))(a a))) 3. ==[ beta ]==> ((^y.y)(((a a)(a a))(a a))) 4. ==[ alpha ]==> ((^x.x)(((a a)(a a))(a a))) 5. ==[ beta ]==> (((a a)(a a))(a a)) REDUCED to normal form. ------ 199191/23830581. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^b.b) c)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.z) c)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.z) c)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.y) c)) 5. ==[ beta ]==> ((a (^x.(a a))) c) REDUCED to normal form. ------ 199192/23830599. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a b))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(a b))((a (^y.(^z.z)))((^x1.x1) a))) 4. ==[ alpha ]==> (((a b)(a b))((a (^x.(^y.y)))((^z.z) a))) 5. ==[ beta ]==> (((a b)(a b))((a (^x.(^y.y))) a)) REDUCED to normal form. ------ 199193/23830680. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (b (((^y.y)(a a))((a a) a))) 4. ==[ alpha ]==> (b (((^x.x)(a a))((a a) a))) 5. ==[ beta ]==> (b ((a a)((a a) a))) REDUCED to normal form. ------ 199194/23830788. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))((a (a a))(b a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))(b a))) REDUCED to normal form. ------ 199195/23830860. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))(b (^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))(b (^z.(a a)))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))(b (^z.(a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))(b (^y.(a a)))) 5. ==[ beta ]==> ((a (a a))(b (^y.(a a)))) 6. ==[ alpha ]==> ((a (a a))(b (^x.(a a)))) REDUCED to normal form. ------ 199196/23830941. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))((^z.z)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))((^z.z)(a (^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.y)(a (^z.z)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 199197/23830968. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.(^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a b)(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 199198/23831067. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((a b)(^x1.b))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(^x1.b))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(^z.b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199199/23831076. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^a.b)(a b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.b)(a b))) 3. ==[ beta ]==> ((a (a (^x.(^y.y)))) b) REDUCED to normal form. ------ 199200/23831544. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))(c (a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (c (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (c (a (^x.(^y.y))))) REDUCED to normal form. ------ 199201/23831607. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^c.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.(a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(a a)) REDUCED to normal form. ------ 199202/23831652. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199203/23831679. ------ 1. ==[ start ]==> ((a (^b.b))((b a)((^a.a) a))) 2. ==[ alpha ]==> ((a (^x.x))((b a)((^y.y) a))) 3. ==[ beta ]==> ((a (^x.x))((b a) a)) REDUCED to normal form. ------ 199204/23831913. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))(b (^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))(b (^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)(b (^z.z))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)(b (^y.y))) REDUCED to normal form. ------ 199205/23831958. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(((^x1.x1) b)(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199206/23831967. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))((^b.b)(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))((^z.z)(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(a a)) REDUCED to normal form. ------ 199207/23831994. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> ((a b)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 4. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(a (^x1.x1)))) 5. ==[ beta ]==> ((a b)(^y.(^z.z))) 6. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 199208/23832282. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(((^a.a) b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(((^z.z) b) a)) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)(b a)) REDUCED to normal form. ------ 199209/23832309. ------ 1. ==[ start ]==> ((((^a.a) b) a)((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) b) a)((a (^y.(^z.z))) b)) 3. ==[ beta ]==> ((b a)((a (^y.(^z.z))) b)) 4. ==[ alpha ]==> ((b a)((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 199210/23832336. ------ 1. ==[ start ]==> (((a a)(^b.b))((b a) c)) 2. ==[ alpha ]==> (((a a)(^x.x))((b a) c)) REDUCED to normal form. ------ 199211/23832597. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(a ((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(a ((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(a ((^z.z) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199212/23832606. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^b.b) a)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1) a)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1))) a) REDUCED to normal form. ------ 199213/23832633. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^a.(^a.(^a.a))) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.(^x1.(^y1.y1))) b)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.(^y1.y1))) b)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.(^x1.x1))) b)) 5. ==[ beta ]==> ((b (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199214/23832885. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))(b (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))(b (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 199215/23832939. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((^x1.(^y1.(^z1.z1)))(a a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.z)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 199216/23833515. ------ 1. ==[ start ]==> (((^a.b)(a b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a b))(a (a (^y.(^z.z))))) 3. ==[ beta ]==> (b (a (a (^y.(^z.z))))) 4. ==[ alpha ]==> (b (a (a (^x.(^y.y))))) REDUCED to normal form. ------ 199217/23833524. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> (((a b)(^x.b))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 199218/23833578. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))((^c.(^a.a)) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))((^x1.(^y1.y1)) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 199219/23833623. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))((a b)(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a b)(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a b)(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199220/23833749. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(c (^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(c (^z.(^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) b)(c (^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(c (^y.(^z.z)))) REDUCED to normal form. ------ 199221/23833803. ------ 1. ==[ start ]==> (((a (a a))(b a))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))(b a))(a (^x.(^y.(^z.z))))) REDUCED to normal form. ------ 199222/23833884. ------ 1. ==[ start ]==> (((a b)(a b))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(a a))((^y.y) a))) 3. ==[ beta ]==> (((a b)(a b))(a a)) REDUCED to normal form. ------ 199223/23833911. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.b)(a (a a)))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.b)(a (a a)))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.b)(a (a a)))) 5. ==[ beta ]==> (((a a)((a a) a)) b) REDUCED to normal form. ------ 199224/23833992. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^a.(a a))(a b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(x1 x1))(a b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(x1 x1))(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(z z))(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)((a b)(a b))) REDUCED to normal form. ------ 199225/23834019. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.a)((^z.z)(a a)))) 5. ==[ beta ]==> ((b (a (^x.x))) a) REDUCED to normal form. ------ 199226/23834046. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.(^y.y))((a a)(^z.z)))) 3. ==[ beta ]==> ((((a a)(a a))(a a))(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a))(a a))(^x.x)) REDUCED to normal form. ------ 199227/23834073. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.a)(b a))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.y)(b a))) 3. ==[ beta ]==> ((a (b (^x.x)))(b a)) REDUCED to normal form. ------ 199228/23834352. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(a (b a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(a (b a))) 3. ==[ beta ]==> ((^y.(^z.z))(a (b a))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (b a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199229/23834388. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.(^z.z)) b)) 3. ==[ beta ]==> ((b c)((^y.(^z.z)) b)) 4. ==[ alpha ]==> ((b c)((^x.(^y.y)) b)) 5. ==[ beta ]==> ((b c)(^y.y)) 6. ==[ alpha ]==> ((b c)(^x.x)) REDUCED to normal form. ------ 199230/23834415. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^b.(a a)) c)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(a a)) c)) 3. ==[ beta ]==> ((((a a)(a a)) b)(a a)) REDUCED to normal form. ------ 199231/23834460. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((b (^y.y))(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((b (^x.x))(((a a) a)(a (a a)))) REDUCED to normal form. ------ 199232/23834487. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((^a.a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.x1)(^y1.y1))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.z)(^x1.x1))) 7. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199233/23834541. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))(((^x1.x1) a)(a b))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(((^y1.y1) a)(a b))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))(a (a b))) REDUCED to normal form. ------ 199234/23834631. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 199235/23834658. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((^a.a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((^z.z)(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.b))(((^z.z)(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.b))((a a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.b))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 199236/23834739. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((^x1.x1)(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))((^y1.y1)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))((^x1.x1)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(z z)))(^y1.(^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 199237/23834766. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((a (a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((a (a a))(^z.a))) 3. ==[ beta ]==> ((b (^y.a))((a (a a))(^z.a))) 4. ==[ alpha ]==> ((b (^x.a))((a (a a))(^y.a))) REDUCED to normal form. ------ 199238/23834793. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))(((^a.a) a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(((^z.z) a)(^x1.b))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(a (^x1.b))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))(a (^z.b))) REDUCED to normal form. ------ 199239/23834856. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 199240/23834910. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a b)((^y.(a a))(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a b)((^x.(a a))(^y.(^z.z)))) 7. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 199241/23834937. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^a.b)(^b.a))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y)))) b) REDUCED to normal form. ------ 199242/23834964. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^c.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.a)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.a)(^z.(z z)))) 5. ==[ beta ]==> ((b a)((^y.a)(^z.(z z)))) 6. ==[ alpha ]==> ((b a)((^x.a)(^y.(y y)))) 7. ==[ beta ]==> ((b a) a) REDUCED to normal form. ------ 199243/23834991. ------ 1. ==[ start ]==> ((((a a) a)((a a)(^a.a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)((a a)(^x.x)))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 199244/23835018. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a b)(a a))((^y.(y y))(^z.a))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(x x))(^y.a))) 5. ==[ beta ]==> (((a b)(a a))((^y.a)(^y.a))) 6. ==[ alpha ]==> (((a b)(a a))((^x.a)(^y.a))) 7. ==[ beta ]==> (((a b)(a a)) a) REDUCED to normal form. ------ 199245/23835045. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.a)(^z.b))) 3. ==[ beta ]==> (((a a)(a b))((^y.a)(^z.b))) 4. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.b))) 5. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 199246/23835072. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^a.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))(^y.y)) REDUCED to normal form. ------ 199247/23835324. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a a)((^z.z)(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a a)((^z.z)(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z)(a a)))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.z)(a a)))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(a a)))) 7. ==[ beta ]==> ((a a)((^y.y)(a a))) 8. ==[ alpha ]==> ((a a)((^x.x)(a a))) 9. ==[ beta ]==> ((a a)(a a)) REDUCED to normal form. ------ 199248/23835729. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))(c ((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))(c ((a a) a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))(c ((a a) a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))(c ((a a) a))) 5. ==[ beta ]==> ((b ((^y.y) b))(c ((a a) a))) 6. ==[ alpha ]==> ((b ((^x.x) b))(c ((a a) a))) 7. ==[ beta ]==> ((b b)(c ((a a) a))) REDUCED to normal form. ------ 199249/23835810. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((a b)(a a))) 3. ==[ beta ]==> (b ((a b)(a a))) REDUCED to normal form. ------ 199250/23835819. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^a.b) b)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b) b)) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 199251/23835846. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^c.a) c)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.a) c)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.a) c)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.a) c)) 5. ==[ beta ]==> (((a a)(^x.(a a))) a) REDUCED to normal form. ------ 199252/23835918. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))(((^z1.z1) a)((^x2.x2)(^y2.y2)))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)((^x2.x2)(^y2.y2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199253/23836035. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(((a a) a)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(((a a) a)(^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(((a a) a)(^y.(^z.z)))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 199254/23836071. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 199255/23836098. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(z z))(a (a a)))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 199256/23836125. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(a a))) a) REDUCED to normal form. ------ 199257/23836152. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.(^z.z))((a a) a))) 3. ==[ beta ]==> (((a (a a)) b)((^y.(^z.z))((a a) a))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.(^y.y))((a a) a))) 5. ==[ beta ]==> (((a (a a)) b)(^y.y)) 6. ==[ alpha ]==> (((a (a a)) b)(^x.x)) REDUCED to normal form. ------ 199258/23836179. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.y1)(a b))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.y1)(a b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.x1)(a b))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.x1)(a b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)(a b))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(a b)) REDUCED to normal form. ------ 199259/23836206. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.b)(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.b)(^y.y))) 3. ==[ beta ]==> ((((a a) a)(b a)) b) REDUCED to normal form. ------ 199260/23836233. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^c.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) a) REDUCED to normal form. ------ 199261/23836260. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(a a)))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(a a)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)((^y.y)(a a)))((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.a))) 6. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.a))) 7. ==[ beta ]==> (((a a)(a a))(^y.y)) 8. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 199262/23836287. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^a.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))(^z.(z z)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))((^z.(z z))(^z.(z z)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(y y))(^z.(z z)))) IRREDUCIBLE: cycle. ------ 199263/23836368. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.y)(^z.b))) 3. ==[ beta ]==> ((b (a (a a)))((^y.y)(^z.b))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.x)(^y.b))) 5. ==[ beta ]==> ((b (a (a a)))(^y.b)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.b)) REDUCED to normal form. ------ 199264/23836485. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))(((^a.a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))(((^x1.x1) a)(a (a a)))) 3. ==[ beta ]==> ((^y.(y (^z.z)))(((^x1.x1) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))(((^z.z) a)(a (a a)))) 5. ==[ beta ]==> ((((^z.z) a)(a (a a)))(^y.y)) 6. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(^y.y)) 7. ==[ beta ]==> ((a (a (a a)))(^y.y)) 8. ==[ alpha ]==> ((a (a (a a)))(^x.x)) REDUCED to normal form. ------ 199265/23836890. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(a ((a a) a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(a ((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(a ((a a) a))) 5. ==[ beta ]==> ((^y.y)(a ((a a) a))) 6. ==[ alpha ]==> ((^x.x)(a ((a a) a))) 7. ==[ beta ]==> (a ((a a) a)) REDUCED to normal form. ------ 199266/23836917. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> ((a (a (^y.y)))(((^z.z)(^x1.x1))(a a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> ((a (a (^x.x)))((^z.z)(a a))) 6. ==[ alpha ]==> ((a (a (^x.x)))((^y.y)(a a))) 7. ==[ beta ]==> ((a (a (^x.x)))(a a)) REDUCED to normal form. ------ 199267/23836926. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.(^x1.x1)) b)) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(^x1.x1)) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.z)) REDUCED to normal form. ------ 199268/23836944. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((a (a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((a (a a))(a (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((a (a a))(a (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((a (a a))(a (^y.y)))) 5. ==[ beta ]==> ((a (a a))(a (^y.y))) 6. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 199269/23836998. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))((a (^a.a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))((a (^y.y))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))((a (^y.y))(a (a a)))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))((a (^x.x))(a (a a)))) REDUCED to normal form. ------ 199270/23837061. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.(^a.a))))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))((^x1.x1)(^y1.y1))) 5. ==[ beta ]==> ((((a a) a)(^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((((a a) a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 199271/23837142. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((a (^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((a (^z.z))(^x1.(x1 x1)))) REDUCED to normal form. ------ 199272/23837223. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((a (a a)) b)) 3. ==[ beta ]==> ((b (^y.(^z.z)))((a (a a)) b)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((a (a a)) b)) REDUCED to normal form. ------ 199273/23837322. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a a)(^y.y))(a ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(a ((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a a)(^x.x))(a (^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.y))) REDUCED to normal form. ------ 199274/23837331. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^b.(^a.a)) a)) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.(^x1.x1)) a)) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.x1)) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.z)) REDUCED to normal form. ------ 199275/23837349. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a (a a))(a a))) REDUCED to normal form. ------ 199276/23837421. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(b (^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(b (^z.(z z)))) 3. ==[ beta ]==> ((a (b (^y.y)))(b (^z.(z z)))) 4. ==[ alpha ]==> ((a (b (^x.x)))(b (^y.(y y)))) REDUCED to normal form. ------ 199277/23837448. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(a (^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 199278/23837475. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((^x1.(x1 x1))(a a))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((^x1.(x1 x1))(a a))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(z z))(a a))) 5. ==[ beta ]==> (((^y.y) b)((^z.(z z))(a a))) 6. ==[ alpha ]==> (((^x.x) b)((^y.(y y))(a a))) 7. ==[ beta ]==> (b ((^y.(y y))(a a))) 8. ==[ alpha ]==> (b ((^x.(x x))(a a))) 9. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 199279/23837502. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.a)(a (^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y)))) a) REDUCED to normal form. ------ 199280/23837529. ------ 1. ==[ start ]==> (((a b)(b a))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a b)(b a))((^x.(^y.y))((^z.z) a))) 3. ==[ beta ]==> (((a b)(b a))(^y.y)) 4. ==[ alpha ]==> (((a b)(b a))(^x.x)) REDUCED to normal form. ------ 199281/23837556. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.z)(a (a a)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.z)(a (a a)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.y)(a (a a)))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(a (a a))) REDUCED to normal form. ------ 199282/23837583. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.(a a))(^a.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.(z z))(^x1.x1))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.(z z))(^x1.x1))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.(y y))(^z.z))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(^z.z))) 6. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(^z.z))) 7. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.z)) 8. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.y)) REDUCED to normal form. ------ 199283/23837637. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))(^z.z)) REDUCED to normal form. ------ 199284/23837664. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.x1)(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.z)(^x1.(x1 x1)))) 5. ==[ beta ]==> ((b (^y.y))((^z.z)(^x1.(x1 x1)))) 6. ==[ alpha ]==> ((b (^x.x))((^y.y)(^z.(z z)))) 7. ==[ beta ]==> ((b (^x.x))(^z.(z z))) 8. ==[ alpha ]==> ((b (^x.x))(^y.(y y))) REDUCED to normal form. ------ 199285/23837745. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))(b (^b.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))(b (^x1.a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(b (^x1.a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(b (^z.a))) 5. ==[ beta ]==> ((a (^y.y))(b (^z.a))) 6. ==[ alpha ]==> ((a (^x.x))(b (^y.a))) REDUCED to normal form. ------ 199286/23837772. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(a (^a.(a a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(a (^y.(y y)))) REDUCED to normal form. ------ 199287/23837799. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))((^x1.a)(a a))) 3. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.a)(a a))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.a)(a a))) 5. ==[ beta ]==> ((a (^x.(^y.y))) a) REDUCED to normal form. ------ 199288/23837808. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(c b)) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(c b)) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(c b)) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(c b)) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199289/23837835. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))(b c)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))(b c)) 3. ==[ beta ]==> ((^y.y)(b c)) 4. ==[ alpha ]==> ((^x.x)(b c)) 5. ==[ beta ]==> (b c) REDUCED to normal form. ------ 199290/23837970. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((a (^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((a (^y1.y1))(a a))) 3. ==[ beta ]==> (b ((a (^y1.y1))(a a))) 4. ==[ alpha ]==> (b ((a (^x.x))(a a))) REDUCED to normal form. ------ 199291/23838078. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(a c)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(a c)) 3. ==[ beta ]==> ((^y.(^z.z))(a c)) 4. ==[ alpha ]==> ((^x.(^y.y))(a c)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199292/23838213. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(a b)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(a b)) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(a b)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(a b)) 5. ==[ beta ]==> ((^y.y)(a b)) 6. ==[ alpha ]==> ((^x.x)(a b)) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 199293/23838222. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)((a a) a)) 2. ==[ alpha ]==> (((a (a (^x.x))) b)((a a) a)) REDUCED to normal form. ------ 199294/23838249. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)((^a.a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)((^x1.x1) a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z) a)) 5. ==[ beta ]==> ((^y.y)((^z.z) a)) 6. ==[ alpha ]==> ((^x.x)((^y.y) a)) 7. ==[ beta ]==> ((^y.y) a) 8. ==[ alpha ]==> ((^x.x) a) 9. ==[ beta ]==> a REDUCED to normal form. ------ 199295/23838267. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))(a a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a a)) 5. ==[ beta ]==> ((^y.(^z.z))(a a)) 6. ==[ alpha ]==> ((^x.(^y.y))(a a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199296/23838275. ------ 1. ==[ start ]==> (^a.((a a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (^x.((x x)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 199297/23838276. ------ 1. ==[ start ]==> (a ((a a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (a ((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 199298/23838288. ------ 1. ==[ start ]==> ((^a.(^a.a))(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199299/23846028. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))(^c.(^d.a))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))(^z.(^x1.a))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199300/23850225. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a)))) b) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1)))) b) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1))) b) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) b) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199301/23850234. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a)))) a) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 199302/23850240. ------ 1. ==[ start ]==> ((^a.a)((a a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.x)((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199303/23850249. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199304/23850252. ------ 1. ==[ start ]==> ((a (^a.a))(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.x))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 199305/23850267. ------ 1. ==[ start ]==> ((^a.(a a))(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(x x))(((^y.y)(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((((^y.y)(^z.(^x1.x1))) a)(((^y.y)(^z.(^x1.x1))) a)) 4. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(((^x1.x1)(^y1.(^z1.z1))) a)) 5. ==[ beta ]==> (((^y.(^z.z)) a)(((^x1.x1)(^y1.(^z1.z1))) a)) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(((^z.z)(^x1.(^y1.y1))) a)) 7. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.(^y1.y1))) a)) 8. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.(^x1.x1))) a)) 9. ==[ beta ]==> (((^y.y)(^z.(^x1.x1))) a) 10. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) a) 11. ==[ beta ]==> ((^y.(^z.z)) a) 12. ==[ alpha ]==> ((^x.(^y.y)) a) 13. ==[ beta ]==> (^y.y) 14. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199306/23850294. ------ 1. ==[ start ]==> ((^a.b)((a (a (^a.a))) b)) 2. ==[ alpha ]==> ((^x.b)((a (a (^y.y))) b)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 199307/23850492. ------ 1. ==[ start ]==> ((^a.(^b.a))((^c.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.x))((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (^y.((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (^x.((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^x.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199308/23850720. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.x))(^y.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 199309/23851152. ------ 1. ==[ start ]==> (((^a.(a a)) b)(^c.(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(^y.(a (a (^z.z))))) 3. ==[ beta ]==> ((b b)(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> ((b b)(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 199310/23851185. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199311/23851617. ------ 1. ==[ start ]==> ((^a.((a a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((^x.((x x) x))((a (a (^y.y))) a)) 3. ==[ beta ]==> ((((a (a (^y.y))) a)((a (a (^y.y))) a))((a (a (^y.y))) a)) 4. ==[ alpha ]==> ((((a (a (^x.x))) a)((a (a (^y.y))) a))((a (a (^z.z))) a)) REDUCED to normal form. ------ 199312/23851950. ------ 1. ==[ start ]==> ((^a.(^a.b))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(z z))(^x1.(a a)))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 199313/23852130. ------ 1. ==[ start ]==> ((^a.(a b))((^c.(a a)) d)) 2. ==[ alpha ]==> ((^x.(x b))((^y.(a a)) d)) 3. ==[ beta ]==> (((^y.(a a)) d) b) 4. ==[ alpha ]==> (((^x.(a a)) d) b) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 199314/23852448. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))(^c.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))(^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))(^z.((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((^y.a)(^z.((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((^x.a)(^y.((^z.(^x1.x1)) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 199315/23854992. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((a b)(^a.b))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((a b)(^x1.b))) 3. ==[ beta ]==> (((a b)(^x1.b))(^y.(^z.z))) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.z))) REDUCED to normal form. ------ 199316/23855166. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^b.((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((a a)(a a)))) 3. ==[ beta ]==> (b (^x1.((a a)(a a)))) 4. ==[ alpha ]==> (b (^x.((a a)(a a)))) REDUCED to normal form. ------ 199317/23855526. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^a.((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.((z z)(z z)))) REDUCED to normal form. ------ 199318/23855910. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 199319/23856192. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))(^b.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.((^x2.x2) z1))) 3. ==[ eta ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^x2.x2)) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(^z1.z1)) 5. ==[ beta ]==> ((^y.(^z.z))(^z1.z1)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.z)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199320/23856516. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(^y1.(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199321/23856525. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^a.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.((^z1.z1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.b)) REDUCED to normal form. ------ 199322/23856909. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))(((a a)(^y.y))(^z.a))) 3. ==[ beta ]==> (((((a a)(^y.y))(^z.a))(((a a)(^y.y))(^z.a)))((((a a)(^y.y))(^z.a))(((a a)(^y.y))(^z.a)))) 4. ==[ alpha ]==> (((((a a)(^x.x))(^y.a))(((a a)(^z.z))(^x1.a)))((((a a)(^y1.y1))(^z1.a))(((a a)(^x2.x2))(^y2.a)))) REDUCED to normal form. ------ 199323/23857434. ------ 1. ==[ start ]==> (((^a.b)(a b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a b))(^y.(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b (^y.(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b (^x.(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 199324/23857443. ------ 1. ==[ start ]==> (((a b)(^a.b))(^a.(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(y (^z.(^x1.x1))))) REDUCED to normal form. ------ 199325/23857992. ------ 1. ==[ start ]==> ((a (b (^a.a)))(^c.(^d.a))) 2. ==[ alpha ]==> ((a (b (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 199326/23858775. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))(^c.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 199327/23859900. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(^c.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(^y.(a b))) REDUCED to normal form. ------ 199328/23860809. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(^x1.(^y1.a))) 3. ==[ beta ]==> (((^z.z)(^y.y))(^x1.(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.a))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.a))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.a))) 7. ==[ beta ]==> (^y.(^z.a)) 8. ==[ alpha ]==> (^x.(^y.a)) REDUCED to normal form. ------ 199329/23860818. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^a.((a a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.((y y) y))) REDUCED to normal form. ------ 199330/23860953. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(^c.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.y1)))) 6. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.x1)))) 7. ==[ beta ]==> (^y.((^z.z)(^x1.x1))) 8. ==[ alpha ]==> (^x.((^y.y)(^z.z))) 9. ==[ beta ]==> (^x.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199331/23861106. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))(^b.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199332/23861241. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(^z.(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 199333/23861250. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^z.(^y1.y1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 199334/23861583. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(^c.d)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(^x1.d)) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(^x1.d)) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(^z.d)) 5. ==[ beta ]==> ((b (^y.y))(^z.d)) 6. ==[ alpha ]==> ((b (^x.x))(^y.d)) REDUCED to normal form. ------ 199335/23861682. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(^c.((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(^z.((^x1.x1) a))) 3. ==[ beta ]==> ((b (^y.y))(^z.((^x1.x1) a))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((^z.z) a))) 5. ==[ beta ]==> ((b (^x.x))(^y.a)) REDUCED to normal form. ------ 199336/23861715. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(((^y1.y1) a)(^z1.z1))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199337/23861997. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^b.(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199338/23862132. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(^b.(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(^y1.(a a))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(^y1.(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(^x1.(a a))) 5. ==[ beta ]==> ((^y.y)(^x1.(a a))) 6. ==[ alpha ]==> ((^x.x)(^y.(a a))) 7. ==[ beta ]==> (^y.(a a)) 8. ==[ alpha ]==> (^x.(a a)) REDUCED to normal form. ------ 199339/23862141. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^a.b)) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.b)) REDUCED to normal form. ------ 199340/23862168. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)(^a.(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(^x1.(x1 x1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(x1 x1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(z z))) 5. ==[ beta ]==> ((^y.y)(^z.(z z))) 6. ==[ alpha ]==> ((^x.x)(^y.(y y))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 199341/23862186. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))(^y1.(^z1.z1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(^z1.z1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.x1))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199342/23862195. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a))))(^a.a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 199343/23862207. ------ 1. ==[ start ]==> ((a a)((a a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a a)((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 199344/23862216. ------ 1. ==[ start ]==> ((a (^a.a))((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((^y.y)((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.x))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199345/23862234. ------ 1. ==[ start ]==> ((a (a a))(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (a a))(((^x.x)(^y.(^z.z))) a)) 3. ==[ beta ]==> ((a (a a))((^y.(^z.z)) a)) 4. ==[ alpha ]==> ((a (a a))((^x.(^y.y)) a)) 5. ==[ beta ]==> ((a (a a))(^y.y)) 6. ==[ alpha ]==> ((a (a a))(^x.x)) REDUCED to normal form. ------ 199346/23862243. ------ 1. ==[ start ]==> (((^a.a)(^a.a))((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(^z1.z1))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(^z1.z1))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(^y1.y1))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.y1)) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.x1)) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199347/23862261. ------ 1. ==[ start ]==> ((a b)((a (a (^a.a))) b)) 2. ==[ alpha ]==> ((a b)((a (a (^x.x))) b)) REDUCED to normal form. ------ 199348/23862270. ------ 1. ==[ start ]==> (((^a.a)(a a))((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(a a))((^y.(y (^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a a)((^y.(y (^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a a)((^x.(x (^y.y)))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a a)((^z.(^x1.x1))(^y.y))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 199349/23862378. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.a))((^b.b)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.x1)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.a))) 5. ==[ beta ]==> ((^y.y)(^z.a)) 6. ==[ alpha ]==> ((^x.x)(^y.a)) 7. ==[ beta ]==> (^y.a) 8. ==[ alpha ]==> (^x.a) REDUCED to normal form. ------ 199350/23862405. ------ 1. ==[ start ]==> (((^a.a)(a (^a.a)))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((^x.x)(a (^y.y)))((^z.(^x1.(^y1.y1)))(^z1.b))) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.(^y1.y1)))(^z1.b))) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1)))(^y1.b))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199351/23862459. ------ 1. ==[ start ]==> ((a (^b.a))((^c.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.a))(^z.z)) 4. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 199352/23862540. ------ 1. ==[ start ]==> (((^a.a)(^b.a))((^c.a)(^b.b))) 2. ==[ alpha ]==> (((^x.x)(^y.a))((^z.a)(^x1.x1))) 3. ==[ beta ]==> ((^y.a)((^z.a)(^x1.x1))) 4. ==[ alpha ]==> ((^x.a)((^y.a)(^z.z))) 5. ==[ beta ]==> a REDUCED to normal form. ------ 199353/23862567. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.a)))((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(a a)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(^x2.(a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199354/23862630. ------ 1. ==[ start ]==> (((a a)(^b.a))(c ((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((a a)(^x.a))(c ((^y.(^z.z)) a))) 3. ==[ beta ]==> (((a a)(^x.a))(c (^z.z))) 4. ==[ alpha ]==> (((a a)(^x.a))(c (^y.y))) REDUCED to normal form. ------ 199355/23862648. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.z)))((^x1.(^y1.y1))(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(z1 (^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 (^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 (^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z (^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199356/23862657. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))(b (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(b (a (a (^x1.x1))))) REDUCED to normal form. ------ 199357/23862684. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(a ((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(a ((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a (^x.x))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.z)))) REDUCED to normal form. ------ 199358/23862720. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((^a.(a (^a.a))) b)) 2. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(y (^z.z))) b)) 3. ==[ beta ]==> (((a a) a)((^y.(y (^z.z))) b)) 4. ==[ alpha ]==> (((a a) a)((^x.(x (^y.y))) b)) 5. ==[ beta ]==> (((a a) a)(b (^y.y))) 6. ==[ alpha ]==> (((a a) a)(b (^x.x))) REDUCED to normal form. ------ 199359/23862792. ------ 1. ==[ start ]==> (((^a.(a a)) a)(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(x x)) a)(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((a a)(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 199360/23862873. ------ 1. ==[ start ]==> ((((^a.a) a) b)((b a)(a b))) 2. ==[ alpha ]==> ((((^x.x) a) b)((b a)(a b))) 3. ==[ beta ]==> ((a b)((b a)(a b))) REDUCED to normal form. ------ 199361/23862900. ------ 1. ==[ start ]==> (((a (a a)) a)(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (a a)) a)(((a a)(^x.x))((^y.y)(a a)))) 3. ==[ beta ]==> (((a (a a)) a)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 199362/23862927. ------ 1. ==[ start ]==> (((a a)(^a.(a a)))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.(x x)))(((^y.y)(a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a a)(^x.(x x)))((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((a a)((a a)(^y.y)))) REDUCED to normal form. ------ 199363/23862954. ------ 1. ==[ start ]==> (((a (^a.a))(^b.a))((a b)(b a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.a))((a b)(b a))) REDUCED to normal form. ------ 199364/23862981. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.a)))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((a a) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((a a) a)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((a a) a)(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 199365/23863008. ------ 1. ==[ start ]==> (((a (a a))(^a.a))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(((^y.y)(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (a a))(^x.x))((^z.z)((^x1.x1) b))) 4. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y)((^z.z) b))) 5. ==[ beta ]==> (((a (a a))(^x.x))((^z.z) b)) 6. ==[ alpha ]==> (((a (a a))(^x.x))((^y.y) b)) 7. ==[ beta ]==> (((a (a a))(^x.x)) b) REDUCED to normal form. ------ 199366/23863116. ------ 1. ==[ start ]==> (((^a.(a a)) b)((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)((a a)(a (a (^y.y))))) 3. ==[ beta ]==> ((b b)((a a)(a (a (^y.y))))) 4. ==[ alpha ]==> ((b b)((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 199367/23863152. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (a (^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.y))((a (a (^z.z)))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))((a (a (^y.y)))(^z.z))) REDUCED to normal form. ------ 199368/23863161. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((^a.(a (^a.a)))(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(a a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(x1 (^y1.y1)))(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(z (^x1.x1)))(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199369/23863296. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.(^y1.(^z1.z1)))((a a) a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.(^y1.(^z1.z1)))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))((a a) a))) 5. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))((a a) a))) 6. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))((a a) a))) 7. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a a) a)) 8. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a a) a)) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199370/23863377. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (^y.y))(a (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.(a a))((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a a)) REDUCED to normal form. ------ 199371/23863449. ------ 1. ==[ start ]==> (((a a)((^a.a)(^a.a)))(((^a.a)(^a.a))(^b.b))) 2. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z)(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.z))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 199372/23863557. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((a a)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.(y (^z.z))))) 5. ==[ beta ]==> ((a a)((a a)(^y.(y (^z.z))))) 6. ==[ alpha ]==> ((a a)((a a)(^x.(x (^y.y))))) REDUCED to normal form. ------ 199373/23863584. ------ 1. ==[ start ]==> ((a ((a a) a))((a (a (^a.a))) a)) 2. ==[ alpha ]==> ((a ((a a) a))((a (a (^x.x))) a)) REDUCED to normal form. ------ 199374/23863674. ------ 1. ==[ start ]==> (((^a.(a a))(^b.a))((^c.(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.a))((^z.(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.a)(^y.a))((^z.(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.a)(^y.a))((^z.(a a))(^x1.(x1 x1)))) 5. ==[ beta ]==> (a ((^z.(a a))(^x1.(x1 x1)))) 6. ==[ alpha ]==> (a ((^x.(a a))(^y.(y y)))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 199375/23863917. ------ 1. ==[ start ]==> ((a (^a.b))((^a.(a a))(^c.(a a)))) 2. ==[ alpha ]==> ((a (^x.b))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> ((a (^x.b))((^z.(a a))(^z.(a a)))) 4. ==[ alpha ]==> ((a (^x.b))((^y.(a a))(^z.(a a)))) 5. ==[ beta ]==> ((a (^x.b))(a a)) REDUCED to normal form. ------ 199376/23864016. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.(a (^a.a))) a)) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.(y (^z.z))) a)) 3. ==[ beta ]==> (((a (a a)) a)((^y.(y (^z.z))) a)) 4. ==[ alpha ]==> (((a (a a)) a)((^x.(x (^y.y))) a)) 5. ==[ beta ]==> (((a (a a)) a)(a (^y.y))) 6. ==[ alpha ]==> (((a (a a)) a)(a (^x.x))) REDUCED to normal form. ------ 199377/23864088. ------ 1. ==[ start ]==> (((^a.b) a)(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.b) a)(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> (b (((a a)(a a))((^y.y) a))) 4. ==[ alpha ]==> (b (((a a)(a a))((^x.x) a))) 5. ==[ beta ]==> (b (((a a)(a a)) a)) REDUCED to normal form. ------ 199378/23864097. ------ 1. ==[ start ]==> ((a (a b))((^c.(a a)) d)) 2. ==[ alpha ]==> ((a (a b))((^x.(a a)) d)) 3. ==[ beta ]==> ((a (a b))(a a)) REDUCED to normal form. ------ 199379/23864250. ------ 1. ==[ start ]==> ((((a a) a) b)((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a) b)((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 199380/23864277. ------ 1. ==[ start ]==> (((a b) a)(((a a) a)(b a))) REDUCED to normal form. ------ 199381/23864304. ------ 1. ==[ start ]==> (((a a)(^a.b))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)(^x.b))(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a a)(^x.b))((^z.z)(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.y)(a (^z.(^x1.x1))))) 5. ==[ beta ]==> (((a a)(^x.b))(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.b))(a (^y.(^z.z)))) REDUCED to normal form. ------ 199382/23864358. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(^a.a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.z)))(((^x1.x1) a)((a a)(a a)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)((a a)(a a)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)((a a)(a a)))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a ((a a)(a a)))) REDUCED to normal form. ------ 199383/23864385. ------ 1. ==[ start ]==> (((a (a a))(^a.(a a)))((a (^a.a))(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(x x)))((a (^y.y))(b (^z.z)))) REDUCED to normal form. ------ 199384/23864412. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.a))((a a)((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.a))((a a)((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> (((^y.y)(^z.a))((a a)((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> (((^x.x)(^y.a))((a a)((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((^y.a)((a a)((^z.(^x1.x1)) a))) 6. ==[ alpha ]==> ((^x.a)((a a)((^y.(^z.z)) a))) 7. ==[ beta ]==> a REDUCED to normal form. ------ 199385/23864502. ------ 1. ==[ start ]==> (((a a)(a b))(((a a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(a b))(((a a)(a a))(^x.a))) REDUCED to normal form. ------ 199386/23864529. ------ 1. ==[ start ]==> (((a (^a.a))((a a) a))(((^a.a) b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a) a))(((^y.y) b)(^z.(z z)))) 3. ==[ beta ]==> (((a (^x.x))((a a) a))(b (^z.(z z)))) 4. ==[ alpha ]==> (((a (^x.x))((a a) a))(b (^y.(y y)))) REDUCED to normal form. ------ 199387/23864556. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((a (^a.(^a.a)))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((a (^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 199388/23864583. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((b a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((b a)(^x.a))) REDUCED to normal form. ------ 199389/23864610. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) a))(((a a)(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) a))(((a a)(^x1.x1))(^y1.b))) 3. ==[ beta ]==> (((^y.y)((^z.z) a))(((a a)(^x1.x1))(^y1.b))) 4. ==[ alpha ]==> (((^x.x)((^y.y) a))(((a a)(^z.z))(^x1.b))) 5. ==[ beta ]==> (((^y.y) a)(((a a)(^z.z))(^x1.b))) 6. ==[ alpha ]==> (((^x.x) a)(((a a)(^y.y))(^z.b))) 7. ==[ beta ]==> (a (((a a)(^y.y))(^z.b))) 8. ==[ alpha ]==> (a (((a a)(^x.x))(^y.b))) REDUCED to normal form. ------ 199390/23864637. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.a)))(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.x)))(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.x)))((a a)(^z.(a a)))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.x)))((a a)(^y.(a a)))) REDUCED to normal form. ------ 199391/23864664. ------ 1. ==[ start ]==> (((a b)(a a))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(a a))((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 199392/23864700. ------ 1. ==[ start ]==> (((^a.a)(^b.(a a)))((^c.a)(b a))) 2. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.a)(b a))) 3. ==[ beta ]==> ((^y.(a a))((^z.a)(b a))) 4. ==[ alpha ]==> ((^x.(a a))((^y.a)(b a))) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 199393/23864727. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))((^b.(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(a (^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199394/23864781. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))((^b.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))((^x1.a)((a a)(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))((^x1.a)((a a)(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))((^y1.a)((a a)(a a)))) 5. ==[ beta ]==> ((^y.y)((^y1.a)((a a)(a a)))) 6. ==[ alpha ]==> ((^x.x)((^y.a)((a a)(a a)))) 7. ==[ beta ]==> ((^y.a)((a a)(a a))) 8. ==[ alpha ]==> ((^x.a)((a a)(a a))) 9. ==[ beta ]==> a REDUCED to normal form. ------ 199395/23864943. ------ 1. ==[ start ]==> (((^a.(^a.a))(a b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(a b))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.y)((^z.z)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.x)((^y.y)(^z.(z z)))) 5. ==[ beta ]==> ((^y.y)(^z.(z z))) 6. ==[ alpha ]==> ((^x.x)(^y.(y y))) 7. ==[ beta ]==> (^y.(y y)) 8. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 199396/23865078. ------ 1. ==[ start ]==> (((^a.b)(a (^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 199397/23865303. ------ 1. ==[ start ]==> (((^a.b) c)(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b) c)(((a a)(a a))(a (^y.y)))) 3. ==[ beta ]==> (b (((a a)(a a))(a (^y.y)))) 4. ==[ alpha ]==> (b (((a a)(a a))(a (^x.x)))) REDUCED to normal form. ------ 199398/23865312. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))((^c.(a a)) c)) 2. ==[ alpha ]==> (((a b)(a (^x.x)))((^y.(a a)) c)) 3. ==[ beta ]==> (((a b)(a (^x.x)))(a a)) REDUCED to normal form. ------ 199399/23865546. ------ 1. ==[ start ]==> (((a b) c)((a (a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b) c)((a (a a))(a (^x.(^y.y))))) REDUCED to normal form. ------ 199400/23865573. ------ 1. ==[ start ]==> ((((^a.a)(a a)) b)(((^a.a) a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a)) b)(((^y.y) a)((^z.z) b))) 3. ==[ beta ]==> (((a a) b)(((^y.y) a)((^z.z) b))) 4. ==[ alpha ]==> (((a a) b)(((^x.x) a)((^y.y) b))) 5. ==[ beta ]==> (((a a) b)(a ((^y.y) b))) 6. ==[ alpha ]==> (((a a) b)(a ((^x.x) b))) 7. ==[ beta ]==> (((a a) b)(a b)) REDUCED to normal form. ------ 199401/23865600. ------ 1. ==[ start ]==> ((((a a)(^a.a)) a)((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 199402/23865933. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((a (a a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((a (a a))(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a b))((a (a a))(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((a (a b))((a (a a))(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 199403/23865960. ------ 1. ==[ start ]==> (((a (a a))((a a) a))(((^a.a) a)(^b.b))) 2. ==[ alpha ]==> (((a (a a))((a a) a))(((^x.x) a)(^y.y))) 3. ==[ beta ]==> (((a (a a))((a a) a))(a (^y.y))) 4. ==[ alpha ]==> (((a (a a))((a a) a))(a (^x.x))) REDUCED to normal form. ------ 199404/23866041. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((b (^a.a)) a)) 2. ==[ alpha ]==> (((a b)((^x.x) a))((b (^y.y)) a)) 3. ==[ beta ]==> (((a b) a)((b (^y.y)) a)) 4. ==[ alpha ]==> (((a b) a)((b (^x.x)) a)) REDUCED to normal form. ------ 199405/23866068. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (^a.a)))(((a a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (^y.y)))(((a a)(a a)) b)) 3. ==[ beta ]==> (((a a)(a (^y.y)))(((a a)(a a)) b)) 4. ==[ alpha ]==> (((a a)(a (^x.x)))(((a a)(a a)) b)) REDUCED to normal form. ------ 199406/23866095. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(a a))(((^y.y) b) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(b c)) REDUCED to normal form. ------ 199407/23866212. ------ 1. ==[ start ]==> (((^a.(a a))(^a.b))((^b.(a a))(^a.b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.b))((^z.(a a))(^x1.b))) 3. ==[ beta ]==> (((^y.b)(^y.b))((^z.(a a))(^x1.b))) 4. ==[ alpha ]==> (((^x.b)(^y.b))((^z.(a a))(^x1.b))) 5. ==[ beta ]==> (b ((^z.(a a))(^x1.b))) 6. ==[ alpha ]==> (b ((^x.(a a))(^y.b))) 7. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 199408/23866356. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)(c ((^a.a) b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)(c ((^y.y) b))) 3. ==[ beta ]==> ((((a a)(^x.x)) b)(c b)) REDUCED to normal form. ------ 199409/23866464. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))(((^z.z) b)(a (^x1.x1)))) 3. ==[ beta ]==> ((a (^y.(a a)))(((^z.z) b)(a (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(a a)))(((^y.y) b)(a (^z.z)))) 5. ==[ beta ]==> ((a (^x.(a a)))(b (a (^z.z)))) 6. ==[ alpha ]==> ((a (^x.(a a)))(b (a (^y.y)))) REDUCED to normal form. ------ 199410/23866491. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((a (^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.b))((a (^y.(^z.z)))((^x1.x1) a))) 3. ==[ beta ]==> (((a (a a))(^x.b))((a (^y.(^z.z))) a)) REDUCED to normal form. ------ 199411/23866545. ------ 1. ==[ start ]==> ((((a a) a)(^b.(^a.a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))(^y1.y1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(((a a)(^z.z))(^x1.x1))) REDUCED to normal form. ------ 199412/23866572. ------ 1. ==[ start ]==> (((a b)(^a.(a a)))(((^a.a)(a a))((a a) a))) 2. ==[ alpha ]==> (((a b)(^x.(x x)))(((^y.y)(a a))((a a) a))) 3. ==[ beta ]==> (((a b)(^x.(x x)))((a a)((a a) a))) REDUCED to normal form. ------ 199413/23866599. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.a))((a b)(a b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.a))((a b)(a b))) 3. ==[ beta ]==> (((a a)(^y.a))((a b)(a b))) 4. ==[ alpha ]==> (((a a)(^x.a))((a b)(a b))) REDUCED to normal form. ------ 199414/23866626. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.(^a.a)))(((a a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a) a)(a a))) REDUCED to normal form. ------ 199415/23866797. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a) a))(((a a)(a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a) a))(((a a)(a a))(^z.z))) 3. ==[ beta ]==> (((^y.y)((a a) a))(((a a)(a a))(^z.z))) 4. ==[ alpha ]==> (((^x.x)((a a) a))(((a a)(a a))(^y.y))) 5. ==[ beta ]==> (((a a) a)(((a a)(a a))(^y.y))) 6. ==[ alpha ]==> (((a a) a)(((a a)(a a))(^x.x))) REDUCED to normal form. ------ 199416/23866824. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(^a.a)))(((^a.a) b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(^y.y)))(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(^y.y))(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> ((((a a) a)(^x.x))(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((((a a) a)(^x.x))(b (^y.(^z.z)))) REDUCED to normal form. ------ 199417/23866851. ------ 1. ==[ start ]==> (((a b)(a (a a)))((a (^a.(^a.a)))(^b.a))) 2. ==[ alpha ]==> (((a b)(a (a a)))((a (^x.(^y.y)))(^z.a))) REDUCED to normal form. ------ 199418/23866878. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((b a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((b a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)((^y.y) a))((b a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((b a)(^y.(y y)))) 5. ==[ beta ]==> (((a a) a)((b a)(^y.(y y)))) 6. ==[ alpha ]==> (((a a) a)((b a)(^x.(x x)))) REDUCED to normal form. ------ 199419/23866905. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (^a.a)))(((a a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (^y.y)))(((a a)(^z.z))(^x1.(^y1.y1)))) REDUCED to normal form. ------ 199420/23866959. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((a b)(^a.b))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a b)(^z.b))) REDUCED to normal form. ------ 199421/23866968. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((^a.b)(a b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.b)(a b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.b)(a b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.b)(a b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199422/23867049. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(a a)))((^a.(a a))(b a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(a a)))((^z.(z z))(b a))) 3. ==[ beta ]==> (((^y.(a a))(^y.(a a)))((^z.(z z))(b a))) 4. ==[ alpha ]==> (((^x.(a a))(^y.(a a)))((^z.(z z))(b a))) 5. ==[ beta ]==> ((a a)((^z.(z z))(b a))) 6. ==[ alpha ]==> ((a a)((^x.(x x))(b a))) 7. ==[ beta ]==> ((a a)((b a)(b a))) REDUCED to normal form. ------ 199423/23867130. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((^a.a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.x1)((a a)(a a)))) 3. ==[ beta ]==> (b ((^x1.x1)((a a)(a a)))) 4. ==[ alpha ]==> (b ((^x.x)((a a)(a a)))) 5. ==[ beta ]==> (b ((a a)(a a))) REDUCED to normal form. ------ 199424/23867292. ------ 1. ==[ start ]==> (((^a.(^a.a))(b a))((^b.(a a))(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(b a))((^z.(a a))(^x1.a))) 3. ==[ beta ]==> ((^y.y)((^z.(a a))(^x1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(^z.a))) 5. ==[ beta ]==> ((^y.(a a))(^z.a)) 6. ==[ alpha ]==> ((^x.(a a))(^y.a)) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 199425/23867427. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(^z.z)))((^x1.a)(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (b ((^x1.a)(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (b ((^x.a)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 199426/23867436. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))(c (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(c (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 199427/23867463. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))(b ((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))(b ((^z.z) b))) 3. ==[ beta ]==> (((a a)(^y.(y y)))(b ((^z.z) b))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))(b ((^y.y) b))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(b b)) REDUCED to normal form. ------ 199428/23867490. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(a ((a a)(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(a ((a a)(a a)))) REDUCED to normal form. ------ 199429/23867544. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((a (^x1.(^y1.y1)))(a (^z1.z1)))) REDUCED to normal form. ------ 199430/23867850. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a a))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(a a))(b (^x1.x1))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a a))(b (^z.z))) REDUCED to normal form. ------ 199431/23867877. ------ 1. ==[ start ]==> ((a ((^a.a) b))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x) b))((a (^y.(^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a b)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a b)((a (^x.(^y.y)))(^z.(^x1.x1)))) REDUCED to normal form. ------ 199432/23867886. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((^a.(^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((^z.(^x1.(^y1.y1)))(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.(^x1.x1)))(a (^y1.y1)))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(a (^y1.y1))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(a (^x1.x1))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199433/23868048. ------ 1. ==[ start ]==> (((^a.b)(^c.a))((^b.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))((^z.z)(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199434/23868156. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.z1)((^x2.x2) b))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.z1)((^x2.x2) b))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199435/23868210. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.(^y1.y1)))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 5. ==[ beta ]==> (b ((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (b ((^x.(^y.(^z.z)))(^x1.(^y1.y1)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 199436/23868291. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(^a.a)))((^b.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^y.y))((a a)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))((a a)(^y.y)))((^z.(a a))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(^x.x))((a a)(^y.y)))(a a)) REDUCED to normal form. ------ 199437/23868372. ------ 1. ==[ start ]==> (((^a.b)((a a) a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a) a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199438/23868480. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199439/23868489. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(a ((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^y1.y1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a b)) REDUCED to normal form. ------ 199440/23868516. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((a (^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((a (^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((b (^y.y))((a (^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((b (^x.x))((a (^y.(^z.z)))(a a))) REDUCED to normal form. ------ 199441/23868822. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))((a (^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))((a (^x1.(^y1.y1)))(^z1.z1))) REDUCED to normal form. ------ 199442/23868849. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((b (a a))((b a)(^y.(^z.z)))) 4. ==[ alpha ]==> ((b (a a))((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 199443/23868876. ------ 1. ==[ start ]==> ((a ((a a)(a a)))(((a a)(^a.a))(^b.a))) 2. ==[ alpha ]==> ((a ((a a)(a a)))(((a a)(^x.x))(^y.a))) REDUCED to normal form. ------ 199444/23868912. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))((^b.(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.y)((^x1.(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.x)((^y.(a a))(a (a a)))) 5. ==[ beta ]==> ((^y.(a a))(a (a a))) 6. ==[ alpha ]==> ((^x.(a a))(a (a a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 199445/23869047. ------ 1. ==[ start ]==> (((^a.b)(^a.b))((^b.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))((^z.a)((a a)(^x1.x1)))) 3. ==[ beta ]==> (b ((^z.a)((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b ((^x.a)((a a)(^y.y)))) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 199446/23869236. ------ 1. ==[ start ]==> (((^a.a)((a a)(a a)))((^a.b)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(a a)))((^y.b)(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a a)(a a))((^y.b)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a a)(a a))((^x.b)(^y.(^z.z)))) 5. ==[ beta ]==> (((a a)(a a)) b) REDUCED to normal form. ------ 199447/23869263. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) b))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) b))((^x1.a)(^y1.a))) 3. ==[ beta ]==> ((^y.y)((^x1.a)(^y1.a))) 4. ==[ alpha ]==> ((^x.x)((^y.a)(^z.a))) 5. ==[ beta ]==> ((^y.a)(^z.a)) 6. ==[ alpha ]==> ((^x.a)(^y.a)) 7. ==[ beta ]==> a REDUCED to normal form. ------ 199448/23869317. ------ 1. ==[ start ]==> (((^a.(a a))(b a))((^a.(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(b a))((^y.(y y))(^z.(a a)))) 3. ==[ beta ]==> (((b a)(b a))((^y.(y y))(^z.(a a)))) 4. ==[ alpha ]==> (((b a)(b a))((^x.(x x))(^y.(a a)))) 5. ==[ beta ]==> (((b a)(b a))((^y.(a a))(^y.(a a)))) 6. ==[ alpha ]==> (((b a)(b a))((^x.(a a))(^y.(a a)))) 7. ==[ beta ]==> (((b a)(b a))(a a)) REDUCED to normal form. ------ 199449/23869380. ------ 1. ==[ start ]==> ((((a a) a)(^b.(a a)))(b (b a))) 2. ==[ alpha ]==> ((((a a) a)(^x.(a a)))(b (b a))) REDUCED to normal form. ------ 199450/23869398. ------ 1. ==[ start ]==> (((^a.b)(a b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a b))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (b ((^y.y)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (b ((^x.x)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199451/23869407. ------ 1. ==[ start ]==> (((a b)(^a.b))(a (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.b))(a (a (^y.(^z.z))))) REDUCED to normal form. ------ 199452/23869461. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(^a.a)))(((a a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(^z.z)))(((a a)(^x1.x1))(a (^y1.y1)))) REDUCED to normal form. ------ 199453/23869515. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.a))((a b)(a (a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.a))((a b)(a (a a)))) REDUCED to normal form. ------ 199454/23869542. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(^a.a)))(((a a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((a a) a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((a a) a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a) a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(((a a) a)(^x1.x1))) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(((a a) a)(^z.z))) REDUCED to normal form. ------ 199455/23869569. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.a))(((^a.a)(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.x))(((^y.y)(^z.z))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.x))((^z.z)((a a) a))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.x))((^y.y)((a a) a))) 5. ==[ beta ]==> ((((a a)(a a))(^x.x))((a a) a)) REDUCED to normal form. ------ 199456/23869713. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))((b a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))((b a)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))((b a)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((b a)(^z.z))) 5. ==[ beta ]==> (((a a)(^y.y))((b a)(^z.z))) 6. ==[ alpha ]==> (((a a)(^x.x))((b a)(^y.y))) REDUCED to normal form. ------ 199457/23869740. ------ 1. ==[ start ]==> ((((a a) a)((^a.a)(a a)))(((a a)(^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)((^x.x)(a a)))(((a a)(^y.y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a) a)(a a))(((a a)(^y.y))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a) a)(a a))(((a a)(^x.x))(^y.(^z.z)))) REDUCED to normal form. ------ 199458/23869767. ------ 1. ==[ start ]==> (((a b)(a b))(((^a.a)(a a))(^b.a))) 2. ==[ alpha ]==> (((a b)(a b))(((^x.x)(a a))(^y.a))) 3. ==[ beta ]==> (((a b)(a b))((a a)(^y.a))) 4. ==[ alpha ]==> (((a b)(a b))((a a)(^x.a))) REDUCED to normal form. ------ 199459/23869794. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((a b)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((a b)(^y.(y y)))) 3. ==[ beta ]==> (((a a)((a a) a))((a b)(^y.(y y)))) 4. ==[ alpha ]==> (((a a)((a a) a))((a b)(^x.(x x)))) REDUCED to normal form. ------ 199460/23869821. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))(((a a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))(((a a) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 199461/23869875. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((a (a a))(^a.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((a (a a))(^x1.b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((a (a a))(^x1.b))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((a (a a))(^z.b))) REDUCED to normal form. ------ 199462/23869902. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))(((^a.a) a)(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))(((^z.z) a)(^x1.(a a)))) 3. ==[ beta ]==> ((b (a (^y.y)))(((^z.z) a)(^x1.(a a)))) 4. ==[ alpha ]==> ((b (a (^x.x)))(((^y.y) a)(^z.(a a)))) 5. ==[ beta ]==> ((b (a (^x.x)))(a (^z.(a a)))) 6. ==[ alpha ]==> ((b (a (^x.x)))(a (^y.(a a)))) REDUCED to normal form. ------ 199463/23870046. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.(^a.a))))((^b.(a a))(^b.a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.a))) 3. ==[ beta ]==> (((^y.(^z.(^x1.x1)))(^y.(^z.(^x1.x1))))((^y1.(a a))(^z1.a))) 4. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.(^z1.z1))))((^x2.(a a))(^y2.a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x2.(a a))(^y2.a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199464/23870127. ------ 1. ==[ start ]==> (((^a.b)(^b.(a a)))((^b.(^a.a))(^c.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(a a)))((^z.(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (b ((^z.(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199465/23870271. ------ 1. ==[ start ]==> ((((^a.a) b) c)(((a a)(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(((a a)(^y.y))(a a))) 3. ==[ beta ]==> ((b c)(((a a)(^y.y))(a a))) 4. ==[ alpha ]==> ((b c)(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 199466/23870298. ------ 1. ==[ start ]==> ((((a a)(a a)) b)(((^a.a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a)) b)(((^x.x)(a a))(a (^y.y)))) 3. ==[ beta ]==> ((((a a)(a a)) b)((a a)(a (^y.y)))) 4. ==[ alpha ]==> ((((a a)(a a)) b)((a a)(a (^x.x)))) REDUCED to normal form. ------ 199467/23870406. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.b))((a (a a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((a (a a))((a a) a))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))((a a) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))((a a) a))) REDUCED to normal form. ------ 199468/23870433. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.(^a.a))))(((^a.a) a)(a b))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.(^z.z))))(((^x1.x1) a)(a b))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.(^z.z))))(a (a b))) REDUCED to normal form. ------ 199469/23870739. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((a a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((a a)(^y.(^z.z)))) REDUCED to normal form. ------ 199470/23870766. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(((a a)(^a.a)) a)) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(((a a)(^y.y)) a)) REDUCED to normal form. ------ 199471/23870793. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))(((^a.a)(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))(((^z.z)(a a)) b)) 3. ==[ beta ]==> ((a ((^y.y) b))(((^z.z)(a a)) b)) 4. ==[ alpha ]==> ((a ((^x.x) b))(((^y.y)(a a)) b)) 5. ==[ beta ]==> ((a b)(((^y.y)(a a)) b)) 6. ==[ alpha ]==> ((a b)(((^x.x)(a a)) b)) 7. ==[ beta ]==> ((a b)((a a) b)) REDUCED to normal form. ------ 199472/23870820. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((a b) c)) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((a b) c)) REDUCED to normal form. ------ 199473/23871036. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))((^b.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))((^z.(a a)) b)) 3. ==[ beta ]==> ((b ((^y.y) a))((^z.(a a)) b)) 4. ==[ alpha ]==> ((b ((^x.x) a))((^y.(a a)) b)) 5. ==[ beta ]==> ((b a)((^y.(a a)) b)) 6. ==[ alpha ]==> ((b a)((^x.(a a)) b)) 7. ==[ beta ]==> ((b a)(a a)) REDUCED to normal form. ------ 199474/23871063. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((^a.b) c)) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((^y.b) c)) 3. ==[ beta ]==> ((((a a)(a a))(a (^x.x))) b) REDUCED to normal form. ------ 199475/23871207. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))(b (^b.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))(b (^z.(a a)))) 3. ==[ beta ]==> (((^y.y)(^y.y))(b (^z.(a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(a a)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(a a)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(a a)))) 7. ==[ beta ]==> (b (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 199476/23871288. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((^a.b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((^x1.b)(a (^y1.y1)))) 3. ==[ beta ]==> (b ((^x1.b)(a (^y1.y1)))) 4. ==[ alpha ]==> (b ((^x.b)(a (^y.y)))) 5. ==[ beta ]==> (b b) REDUCED to normal form. ------ 199477/23871396. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))((^b.a)((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((^z1.a)((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^z1.a)((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.a)((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199478/23871558. ------ 1. ==[ start ]==> (((^a.(^a.a))(b (^a.a)))((^b.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(b (^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)((^x1.(^y1.y1))(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(^x1.(x1 x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199479/23871612. ------ 1. ==[ start ]==> (((^a.(a a))((^a.a) b))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((^x.(x x))((^y.y) b))((^z.a)(^x1.a))) 3. ==[ beta ]==> ((((^y.y) b)((^y.y) b))((^z.a)(^x1.a))) 4. ==[ alpha ]==> ((((^x.x) b)((^y.y) b))((^z.a)(^x1.a))) 5. ==[ beta ]==> ((b ((^y.y) b))((^z.a)(^x1.a))) 6. ==[ alpha ]==> ((b ((^x.x) b))((^y.a)(^z.a))) 7. ==[ beta ]==> ((b b)((^y.a)(^z.a))) 8. ==[ alpha ]==> ((b b)((^x.a)(^y.a))) 9. ==[ beta ]==> ((b b) a) REDUCED to normal form. ------ 199480/23871621. ------ 1. ==[ start ]==> (((a (a a))(^b.b))(c ((a a) a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))(c ((a a) a))) REDUCED to normal form. ------ 199481/23871648. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))(b (a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))(b (a b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))(b (a b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(b (a b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(b (a b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))(b (a b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199482/23871702. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((a b)(a a))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(a a))) REDUCED to normal form. ------ 199483/23871729. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))(((a a) a)(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))(((a a) a)(a (^z.z)))) 3. ==[ beta ]==> (((a a)(^y.(a a)))(((a a) a)(a (^z.z)))) 4. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a) a)(a (^y.y)))) REDUCED to normal form. ------ 199484/23871756. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))(((^a.a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))(((^z.z)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1)((^y1.y1) a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z)((^x1.x1) a))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.b))((^x1.x1) a)) 6. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.z) a)) 7. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 199485/23871810. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(((^y1.y1) a)((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^z1.z1)(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a ((^y1.y1)(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^z1.z1))) 6. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(a (^y1.y1))) REDUCED to normal form. ------ 199486/23871837. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))((a (^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))((a (^z.z))((a a) a))) 3. ==[ beta ]==> ((b (^y.(y y)))((a (^z.z))((a a) a))) 4. ==[ alpha ]==> ((b (^x.(x x)))((a (^y.y))((a a) a))) REDUCED to normal form. ------ 199487/23871864. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))((a a)(a b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))((a a)(a b))) REDUCED to normal form. ------ 199488/23871954. ------ 1. ==[ start ]==> (((a a)((^a.(^a.a)) a))(((^a.a)(^a.a))(^b.a))) 2. ==[ alpha ]==> (((a a)((^x.(^y.y)) a))(((^z.z)(^x1.x1))(^y1.a))) 3. ==[ beta ]==> (((a a)(^y.y))(((^z.z)(^x1.x1))(^y1.a))) 4. ==[ alpha ]==> (((a a)(^x.x))(((^y.y)(^z.z))(^x1.a))) 5. ==[ beta ]==> (((a a)(^x.x))((^z.z)(^x1.a))) 6. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.a))) 7. ==[ beta ]==> (((a a)(^x.x))(^z.a)) 8. ==[ alpha ]==> (((a a)(^x.x))(^y.a)) REDUCED to normal form. ------ 199489/23871981. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((a (a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((a (a a))(^z.(z z)))) REDUCED to normal form. ------ 199490/23872008. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))(((^a.a) a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))(((^y.y) a)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((a ((a a)(a a)))(((^y.y) a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))(((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> ((a ((a a)(a a)))(a (^y.(^z.z)))) 6. ==[ alpha ]==> ((a ((a a)(a a)))(a (^x.(^y.y)))) REDUCED to normal form. ------ 199491/23872035. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((a (^a.a))(^c.a))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((a (^y.y))(^z.a))) 3. ==[ beta ]==> (((a (a a)) b)((a (^y.y))(^z.a))) 4. ==[ alpha ]==> (((a (a a)) b)((a (^x.x))(^y.a))) REDUCED to normal form. ------ 199492/23872062. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((a a)(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((a a)(^y1.b))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((a a)(^y1.b))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((a a)(^x1.b))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((a a)(^x1.b))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((a a)(^z.b))) REDUCED to normal form. ------ 199493/23872089. ------ 1. ==[ start ]==> ((((a a) a)(b a))((a b) a)) REDUCED to normal form. ------ 199494/23872116. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))(((a a) a) b)) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))(((a a) a) b)) REDUCED to normal form. ------ 199495/23872278. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.b) a)) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.b) a)) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.b) a)) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.b) a)) 5. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 199496/23872332. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((a a)((^y.(^z.z)) c)) 6. ==[ alpha ]==> ((a a)((^x.(^y.y)) c)) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 199497/23872350. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((a (a a))((^z.z) a))) 3. ==[ beta ]==> ((a (^y.y))((a (a a))((^z.z) a))) 4. ==[ alpha ]==> ((a (^x.x))((a (a a))((^y.y) a))) 5. ==[ beta ]==> ((a (^x.x))((a (a a)) a)) REDUCED to normal form. ------ 199498/23872755. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)(b ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((^y.y) b)(b ((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((^x.x) b)(b ((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (b ((^y.y)(^z.z)))) 6. ==[ alpha ]==> (b (b ((^x.x)(^y.y)))) 7. ==[ beta ]==> (b (b (^y.y))) 8. ==[ alpha ]==> (b (b (^x.x))) REDUCED to normal form. ------ 199499/23872782. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(a ((a a) a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(a ((a a) a))) REDUCED to normal form. ------ 199500/23872809. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(((^z.z)(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^x.(x (^y.y))))((^x1.x1)(a a))) 4. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))((^z.z)(a a))) 5. ==[ beta ]==> (((a a)(^x.(x (^y.y))))(a a)) REDUCED to normal form. ------ 199501/23872917. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))((a a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((a a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a a)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a a)((^y.y)(^z.z))) 8. ==[ alpha ]==> ((a a)((^x.x)(^y.y))) 9. ==[ beta ]==> ((a a)(^y.y)) 10. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 199502/23872962. ------ 1. ==[ start ]==> (((^a.b)(b a))((^b.(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.b)(b a))((^y.(^z.z))(a a))) 3. ==[ beta ]==> (b ((^y.(^z.z))(a a))) 4. ==[ alpha ]==> (b ((^x.(^y.y))(a a))) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199503/23873025. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(c d)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(c d)) REDUCED to normal form. ------ 199504/23873070. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((^a.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((^x1.x1)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199505/23873187. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))(b (a (a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))(b (a (a a)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(b (a (a a)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(b (a (a a)))) 5. ==[ beta ]==> ((^y.(^z.z))(b (a (a a)))) 6. ==[ alpha ]==> ((^x.(^y.y))(b (a (a a)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199506/23873205. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^y.y))((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199507/23873214. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a ((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(a (^x1.x1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(a (^z.z))) REDUCED to normal form. ------ 199508/23873250. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((^a.(a a)) b)) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((^y.(y y)) b)) 3. ==[ beta ]==> (((a a)(a (a (^x.x))))(b b)) REDUCED to normal form. ------ 199509/23873277. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))((^b.a) c)) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))((^x1.a) c)) 3. ==[ beta ]==> (((a (^x.x))(^z.z))((^x1.a) c)) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a) c)) 5. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 199510/23873358. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))((a (a a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))((a (a a))(^x1.x1))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))((a (a a))(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (a a))(^z.z))) 5. ==[ beta ]==> (((^y.y) b)((a (a a))(^z.z))) 6. ==[ alpha ]==> (((^x.x) b)((a (a a))(^y.y))) 7. ==[ beta ]==> (b ((a (a a))(^y.y))) 8. ==[ alpha ]==> (b ((a (a a))(^x.x))) REDUCED to normal form. ------ 199511/23873385. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))(((^a.a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))(a (^z.(^x1.x1)))) REDUCED to normal form. ------ 199512/23873412. ------ 1. ==[ start ]==> (((a b)(b a))((a (^a.a))(^b.a))) 2. ==[ alpha ]==> (((a b)(b a))((a (^x.x))(^y.a))) REDUCED to normal form. ------ 199513/23873439. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((a a)(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((a a)(^z.(z z)))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((a a)(^z.(z z)))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((a a)(^y.(y y)))) REDUCED to normal form. ------ 199514/23873466. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((a (a a)) a)) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((a (a a)) a)) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((a (a a)) a)) REDUCED to normal form. ------ 199515/23873574. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.(a a)) a)) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.(x x)) a)) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(a a)) REDUCED to normal form. ------ 199516/23873646. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((a a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((a a)((^z.z) a))) 3. ==[ beta ]==> ((b (^y.y))((a a)((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.x))((a a)((^y.y) a))) 5. ==[ beta ]==> ((b (^x.x))((a a) a)) REDUCED to normal form. ------ 199517/23873682. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(((^x1.x1) a)(^y1.y1))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z) a)(^x1.x1))) 5. ==[ beta ]==> ((a (^x.(^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.z))) REDUCED to normal form. ------ 199518/23873691. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))((^b.a)(a a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.a)(a a))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.a)(a a))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.a)(a a))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199519/23873718. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((^a.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((^y1.(^z1.z1))(a (^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1))(a (^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199520/23873853. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(c (^a.a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(c (^y1.y1))) 3. ==[ beta ]==> (b (c (^y1.y1))) 4. ==[ alpha ]==> (b (c (^x.x))) REDUCED to normal form. ------ 199521/23873961. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((^a.a)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((^y1.y1)(a (^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((^y1.y1)(a (^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199522/23874096. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))((^a.a)(a a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))((^y1.y1)(a a))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))((^y1.y1)(a a))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((^x1.x1)(a a))) 5. ==[ beta ]==> ((^y.y)((^x1.x1)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(a a))) 7. ==[ beta ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 199523/23874105. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(a b)) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(a b)) REDUCED to normal form. ------ 199524/23874132. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)(a (a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(a (a a))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(a (a a))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(a (a a))) 5. ==[ beta ]==> ((^y.y)(a (a a))) 6. ==[ alpha ]==> ((^x.x)(a (a a))) 7. ==[ beta ]==> (a (a a)) REDUCED to normal form. ------ 199525/23874150. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))(a (^y1.y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (^y1.y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (^x1.x1))) 5. ==[ beta ]==> ((^y.(^z.z))(a (^x1.x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (^z.z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199526/23874159. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a))))(a a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(a a)) REDUCED to normal form. ------ 199527/23886126. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a)))) b) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z)))) b) REDUCED to normal form. ------ 199528/23886150. ------ 1. ==[ start ]==> ((^a.(^a.a))((a a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199529/23886162. ------ 1. ==[ start ]==> (((^a.a) a)(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a (^y.((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a (^x.((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a (^x.(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199530/23886621. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 199531/23886636. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 199532/23886735. ------ 1. ==[ start ]==> ((^a.(a (a a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((^x.(x (x x)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))((((a a)(a a))(a (a a)))(((a a)(a a))(a (a a))))) REDUCED to normal form. ------ 199533/23887953. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(^a.(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(^y.(y (y (^z.z))))) 3. ==[ beta ]==> (((a (a a)) a)(^y.(y (y (^z.z))))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.(x (x (^y.y))))) REDUCED to normal form. ------ 199534/23888031. ------ 1. ==[ start ]==> ((^a.(a b))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x b))(((a a)(a a))((^y.y) a))) 3. ==[ beta ]==> ((((a a)(a a))((^y.y) a)) b) 4. ==[ alpha ]==> ((((a a)(a a))((^x.x) a)) b) 5. ==[ beta ]==> ((((a a)(a a)) a) b) REDUCED to normal form. ------ 199535/23888376. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(^z.(^x1.(x1 (^y1.y1))))) REDUCED to normal form. ------ 199536/23888418. ------ 1. ==[ start ]==> ((^a.(^b.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(x x)))((b (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(((b (^z.z))(^x1.(^y1.y1)))((b (^z.z))(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (^x.(((b (^y.y))(^z.(^x1.x1)))((b (^y1.y1))(^z1.(^x2.x2))))) REDUCED to normal form. ------ 199537/23889195. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(^a.((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.((^x1.(^y1.y1)) z))) 3. ==[ eta ]==> ((((^x.x)(^y.y))(a (a a)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(^z.(^x1.x1))) 5. ==[ beta ]==> (((^y.y)(a (a a)))(^z.(^x1.x1))) 6. ==[ alpha ]==> (((^x.x)(a (a a)))(^y.(^z.z))) 7. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 8. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 199538/23889300. ------ 1. ==[ start ]==> ((^a.((a a)(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((^x.((x x)(^y.y)))((a (^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((((a (^z.(^x1.x1)))(a (a a)))((a (^z.(^x1.x1)))(a (a a))))(^y.y)) 4. ==[ alpha ]==> ((((a (^x.(^y.y)))(a (a a)))((a (^z.(^x1.x1)))(a (a a))))(^y1.y1)) REDUCED to normal form. ------ 199539/23890707. ------ 1. ==[ start ]==> (((a (a a))(a b))(^c.((a a)(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(^x.((a a)(a a)))) REDUCED to normal form. ------ 199540/23891067. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))(^c.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.(^y1.(a a)))) 3. ==[ beta ]==> (b (^x1.(^y1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 199541/23891427. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))(^b.(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(^x1.(a a)))) REDUCED to normal form. ------ 199542/23891496. ------ 1. ==[ start ]==> ((^a.(^b.b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.(^y1.y1))) c)) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199543/23891778. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^a.(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.(^y1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199544/23892102. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^b.((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.((^x1.x1) z))) 3. ==[ eta ]==> (((a (^x.(^y.y))) b)(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.z)) REDUCED to normal form. ------ 199545/23892426. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))(^b.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.(^z1.z1))) REDUCED to normal form. ------ 199546/23893344. ------ 1. ==[ start ]==> (((a b)(^a.b))(^b.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 199547/23893623. ------ 1. ==[ start ]==> (((a (a a))(b a))(^c.(b a))) 2. ==[ alpha ]==> (((a (a a))(b a))(^x.(b a))) REDUCED to normal form. ------ 199548/23894946. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^a.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.((z z)(^x1.x1)))) REDUCED to normal form. ------ 199549/23895051. ------ 1. ==[ start ]==> ((^a.((^a.(^a.a)) a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((^x.((^y.(^z.z)) x))(((^x1.x1)(^y1.y1))(a (a a)))) 3. ==[ eta ]==> ((^y.(^z.z))(((^x1.x1)(^y1.y1))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(^x1.x1))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199550/23895870. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))(((a a) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 199551/23896215. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^a.(a b))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.(y b))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(y b))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(x b))) REDUCED to normal form. ------ 199552/23896293. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((a (a a))((^z.z) a))) 3. ==[ beta ]==> (((a (a a))((^z.z) a))(((a (a a))((^z.z) a))(^y.y))) 4. ==[ alpha ]==> (((a (a a))((^x.x) a))(((a (a a))((^y.y) a))(^z.z))) 5. ==[ beta ]==> (((a (a a)) a)(((a (a a))((^y.y) a))(^z.z))) 6. ==[ alpha ]==> (((a (a a)) a)(((a (a a))((^x.x) a))(^y.y))) 7. ==[ beta ]==> (((a (a a)) a)(((a (a a)) a)(^y.y))) 8. ==[ alpha ]==> (((a (a a)) a)(((a (a a)) a)(^x.x))) REDUCED to normal form. ------ 199553/23896719. ------ 1. ==[ start ]==> (((a (a (^a.a))) a)(^b.(^c.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) a)(^y.(^z.a))) REDUCED to normal form. ------ 199554/23897151. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 199555/23897166. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.(^z1.z1)) a)) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199556/23897511. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^a.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(x (x x)))) REDUCED to normal form. ------ 199557/23897898. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(^c.(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.(^z.z))(^y1.(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199558/23898042. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^b.(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.(a a))) REDUCED to normal form. ------ 199559/23898069. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)(^b.(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)(^x1.(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199560/23898087. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))(^y1.a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.a)) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.a)) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199561/23898096. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a))))(^a.(^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 199562/23898126. ------ 1. ==[ start ]==> ((a (^a.a))((a a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.x))((a a)(^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 199563/23898135. ------ 1. ==[ start ]==> (((^a.a) a)((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (a ((^y.y)((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (a ((^x.x)((^y.y)(^z.(^x1.x1))))) 5. ==[ beta ]==> (a ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (a (^y.(^z.z))) 8. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 199564/23898153. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((^x.x)(^y.y))(((^z.z)(^x1.(^y1.y1))) a)) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.(^y1.y1))) a)) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.(^x1.x1))) a)) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1))) a) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z))) a) 7. ==[ beta ]==> ((^y.(^z.z)) a) 8. ==[ alpha ]==> ((^x.(^y.y)) a) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199565/23898162. ------ 1. ==[ start ]==> (((a a) a)((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 4. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 199566/23898180. ------ 1. ==[ start ]==> (((^a.a)(a a))((a (a (^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)(a a))((a (a (^y.y))) b)) 3. ==[ beta ]==> ((a a)((a (a (^y.y))) b)) 4. ==[ alpha ]==> ((a a)((a (a (^x.x))) b)) REDUCED to normal form. ------ 199567/23898189. ------ 1. ==[ start ]==> (((a a)(^a.a))((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(y (^z.z)))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a a)(^x.x))((^x1.(^y1.y1))(^z.z))) 4. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.y)) REDUCED to normal form. ------ 199568/23898270. ------ 1. ==[ start ]==> (((a a) b)((^c.(a a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a a) b)((^x.(a a))(^y.(^z.z)))) 3. ==[ beta ]==> (((a a) b)(a a)) REDUCED to normal form. ------ 199569/23898297. ------ 1. ==[ start ]==> (((a (^a.a)) a)((^b.b)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x)) a)((^y.y)(^z.a))) 3. ==[ beta ]==> (((a (^x.x)) a)(^z.a)) 4. ==[ alpha ]==> (((a (^x.x)) a)(^y.a)) REDUCED to normal form. ------ 199570/23898324. ------ 1. ==[ start ]==> (((a a)(^a.(^a.a)))((^a.(^a.(^a.a)))(^a.b))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))(^z1.b))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 199571/23898486. ------ 1. ==[ start ]==> (((a (^a.a)) b)((^b.(^a.a))(^c.(a a)))) 2. ==[ alpha ]==> (((a (^x.x)) b)((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(^z.z)) 4. ==[ alpha ]==> (((a (^x.x)) b)(^y.y)) REDUCED to normal form. ------ 199572/23898567. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.a)))((^a.(^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 (^x2.x2))))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 199573/23898594. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.a))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))((^z.z)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))((^y.y)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((a (^x.x))(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 199574/23898612. ------ 1. ==[ start ]==> ((a (^a.(a a)))((^b.(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((a (^x.(x x)))((^y.(^z.(^x1.x1))) a)) 3. ==[ beta ]==> ((a (^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 199575/23898630. ------ 1. ==[ start ]==> (((a a)((^a.a) a))((a (a (^a.a)))(a a))) 2. ==[ alpha ]==> (((a a)((^x.x) a))((a (a (^y.y)))(a a))) 3. ==[ beta ]==> (((a a) a)((a (a (^y.y)))(a a))) 4. ==[ alpha ]==> (((a a) a)((a (a (^x.x)))(a a))) REDUCED to normal form. ------ 199576/23898657. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.a)))(((^a.(^a.a)) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(((^z.(^x1.x1)) a)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.y)))((^x1.x1)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))((^z.z)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(a (^y.y)))(a (^x1.x1))) 6. ==[ alpha ]==> (((a (^x.x))(a (^y.y)))(a (^z.z))) REDUCED to normal form. ------ 199577/23898684. ------ 1. ==[ start ]==> ((((^a.a) a)(a a))((b (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a a))((b (^y.y))((^z.z) a))) 3. ==[ beta ]==> ((a (a a))((b (^y.y))((^z.z) a))) 4. ==[ alpha ]==> ((a (a a))((b (^x.x))((^y.y) a))) 5. ==[ beta ]==> ((a (a a))((b (^x.x)) a)) REDUCED to normal form. ------ 199578/23898711. ------ 1. ==[ start ]==> ((a (a (a a)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 199579/23898954. ------ 1. ==[ start ]==> (((a a)(a (a a)))((a (a a))((a a)(a a)))) REDUCED to normal form. ------ 199580/23898981. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) a))(((^a.a) a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) a))(((^z.z) a)(b (^x1.x1)))) 3. ==[ beta ]==> (((a (^x.x)) a)(((^z.z) a)(b (^x1.x1)))) 4. ==[ alpha ]==> (((a (^x.x)) a)(((^y.y) a)(b (^z.z)))) 5. ==[ beta ]==> (((a (^x.x)) a)(a (b (^z.z)))) 6. ==[ alpha ]==> (((a (^x.x)) a)(a (b (^y.y)))) REDUCED to normal form. ------ 199581/23899008. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.a)))((a (^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 3. ==[ beta ]==> ((a (a (^y.y)))((a (^z.z))((^x1.(^y1.y1)) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))((^z.(^x1.x1)) a))) 5. ==[ beta ]==> ((a (a (^x.x)))((a (^y.y))(^x1.x1))) 6. ==[ alpha ]==> ((a (a (^x.x)))((a (^y.y))(^z.z))) REDUCED to normal form. ------ 199582/23899026. ------ 1. ==[ start ]==> (((^a.(a a)) b)(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.(x x)) b)(b (^y.(y (^z.z))))) 3. ==[ beta ]==> ((b b)(b (^y.(y (^z.z))))) 4. ==[ alpha ]==> ((b b)(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 199583/23899035. ------ 1. ==[ start ]==> (((a (a a))(a a))((a a)(a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))((a a)(a (a (^x.x))))) REDUCED to normal form. ------ 199584/23899071. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))((a (a (^a.a)))(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((a (a (^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a (^x1.x1)))(^y1.y1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a (^z.z)))(^x1.x1))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199585/23899098. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a a)))(((^a.(^a.a)) a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z z)))(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)(((^x1.(^y1.y1)) a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a)(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.(^z.z)) a)(^x1.(^y1.y1))) 6. ==[ alpha ]==> (((^x.(^y.y)) a)(^z.(^x1.x1))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 9. ==[ beta ]==> (^y.(^z.z)) 10. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199586/23899152. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(^a.a)))(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((a a)(a a))(^x1.(x1 x1)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((a a)(a a))(^y1.(y1 y1)))) 5. ==[ beta ]==> ((^y.y)(((a a)(a a))(^y1.(y1 y1)))) 6. ==[ alpha ]==> ((^x.x)(((a a)(a a))(^y.(y y)))) 7. ==[ beta ]==> (((a a)(a a))(^y.(y y))) 8. ==[ alpha ]==> (((a a)(a a))(^x.(x x))) REDUCED to normal form. ------ 199587/23899161. ------ 1. ==[ start ]==> (((a (a a)) b)((^c.(a a))(a (a a)))) 2. ==[ alpha ]==> (((a (a a)) b)((^x.(a a))(a (a a)))) 3. ==[ beta ]==> (((a (a a)) b)(a a)) REDUCED to normal form. ------ 199588/23899188. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)((^b.b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)((^z.z)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.z)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.y)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.y)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.x)((^y.y)(^z.z)))) 7. ==[ beta ]==> (a ((^y.y)(^z.z))) 8. ==[ alpha ]==> (a ((^x.x)(^y.y))) 9. ==[ beta ]==> (a (^y.y)) 10. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 199589/23899215. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((^a.(^a.(^a.a)))((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.(^y1.y1)))((a a) a))) 3. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 199590/23899233. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a a)))((b a)(^z.b))) 3. ==[ beta ]==> ((^y.y)((b a)(^z.b))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.b))) 5. ==[ beta ]==> ((b a)(^y.b)) 6. ==[ alpha ]==> ((b a)(^x.b)) REDUCED to normal form. ------ 199591/23899269. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))((^c.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 3. ==[ beta ]==> ((a (^y.a))((^z.(^x1.x1))((^y1.y1)(a a)))) 4. ==[ alpha ]==> ((a (^x.a))((^y.(^z.z))((^x1.x1)(a a)))) 5. ==[ beta ]==> ((a (^x.a))(^z.z)) 6. ==[ alpha ]==> ((a (^x.a))(^y.y)) REDUCED to normal form. ------ 199592/23899296. ------ 1. ==[ start ]==> (((a (a a))(^a.(^a.a)))((^b.(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(^y.y)))((^z.(a a))((a a)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a))(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 199593/23899323. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.a))((^a.b)(b a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))((^x1.b)(b a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(b a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(b a))) 5. ==[ beta ]==> ((^y.y)((^z.b)(b a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(b a))) 7. ==[ beta ]==> ((^y.b)(b a)) 8. ==[ alpha ]==> ((^x.b)(b a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 199594/23899530. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(^a.a)))(((^a.(^a.a)) a) b)) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.(^z1.z1)) a) b)) 3. ==[ beta ]==> ((^y.y)(((^y1.(^z1.z1)) a) b)) 4. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) a) b)) 5. ==[ beta ]==> (((^y.(^z.z)) a) b) 6. ==[ alpha ]==> (((^x.(^y.y)) a) b) 7. ==[ beta ]==> ((^y.y) b) 8. ==[ alpha ]==> ((^x.x) b) 9. ==[ beta ]==> b REDUCED to normal form. ------ 199595/23899620. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) b)((^b.b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) b)((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.(^x1.x1)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 199596/23899701. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(^a.a)))((^c.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(a a)))) 3. ==[ beta ]==> (((a (^x.x))(^y.(^z.z)))(^y1.y1)) 4. ==[ alpha ]==> (((a (^x.x))(^y.(^z.z)))(^x1.x1)) REDUCED to normal form. ------ 199597/23899728. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(a a)))((^b.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((a (^y.(y y)))((^z.(a a))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))((^y.(a a))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^x.(x x)))(a a)) REDUCED to normal form. ------ 199598/23899809. ------ 1. ==[ start ]==> ((((a a) a)(^a.a))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.x))((^y.(^z.z))(^x1.x1))) 3. ==[ beta ]==> ((((a a) a)(^x.x))(^z.z)) 4. ==[ alpha ]==> ((((a a) a)(^x.x))(^y.y)) REDUCED to normal form. ------ 199599/23899899. ------ 1. ==[ start ]==> ((((^a.a) a)(a (a a)))(b ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x) a)(a (a a)))(b ((^y.(^z.z)) a))) 3. ==[ beta ]==> ((a (a (a a)))(b ((^y.(^z.z)) a))) 4. ==[ alpha ]==> ((a (a (a a)))(b ((^x.(^y.y)) a))) 5. ==[ beta ]==> ((a (a (a a)))(b (^y.y))) 6. ==[ alpha ]==> ((a (a (a a)))(b (^x.x))) REDUCED to normal form. ------ 199600/23899926. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(a (a (a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(a (a (a (^y.y))))) 3. ==[ beta ]==> (((a (a a)) a)(a (a (a (^y.y))))) 4. ==[ alpha ]==> (((a (a a)) a)(a (a (a (^x.x))))) REDUCED to normal form. ------ 199601/23899953. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.a)))(((^a.(^a.a)) a)(a a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.z)))(((^x1.(^y1.y1)) a)(a a))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))(((^x1.(^y1.y1)) a)(a a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))(((^z.(^x1.x1)) a)(a a))) 5. ==[ beta ]==> ((a (^y.y))(((^z.(^x1.x1)) a)(a a))) 6. ==[ alpha ]==> ((a (^x.x))(((^y.(^z.z)) a)(a a))) 7. ==[ beta ]==> ((a (^x.x))((^z.z)(a a))) 8. ==[ alpha ]==> ((a (^x.x))((^y.y)(a a))) 9. ==[ beta ]==> ((a (^x.x))(a a)) REDUCED to normal form. ------ 199602/23899980. ------ 1. ==[ start ]==> ((((a a) a)(a a))((b (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((a a) a)(a a))((b (^x.x))(a (^y.y)))) REDUCED to normal form. ------ 199603/23900007. ------ 1. ==[ start ]==> ((a (a b))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a b))(((a a)(a a))((^x.x) a))) 3. ==[ beta ]==> ((a (a b))(((a a)(a a)) a)) REDUCED to normal form. ------ 199604/23900016. ------ 1. ==[ start ]==> (((^a.a)(^a.b))((^c.(a a)) d)) 2. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(a a)) d)) 3. ==[ beta ]==> ((^y.b)((^z.(a a)) d)) 4. ==[ alpha ]==> ((^x.b)((^y.(a a)) d)) 5. ==[ beta ]==> b REDUCED to normal form. ------ 199605/23900349. ------ 1. ==[ start ]==> ((((a a) a)(^a.(^a.a)))(a (^a.(a (^a.a))))) 2. ==[ alpha ]==> ((((a a) a)(^x.(^y.y)))(a (^z.(z (^x1.x1))))) REDUCED to normal form. ------ 199606/23900367. ------ 1. ==[ start ]==> (((^a.b)(a a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((^x.b)(a a))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (b (((^y.(^z.z)) a)(^x1.x1))) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a)(^z.z))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199607/23900394. ------ 1. ==[ start ]==> ((a (^b.(a a)))((b (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(a a)))((b (^y.y))(^z.(^x1.x1)))) REDUCED to normal form. ------ 199608/23900565. ------ 1. ==[ start ]==> (((^a.b) b)((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b) b)((^y.(a a))((^z.z)(a a)))) 3. ==[ beta ]==> (b ((^y.(a a))((^z.z)(a a)))) 4. ==[ alpha ]==> (b ((^x.(a a))((^y.y)(a a)))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 199609/23900637. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.b))(((^a.a)(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.b))(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(^y1.y1))(^z1.(^x2.(^y2.y2))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(^x1.(^y1.(^z1.z1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(^z.(^x1.(^y1.y1)))) 7. ==[ beta ]==> ((^y.y)(^z.(^x1.(^y1.y1)))) 8. ==[ alpha ]==> ((^x.x)(^y.(^z.(^x1.x1)))) 9. ==[ beta ]==> (^y.(^z.(^x1.x1))) 10. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199610/23900691. ------ 1. ==[ start ]==> (((^a.(a a))(^b.(^a.a)))(((^a.a) a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 3. ==[ beta ]==> (((^y.(^z.z))(^y.(^z.z)))(((^x1.x1) a)(^y1.(a a)))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.x1)))(((^y1.y1) a)(^z1.(a a)))) 5. ==[ beta ]==> ((^y.y)(((^y1.y1) a)(^z1.(a a)))) 6. ==[ alpha ]==> ((^x.x)(((^y.y) a)(^z.(a a)))) 7. ==[ beta ]==> (((^y.y) a)(^z.(a a))) 8. ==[ alpha ]==> (((^x.x) a)(^y.(a a))) 9. ==[ beta ]==> (a (^y.(a a))) 10. ==[ alpha ]==> (a (^x.(a a))) REDUCED to normal form. ------ 199611/23900772. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(((^x1.(^y1.y1)) a) a)) 3. ==[ beta ]==> (b (((^x1.(^y1.y1)) a) a)) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a) a)) 5. ==[ beta ]==> (b ((^y.y) a)) 6. ==[ alpha ]==> (b ((^x.x) a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 199612/23900835. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))((^c.(a a))(^b.a))) 2. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.(a a))(^z.a))) 3. ==[ beta ]==> (((a a)(^x.(a a)))(a a)) REDUCED to normal form. ------ 199613/23900862. ------ 1. ==[ start ]==> (((a (^a.a))(^a.b))((^b.b)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.b))((^z.z)(^x1.(x1 x1)))) 3. ==[ beta ]==> (((a (^x.x))(^y.b))(^x1.(x1 x1))) 4. ==[ alpha ]==> (((a (^x.x))(^y.b))(^z.(z z))) REDUCED to normal form. ------ 199614/23900970. ------ 1. ==[ start ]==> ((((a a) a)(^b.a))((^b.(a a))(^b.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.a))((^y.(a a))(^z.(a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.a))(a a)) REDUCED to normal form. ------ 199615/23900997. ------ 1. ==[ start ]==> (((a b)(^a.(^a.a)))((^a.b)(^c.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) b) REDUCED to normal form. ------ 199616/23901141. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(^a.a)))(b (b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(^y.y)))(b (b (^z.z)))) 3. ==[ beta ]==> (((a (a a))(^y.y))(b (b (^z.z)))) 4. ==[ alpha ]==> (((a (a a))(^x.x))(b (b (^y.y)))) REDUCED to normal form. ------ 199617/23901168. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (a a)))(a ((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (a a)))(a ((^z.(^x1.x1)) a))) 3. ==[ beta ]==> (((^y.y)(a (a a)))(a ((^z.(^x1.x1)) a))) 4. ==[ alpha ]==> (((^x.x)(a (a a)))(a ((^y.(^z.z)) a))) 5. ==[ beta ]==> ((a (a a))(a ((^y.(^z.z)) a))) 6. ==[ alpha ]==> ((a (a a))(a ((^x.(^y.y)) a))) 7. ==[ beta ]==> ((a (a a))(a (^y.y))) 8. ==[ alpha ]==> ((a (a a))(a (^x.x))) REDUCED to normal form. ------ 199618/23901195. ------ 1. ==[ start ]==> ((((a a) a)((^a.a) a))((b (^a.a))(a a))) 2. ==[ alpha ]==> ((((a a) a)((^x.x) a))((b (^y.y))(a a))) 3. ==[ beta ]==> ((((a a) a) a)((b (^y.y))(a a))) 4. ==[ alpha ]==> ((((a a) a) a)((b (^x.x))(a a))) REDUCED to normal form. ------ 199619/23901222. ------ 1. ==[ start ]==> (((a b)(a (^a.a)))(((a a)(a a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (^x.x)))(((a a)(a a))(a (^y.y)))) REDUCED to normal form. ------ 199620/23901249. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a a))(((^a.a) b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a a))(((^y.y) b)((^z.z) a))) 3. ==[ beta ]==> (((a a)(a a))(((^y.y) b)((^z.z) a))) 4. ==[ alpha ]==> (((a a)(a a))(((^x.x) b)((^y.y) a))) 5. ==[ beta ]==> (((a a)(a a))(b ((^y.y) a))) 6. ==[ alpha ]==> (((a a)(a a))(b ((^x.x) a))) 7. ==[ beta ]==> (((a a)(a a))(b a)) REDUCED to normal form. ------ 199621/23901276. ------ 1. ==[ start ]==> ((a ((a a)(^a.a)))((a (^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((a ((a a)(^x.x)))((a (^y.(^z.z)))(a (a a)))) REDUCED to normal form. ------ 199622/23901609. ------ 1. ==[ start ]==> (((^a.(a a))((a a) a))(((a a)(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))((a a) a))(((a a)(a a))(^y.(^z.z)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))(((a a)(a a))(^y.(^z.z)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))(((a a)(a a))(^x.(^y.y)))) REDUCED to normal form. ------ 199623/23901645. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))((^b.b)((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)((^z1.z1) a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.y1) a))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1) a))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1) a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199624/23901672. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((^a.(^a.(^a.a)))(a (a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((^y.(^z.(^x1.x1)))(a (a a)))) 3. ==[ beta ]==> ((((a a) a)(^x.(x x)))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((((a a) a)(^x.(x x)))(^y.(^z.z))) REDUCED to normal form. ------ 199625/23901690. ------ 1. ==[ start ]==> (((^a.b)((^a.a) a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y) a))((b a)(^z.(^x1.x1)))) 3. ==[ beta ]==> (b ((b a)(^z.(^x1.x1)))) 4. ==[ alpha ]==> (b ((b a)(^x.(^y.y)))) REDUCED to normal form. ------ 199626/23901753. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))((^b.(a a))(a b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.(a a))(a b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))(a a)) REDUCED to normal form. ------ 199627/23902266. ------ 1. ==[ start ]==> ((((a a)(^a.a)) b)((^b.a)(^b.b))) 2. ==[ alpha ]==> ((((a a)(^x.x)) b)((^y.a)(^z.z))) 3. ==[ beta ]==> ((((a a)(^x.x)) b) a) REDUCED to normal form. ------ 199628/23902392. ------ 1. ==[ start ]==> (((^a.(a a))(a b))((^b.b) c)) 2. ==[ alpha ]==> (((^x.(x x))(a b))((^y.y) c)) 3. ==[ beta ]==> (((a b)(a b))((^y.y) c)) 4. ==[ alpha ]==> (((a b)(a b))((^x.x) c)) 5. ==[ beta ]==> (((a b)(a b)) c) REDUCED to normal form. ------ 199629/23902599. ------ 1. ==[ start ]==> (((a a)(b a))((a (a a))(b a))) REDUCED to normal form. ------ 199630/23902626. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(^a.a)))(((^a.a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(((^z.z) a)(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a (^x.x))((a a)(^y.y)))(a (a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(^y.y)))(a (a (^z.(^x1.x1))))) REDUCED to normal form. ------ 199631/23902653. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(a a)))((a (^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(a a)))((a (^z.z))((^x1.x1) b))) 3. ==[ beta ]==> ((a ((^y.y)(a a)))((a (^z.z))((^x1.x1) b))) 4. ==[ alpha ]==> ((a ((^x.x)(a a)))((a (^y.y))((^z.z) b))) 5. ==[ beta ]==> ((a (a a))((a (^y.y))((^z.z) b))) 6. ==[ alpha ]==> ((a (a a))((a (^x.x))((^y.y) b))) 7. ==[ beta ]==> ((a (a a))((a (^x.x)) b)) REDUCED to normal form. ------ 199632/23902680. ------ 1. ==[ start ]==> (((a (a a))(a b))((a a)((a a)(a a)))) REDUCED to normal form. ------ 199633/23902860. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) a)((^b.(a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) a)((^x1.(a a))((a a) a))) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.(a a))((a a) a))) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.(a a))((a a) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199634/23902878. ------ 1. ==[ start ]==> (((^a.a)(^a.(^a.(^a.a))))((a b)(^a.b))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((a b)(^y1.b))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((a b)(^y1.b))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))((a b)(^x1.b))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199635/23903040. ------ 1. ==[ start ]==> (((^a.b)(^b.(^a.a)))((a a)(^c.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a a)(^x1.(a a)))) 3. ==[ beta ]==> (b ((a a)(^x1.(a a)))) 4. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 199636/23903265. ------ 1. ==[ start ]==> (((a (a a))(^b.(a a)))((^c.a)(^b.(a a)))) 2. ==[ alpha ]==> (((a (a a))(^x.(a a)))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> (((a (a a))(^x.(a a))) a) REDUCED to normal form. ------ 199637/23903292. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.b))((^b.(^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.b))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((^y.y)(^z.b))((^x1.(^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.b))((^z.(^x1.x1))(^y1.(^z1.z1)))) 5. ==[ beta ]==> ((^y.b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 6. ==[ alpha ]==> ((^x.b)((^y.(^z.z))(^x1.(^y1.y1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 199638/23903346. ------ 1. ==[ start ]==> (((a b)(^b.(^a.a)))((^b.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.a)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a b)(^x.(^y.y))) a) REDUCED to normal form. ------ 199639/23903373. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.(a a)))((^a.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (((a a)(^y.(y y)))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> (((a a)(^x.(x x)))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> (((a a)(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 199640/23903400. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.a))((^a.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))((^z.z)(^x1.(a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.a))(^x1.(a a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.a))(^z.(a a))) REDUCED to normal form. ------ 199641/23903445. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))((^b.b) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))((^x1.x1) b)) 3. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((^z.z) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199642/23903472. ------ 1. ==[ start ]==> ((a (^b.b))((^a.(^a.(^a.a))) c)) 2. ==[ alpha ]==> ((a (^x.x))((^y.(^z.(^x1.x1))) c)) 3. ==[ beta ]==> ((a (^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199643/23903490. ------ 1. ==[ start ]==> (((a a)(a (^a.(^a.a))))((b a)((^a.a) a))) 2. ==[ alpha ]==> (((a a)(a (^x.(^y.y))))((b a)((^z.z) a))) 3. ==[ beta ]==> (((a a)(a (^x.(^y.y))))((b a) a)) REDUCED to normal form. ------ 199644/23903517. ------ 1. ==[ start ]==> (((a (^a.a))(b a))(((a a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> (((a (^x.x))(b a))(((a a)(^y.y))(a (a a)))) REDUCED to normal form. ------ 199645/23903544. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(^a.a)))(((^a.a)(a a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a ((a a)(^y.y)))(((^z.z)(a a))((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((a ((a a)(^x.x)))(((^y.y)(a a))((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)((^y.y)(^z.z)))) 7. ==[ beta ]==> ((a ((a a)(^x.x)))((a a)(^z.z))) 8. ==[ alpha ]==> ((a ((a a)(^x.x)))((a a)(^y.y))) REDUCED to normal form. ------ 199646/23903571. ------ 1. ==[ start ]==> (((a (a a))((^a.a)(a a)))((a b)((a a) a))) 2. ==[ alpha ]==> (((a (a a))((^x.x)(a a)))((a b)((a a) a))) 3. ==[ beta ]==> (((a (a a))(a a))((a b)((a a) a))) REDUCED to normal form. ------ 199647/23903598. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a b))(((a a) a)(a b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a b))(((a a) a)(a b))) 3. ==[ beta ]==> (((^y.y)(a b))(((a a) a)(a b))) 4. ==[ alpha ]==> (((^x.x)(a b))(((a a) a)(a b))) 5. ==[ beta ]==> ((a b)(((a a) a)(a b))) REDUCED to normal form. ------ 199648/23903625. ------ 1. ==[ start ]==> ((((a a) a)((a a) a))(((^a.a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)((a a) a))(((^x.x)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)((^z.z)(a a)))) 4. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)((^y.y)(a a)))) 5. ==[ beta ]==> ((((a a) a)((a a) a))((^y.y)(a a))) 6. ==[ alpha ]==> ((((a a) a)((a a) a))((^x.x)(a a))) 7. ==[ beta ]==> ((((a a) a)((a a) a))(a a)) REDUCED to normal form. ------ 199649/23903652. ------ 1. ==[ start ]==> (((a b)((^a.a)(^a.a)))((a (a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(^y.y)))((a (a a))((a a)(^z.z)))) 3. ==[ beta ]==> (((a b)(^y.y))((a (a a))((a a)(^z.z)))) 4. ==[ alpha ]==> (((a b)(^x.x))((a (a a))((a a)(^y.y)))) REDUCED to normal form. ------ 199650/23903679. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a (a a)))(((^a.a) a)(b a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a (a a)))(((^y.y) a)(b a))) 3. ==[ beta ]==> (((a a)(a (a a)))(((^y.y) a)(b a))) 4. ==[ alpha ]==> (((a a)(a (a a)))(((^x.x) a)(b a))) 5. ==[ beta ]==> (((a a)(a (a a)))(a (b a))) REDUCED to normal form. ------ 199651/23903706. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a) a))((a (^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y) a))((a (^z.z))(a (^x1.(^y1.y1))))) 3. ==[ beta ]==> ((((a a)(^x.x)) a)((a (^z.z))(a (^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((((a a)(^x.x)) a)((a (^y.y))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 199652/23903751. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(a (^c.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(a (^x1.(a a)))) 3. ==[ beta ]==> ((^y.(^z.z))(a (^x1.(a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (^z.(a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199653/23903796. ------ 1. ==[ start ]==> (((^a.a)(^b.b))((a (^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)((a (^z.(^x1.x1)))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.(^z.z)))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.x1))) REDUCED to normal form. ------ 199654/23903823. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(^a.(^a.a))))((b a)(^b.a))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(^x1.(^y1.y1))))((b a)(^z1.a))) 3. ==[ beta ]==> ((^y.y)((b a)(^z1.a))) 4. ==[ alpha ]==> ((^x.x)((b a)(^y.a))) 5. ==[ beta ]==> ((b a)(^y.a)) 6. ==[ alpha ]==> ((b a)(^x.a)) REDUCED to normal form. ------ 199655/23903958. ------ 1. ==[ start ]==> (((^a.b)(^c.a))(((^a.a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(^x1.x1))(^y1.(a a)))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(^y1.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.(a a)))) 5. ==[ beta ]==> (b ((^y.y)(^z.(a a)))) 6. ==[ alpha ]==> (b ((^x.x)(^y.(a a)))) 7. ==[ beta ]==> (b (^y.(a a))) 8. ==[ alpha ]==> (b (^x.(a a))) REDUCED to normal form. ------ 199656/23904066. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(^a.a)))((a a)(^b.b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))((a a)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.z))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199657/23904075. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((^a.a)((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z)((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.(^y.y))) b)((^x1.x1) b)) 4. ==[ alpha ]==> (((a (^x.(^y.y))) b)((^z.z) b)) 5. ==[ beta ]==> (((a (^x.(^y.y))) b) b) REDUCED to normal form. ------ 199658/23904102. ------ 1. ==[ start ]==> ((((^a.a) b) a)((^b.b)(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b) a)((^y.y)(^z.z))) 3. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 4. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 5. ==[ beta ]==> ((b a)(^y.y)) 6. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 199659/23904120. ------ 1. ==[ start ]==> (((^a.a)((^a.a) b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((^x.x)((^y.y) b))((a (^z.(^x1.x1))) b)) 3. ==[ beta ]==> (((^y.y) b)((a (^z.(^x1.x1))) b)) 4. ==[ alpha ]==> (((^x.x) b)((a (^y.(^z.z))) b)) 5. ==[ beta ]==> (b ((a (^y.(^z.z))) b)) 6. ==[ alpha ]==> (b ((a (^x.(^y.y))) b)) REDUCED to normal form. ------ 199660/23904129. ------ 1. ==[ start ]==> (((a a)(^b.b))((^a.(^a.(^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a a)(^x.x))((^y.(^z.(^x1.x1)))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^x.x))(^z.(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199661/23904147. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (^z.(^x1.x1))))((b a) c)) 3. ==[ beta ]==> ((^y.y)((b a) c)) 4. ==[ alpha ]==> ((^x.x)((b a) c)) 5. ==[ beta ]==> ((b a) c) REDUCED to normal form. ------ 199662/23904237. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(a a)))((^a.b)(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(a a)))((^x1.b)(^y1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(a a)))((^x1.b)(^y1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(a a)))((^z.b)(^x1.a))) 5. ==[ beta ]==> ((^y.(a a))((^z.b)(^x1.a))) 6. ==[ alpha ]==> ((^x.(a a))((^y.b)(^z.a))) 7. ==[ beta ]==> (a a) REDUCED to normal form. ------ 199663/23904264. ------ 1. ==[ start ]==> ((((a a) a)(^a.b))((^c.a)(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(^x.b))((^y.a)(^z.b))) 3. ==[ beta ]==> ((((a a) a)(^x.b)) a) REDUCED to normal form. ------ 199664/23904291. ------ 1. ==[ start ]==> (((a b)(^c.a))((^b.(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((^y.(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> (((a b)(^x.a))(^z.z)) 4. ==[ alpha ]==> (((a b)(^x.a))(^y.y)) REDUCED to normal form. ------ 199665/23904318. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(^a.a)))((^a.(a a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((a a)(^y.(^z.z)))((^x1.(x1 x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(z z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((a a)(^x.(^y.y)))((^x1.(^y1.y1))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a a)(^x.(^y.y)))((^z.(^x1.x1))(^y1.(^z1.z1)))) 7. ==[ beta ]==> (((a a)(^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> (((a a)(^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 199666/23904399. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(^a.a)))((^a.a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))((^y1.y1)(^z1.z1))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^z1.z1)) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(^x1.x1)))(^y1.y1)) REDUCED to normal form. ------ 199667/23904462. ------ 1. ==[ start ]==> (((a a)((^a.a) b))((b a)(a (^a.a)))) 2. ==[ alpha ]==> (((a a)((^x.x) b))((b a)(a (^y.y)))) 3. ==[ beta ]==> (((a a) b)((b a)(a (^y.y)))) 4. ==[ alpha ]==> (((a a) b)((b a)(a (^x.x)))) REDUCED to normal form. ------ 199668/23904489. ------ 1. ==[ start ]==> (((a (^a.a))(a (^a.(^a.a))))(((a a)(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a)(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(a (^y.(^z.z))))(((a a)(^x1.x1)) a)) REDUCED to normal form. ------ 199669/23904516. ------ 1. ==[ start ]==> ((((^a.a) a)(b a))(((^a.a)(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(b a))(((^y.y)(a a))(a (a a)))) 3. ==[ beta ]==> ((a (b a))(((^y.y)(a a))(a (a a)))) 4. ==[ alpha ]==> ((a (b a))(((^x.x)(a a))(a (a a)))) 5. ==[ beta ]==> ((a (b a))((a a)(a (a a)))) REDUCED to normal form. ------ 199670/23904543. ------ 1. ==[ start ]==> (((a (a a))((a a)(^a.a)))((a b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a b)((^y.y)(^z.z)))) 3. ==[ beta ]==> (((a (a a))((a a)(^x.x)))((a b)(^z.z))) 4. ==[ alpha ]==> (((a (a a))((a a)(^x.x)))((a b)(^y.y))) REDUCED to normal form. ------ 199671/23904570. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(a a)))(((a a) a)((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(a a)))(((a a) a)((a a) a))) 3. ==[ beta ]==> (((^y.y)((^z.z)(a a)))(((a a) a)((a a) a))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(a a)))(((a a) a)((a a) a))) 5. ==[ beta ]==> (((^y.y)(a a))(((a a) a)((a a) a))) 6. ==[ alpha ]==> (((^x.x)(a a))(((a a) a)((a a) a))) 7. ==[ beta ]==> ((a a)(((a a) a)((a a) a))) REDUCED to normal form. ------ 199672/23904597. ------ 1. ==[ start ]==> ((((a a) a)(a b))(((^a.a)(^a.a))(a b))) 2. ==[ alpha ]==> ((((a a) a)(a b))(((^x.x)(^y.y))(a b))) 3. ==[ beta ]==> ((((a a) a)(a b))((^y.y)(a b))) 4. ==[ alpha ]==> ((((a a) a)(a b))((^x.x)(a b))) 5. ==[ beta ]==> ((((a a) a)(a b))(a b)) REDUCED to normal form. ------ 199673/23904624. ------ 1. ==[ start ]==> (((a b)((a a) a))((a (a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)((a a) a))((a (a a))((^x.x)(a a)))) 3. ==[ beta ]==> (((a b)((a a) a))((a (a a))(a a))) REDUCED to normal form. ------ 199674/23904651. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a)(^a.a)))(((^a.a) a)((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y)(^z.z)))(((^x1.x1) a)((a a)(^y1.y1)))) 3. ==[ beta ]==> (((a a)((^y.y)(^z.z)))(((^x1.x1) a)((a a)(^y1.y1)))) 4. ==[ alpha ]==> (((a a)((^x.x)(^y.y)))(((^z.z) a)((a a)(^x1.x1)))) 5. ==[ beta ]==> (((a a)(^y.y))(((^z.z) a)((a a)(^x1.x1)))) 6. ==[ alpha ]==> (((a a)(^x.x))(((^y.y) a)((a a)(^z.z)))) 7. ==[ beta ]==> (((a a)(^x.x))(a ((a a)(^z.z)))) 8. ==[ alpha ]==> (((a a)(^x.x))(a ((a a)(^y.y)))) REDUCED to normal form. ------ 199675/23904678. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a (a a)))((a (^a.a))(b a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a (a a)))((a (^y.y))(b a))) REDUCED to normal form. ------ 199676/23904822. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.b))(((^a.a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(((^x1.x1)(a a))(^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))(^z.(z z)))) 5. ==[ beta ]==> (((^y.y)(a a))(^z.(z z))) 6. ==[ alpha ]==> (((^x.x)(a a))(^y.(y y))) 7. ==[ beta ]==> ((a a)(^y.(y y))) 8. ==[ alpha ]==> ((a a)(^x.(x x))) REDUCED to normal form. ------ 199677/23904957. ------ 1. ==[ start ]==> (((^a.b)(^a.b))(((^a.a) a)(^c.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.b))(((^z.z) a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (((^z.z) a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b (((^x.x) a)(^y.(^z.z)))) 5. ==[ beta ]==> (b (a (^y.(^z.z)))) 6. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 199678/23905065. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.a))((b a) b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.a))((b a) b)) 3. ==[ beta ]==> ((^y.(^z.z))((b a) b)) 4. ==[ alpha ]==> ((^x.(^y.y))((b a) b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199679/23905101. ------ 1. ==[ start ]==> ((((^a.a) b) b)((^c.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b) b)((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b b)((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b b)((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b b)(^y.y)) 6. ==[ alpha ]==> ((b b)(^x.x)) REDUCED to normal form. ------ 199680/23905128. ------ 1. ==[ start ]==> ((((a a)(a a)) a)((^b.(a a))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a)) a)((^x.(a a))(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a a)) REDUCED to normal form. ------ 199681/23905182. ------ 1. ==[ start ]==> (((a (^a.a))(^b.b))((^c.a)(^c.a))) 2. ==[ alpha ]==> (((a (^x.x))(^y.y))((^z.a)(^x1.a))) 3. ==[ beta ]==> (((a (^x.x))(^y.y)) a) REDUCED to normal form. ------ 199682/23905209. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.(^a.(^a.a))))((^b.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.b))) 3. ==[ beta ]==> ((a (^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.b))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1))(^z1.b))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 199683/23905317. ------ 1. ==[ start ]==> (((a b)(^a.b))((^a.a)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a b)(^x.b))((^y.y)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((a b)(^x.b))(^z.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(^x.b))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 199684/23905515. ------ 1. ==[ start ]==> (((a a)((a a)(a a)))((a (a a))(a b))) REDUCED to normal form. ------ 199685/23905542. ------ 1. ==[ start ]==> (((a (^a.a))((^a.a) b))(((^a.a) a)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.y) b))(((^z.z) a)((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a (^x.x)) b)(((^z.z) a)((^x1.x1)(a a)))) 4. ==[ alpha ]==> (((a (^x.x)) b)(((^y.y) a)((^z.z)(a a)))) 5. ==[ beta ]==> (((a (^x.x)) b)(a ((^z.z)(a a)))) 6. ==[ alpha ]==> (((a (^x.x)) b)(a ((^y.y)(a a)))) 7. ==[ beta ]==> (((a (^x.x)) b)(a (a a))) REDUCED to normal form. ------ 199686/23905569. ------ 1. ==[ start ]==> ((((^a.a) a)(a (^a.(^a.a))))((a (^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) a)(a (^y.(^z.z))))((a (^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((a (a (^y.(^z.z))))((a (^x1.x1))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((a (a (^x.(^y.y))))((a (^z.z))((a a)(^x1.x1)))) REDUCED to normal form. ------ 199687/23905596. ------ 1. ==[ start ]==> (((a (a a))(b a))((a a)(b a))) REDUCED to normal form. ------ 199688/23906451. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))((^c.(^a.a))(a a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))((^z.(^x1.x1))(a a))) 3. ==[ beta ]==> (((a a)(^y.b))((^z.(^x1.x1))(a a))) 4. ==[ alpha ]==> (((a a)(^x.b))((^y.(^z.z))(a a))) 5. ==[ beta ]==> (((a a)(^x.b))(^z.z)) 6. ==[ alpha ]==> (((a a)(^x.b))(^y.y)) REDUCED to normal form. ------ 199689/23906523. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (a a)))(((a a) a)(^x1.(x1 x1)))) 3. ==[ beta ]==> ((^y.(^z.z))(((a a) a)(^x1.(x1 x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(((a a) a)(^z.(z z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199690/23906559. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))((^b.(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.a))((^z.(^x1.x1))((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.a))((^y.(^z.z))((^x1.x1)(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.a))(^z.z)) 6. ==[ alpha ]==> ((b (^x.a))(^y.y)) REDUCED to normal form. ------ 199691/23906586. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(^a.a)))((^a.(a a))((a a) a))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(^y.y)))((^z.(z z))((a a) a))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(^y.y)))(((a a) a)((a a) a))) REDUCED to normal form. ------ 199692/23906919. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(a ((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(a ((a a)(^z.z)))) REDUCED to normal form. ------ 199693/23906946. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a) a))(((^a.a)(a a))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y) a))(((^z.z)(a a))(a a))) 3. ==[ beta ]==> ((b ((^y.y) a))(((^z.z)(a a))(a a))) 4. ==[ alpha ]==> ((b ((^x.x) a))(((^y.y)(a a))(a a))) 5. ==[ beta ]==> ((b a)(((^y.y)(a a))(a a))) 6. ==[ alpha ]==> ((b a)(((^x.x)(a a))(a a))) 7. ==[ beta ]==> ((b a)((a a)(a a))) REDUCED to normal form. ------ 199694/23906973. ------ 1. ==[ start ]==> ((((a a)(a a))(a (^a.a)))((a b)(a (^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (^x.x)))((a b)(a (^y.y)))) REDUCED to normal form. ------ 199695/23907027. ------ 1. ==[ start ]==> ((a ((^a.(^a.a)) a))(((^a.a)(^a.a))(a (a a)))) 2. ==[ alpha ]==> ((a ((^x.(^y.y)) a))(((^z.z)(^x1.x1))(a (a a)))) 3. ==[ beta ]==> ((a (^y.y))(((^z.z)(^x1.x1))(a (a a)))) 4. ==[ alpha ]==> ((a (^x.x))(((^y.y)(^z.z))(a (a a)))) 5. ==[ beta ]==> ((a (^x.x))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 199696/23907198. ------ 1. ==[ start ]==> (((^a.b)(^c.(^a.a)))((a b)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b ((a b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (b ((a b)(^x.(^y.y)))) REDUCED to normal form. ------ 199697/23907306. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^b.(^a.a)))(((^a.a) a)(^c.a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(^y1.y1)))(((^z1.z1) a)(^x2.a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^z1.z1) a)(^x2.a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) a)(^x1.a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199698/23907423. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((^a.b)(^a.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((^z.b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)((^z.b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)((^y.b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a ((^y.b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a ((^x.b)(^y.(^z.z)))) 7. ==[ beta ]==> (a b) REDUCED to normal form. ------ 199699/23907531. ------ 1. ==[ start ]==> (((a (a a))(^b.b))((^b.a)(^c.a))) 2. ==[ alpha ]==> (((a (a a))(^x.x))((^y.a)(^z.a))) 3. ==[ beta ]==> (((a (a a))(^x.x)) a) REDUCED to normal form. ------ 199700/23907558. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^a.(^a.(^a.a))))((^a.(^a.a))(^a.b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.b))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.(^y1.y1))))((^z1.(^x2.x2))(^y2.b))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))((^y1.(^z1.z1))(^x2.b))) 5. ==[ beta ]==> ((^y.(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.b))) 6. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(^y1.y1))(^z1.b))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199701/23907603. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> (b ((^z.(a a)) a)) 4. ==[ alpha ]==> (b ((^x.(a a)) a)) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 199702/23907747. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.(a a)))(c (^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(y y)))(c (^z.a))) 3. ==[ beta ]==> ((b (^y.(y y)))(c (^z.a))) 4. ==[ alpha ]==> ((b (^x.(x x)))(c (^y.a))) REDUCED to normal form. ------ 199703/23907774. ------ 1. ==[ start ]==> ((((a a)(a a))(^b.a))(b (^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.a))(b (^y.b))) REDUCED to normal form. ------ 199704/23907828. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((^a.b)(a a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((^x1.b)(a a))) 3. ==[ beta ]==> (((^y.y)(^z.z))((^x1.b)(a a))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((^z.b)(a a))) 5. ==[ beta ]==> ((^y.y)((^z.b)(a a))) 6. ==[ alpha ]==> ((^x.x)((^y.b)(a a))) 7. ==[ beta ]==> ((^y.b)(a a)) 8. ==[ alpha ]==> ((^x.b)(a a)) 9. ==[ beta ]==> b REDUCED to normal form. ------ 199705/23907846. ------ 1. ==[ start ]==> ((a (^a.(a (^a.a))))(((a a) a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(x (^y.y))))(((a a) a)(^z.(^x1.x1)))) REDUCED to normal form. ------ 199706/23908161. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))(b ((a a) a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))(b ((a a) a))) 3. ==[ beta ]==> ((b (a (a a)))(b ((a a) a))) REDUCED to normal form. ------ 199707/23908188. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(a (a b))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(a (a b))) 3. ==[ beta ]==> ((((a a)(a a)) a)(a (a b))) REDUCED to normal form. ------ 199708/23908242. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a a))(((^a.a)(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a a))(((^z.z)(^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a a))(((^z.z)(^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a a))(((^y.y)(^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a a)(((^y.y)(^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a a)(((^x.x)(^y.y))(a (^z.z)))) 7. ==[ beta ]==> ((a a)((^y.y)(a (^z.z)))) 8. ==[ alpha ]==> ((a a)((^x.x)(a (^y.y)))) 9. ==[ beta ]==> ((a a)(a (^y.y))) 10. ==[ alpha ]==> ((a a)(a (^x.x))) REDUCED to normal form. ------ 199709/23908269. ------ 1. ==[ start ]==> ((a (a (a (^a.a))))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> ((a (a (a (^x.x))))((a (a a))((^y.y) a))) 3. ==[ beta ]==> ((a (a (a (^x.x))))((a (a a)) a)) REDUCED to normal form. ------ 199710/23908665. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) b)((^a.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y) b)((^z.(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x) b)((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> (b ((^y.(^z.z))(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (b ((^x.(^y.y))(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199711/23908737. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))((^b.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))((^y1.(^z1.z1)) b)) 3. ==[ beta ]==> ((^y.y)((^y1.(^z1.z1)) b)) 4. ==[ alpha ]==> ((^x.x)((^y.(^z.z)) b)) 5. ==[ beta ]==> ((^y.(^z.z)) b) 6. ==[ alpha ]==> ((^x.(^y.y)) b) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199712/23908827. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.b))(b (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.z))(b (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(^z.z))(b (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b (^z.(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b (^z.(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b (^y.(^z.z)))) 7. ==[ beta ]==> (b (^y.(^z.z))) 8. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 199713/23908872. ------ 1. ==[ start ]==> (((^a.b)(b a))(((^a.a)(^a.a))(^a.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(((^y.y)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (b (((^y.y)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(^z.z))) 5. ==[ beta ]==> (b ((^y.y)(^z.z))) 6. ==[ alpha ]==> (b ((^x.x)(^y.y))) 7. ==[ beta ]==> (b (^y.y)) 8. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199714/23908935. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))((^b.a)((^a.a) a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))((^z.a)((^x1.x1) a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a))) a) REDUCED to normal form. ------ 199715/23908980. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((a a) a))((a a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((a a) a))((a a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199716/23909016. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))((^b.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 3. ==[ beta ]==> ((b (^y.(^z.z)))((^x1.(^y1.y1))(^z1.z1))) 4. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.(^x1.x1))(^y1.y1))) 5. ==[ beta ]==> ((b (^x.(^y.y)))(^x1.x1)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 199717/23909043. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((^a.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(y y))(^z.(^x1.x1)))) 3. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))((^z.(^x1.x1))(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((^y.(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((((a a)(a a))(^x.(x x)))(^z.z)) 6. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))(^y.y)) REDUCED to normal form. ------ 199718/23909097. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.(^a.a)))((^a.(^a.a))(^a.(a a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(x2 x2)))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.(^z1.z1))(^x2.(x2 x2)))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.(^y1.y1))(^z1.(z1 z1)))) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.(^y1.y1))(^z1.(z1 z1)))) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(^y1.(y1 y1)))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199719/23909124. ------ 1. ==[ start ]==> (((a (a (^a.a)))(^a.a))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))((^z.z)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a (^x.x)))(^y.y))(^x1.(^y1.y1))) 4. ==[ alpha ]==> (((a (a (^x.x)))(^y.y))(^z.(^x1.x1))) REDUCED to normal form. ------ 199720/23909142. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))((^b.(^a.a)) a)) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.(^y1.y1)) a)) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^y1.y1)) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.x1)) REDUCED to normal form. ------ 199721/23909160. ------ 1. ==[ start ]==> (((a a)(a (a (^a.a))))((a (a a))(a a))) 2. ==[ alpha ]==> (((a a)(a (a (^x.x))))((a (a a))(a a))) REDUCED to normal form. ------ 199722/23909187. ------ 1. ==[ start ]==> (((a (^a.a))((^a.(^a.a)) a))(((^a.a) a)(a (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((^y.(^z.z)) a))(((^x1.x1) a)(a (^y1.y1)))) 3. ==[ beta ]==> (((a (^x.x))(^z.z))(((^x1.x1) a)(a (^y1.y1)))) 4. ==[ alpha ]==> (((a (^x.x))(^y.y))(((^z.z) a)(a (^x1.x1)))) 5. ==[ beta ]==> (((a (^x.x))(^y.y))(a (a (^x1.x1)))) 6. ==[ alpha ]==> (((a (^x.x))(^y.y))(a (a (^z.z)))) REDUCED to normal form. ------ 199723/23909214. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))((a (^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))((a (^z.z))((^x1.x1) a))) 3. ==[ beta ]==> ((a (b (^y.y)))((a (^z.z))((^x1.x1) a))) 4. ==[ alpha ]==> ((a (b (^x.x)))((a (^y.y))((^z.z) a))) 5. ==[ beta ]==> ((a (b (^x.x)))((a (^y.y)) a)) REDUCED to normal form. ------ 199724/23909241. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))((a a)(a (a a)))) REDUCED to normal form. ------ 199725/23909322. ------ 1. ==[ start ]==> (((a b)(b a))(c c)) REDUCED to normal form. ------ 199726/23909457. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))(b ((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))(b ((^x1.x1) a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))(b ((^x1.x1) a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))(b ((^z.z) a))) 5. ==[ beta ]==> ((b (^y.y))(b ((^z.z) a))) 6. ==[ alpha ]==> ((b (^x.x))(b ((^y.y) a))) 7. ==[ beta ]==> ((b (^x.x))(b a)) REDUCED to normal form. ------ 199727/23909484. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(a (a (a a)))) REDUCED to normal form. ------ 199728/23909538. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(a (^a.a)))((a (^a.a))(a (^a.a)))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(a (^z.z)))((a (^x1.x1))(a (^y1.y1)))) 3. ==[ beta ]==> (((^y.y)(a (^z.z)))((a (^x1.x1))(a (^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(a (^y.y)))((a (^z.z))(a (^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))((a (^z.z))(a (^x1.x1)))) 6. ==[ alpha ]==> ((a (^x.x))((a (^y.y))(a (^z.z)))) REDUCED to normal form. ------ 199729/23909556. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)(b (^b.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)(b (^z.a))) 3. ==[ beta ]==> ((b (^y.y))(b (^z.a))) 4. ==[ alpha ]==> ((b (^x.x))(b (^y.a))) REDUCED to normal form. ------ 199730/23909565. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))((a a)((^a.a) a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))((a a)((^y.y) a))) 3. ==[ beta ]==> (((a (a (^x.x)))(a a))((a a) a)) REDUCED to normal form. ------ 199731/23909601. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(((^a.a) a)(^a.a))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(((^y1.y1) a)(^z1.z1))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(((^y1.y1) a)(^z1.z1))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1) a)(^y1.y1))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199732/23909628. ------ 1. ==[ start ]==> (((^a.(^a.a))(^a.(a (^a.a))))((a (^a.a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(z (^x1.x1))))((a (^y1.y1))(^z1.(^x2.x2)))) 3. ==[ beta ]==> ((^y.y)((a (^y1.y1))(^z1.(^x2.x2)))) 4. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> ((a (^y.y))(^z.(^x1.x1))) 6. ==[ alpha ]==> ((a (^x.x))(^y.(^z.z))) REDUCED to normal form. ------ 199733/23909763. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))((^b.a) a)) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))((^y1.a) a)) 3. ==[ beta ]==> (b ((^y1.a) a)) 4. ==[ alpha ]==> (b ((^x.a) a)) 5. ==[ beta ]==> (b a) REDUCED to normal form. ------ 199734/23909871. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))((a a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))((a a)(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((^y.(^z.z))((a a)(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a a)(^z.(^x1.x1)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199735/23910006. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))((a a)(^a.a))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))((a a)(^y1.y1))) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))((a a)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))((a a)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((a a)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((a a)(^y.y))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 199736/23910015. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)((^a.a)(a a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)((^y.y)(a a))) 3. ==[ beta ]==> (((a (a (^x.x))) b)(a a)) REDUCED to normal form. ------ 199737/23910042. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)((^a.a)(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)((^x1.x1)(^y1.y1))) 3. ==[ beta ]==> (((^y.(^z.z)) a)((^x1.x1)(^y1.y1))) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((^z.z)(^x1.x1))) 5. ==[ beta ]==> ((^y.y)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)((^y.y)(^z.z))) 7. ==[ beta ]==> ((^y.y)(^z.z)) 8. ==[ alpha ]==> ((^x.x)(^y.y)) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199738/23910060. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))((^y1.y1) a)) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1) a)) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1) a)) 5. ==[ beta ]==> ((^y.(^z.z))((^x1.x1) a)) 6. ==[ alpha ]==> ((^x.(^y.y))((^z.z) a)) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199739/23910069. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a))))(a (^a.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 199740/23910086. ------ 1. ==[ start ]==> (^a.((^a.(^a.a))(a (a (^a.a))))) 2. ==[ alpha ]==> (^x.((^y.(^z.z))(x (x (^x1.x1))))) 3. ==[ beta ]==> (^x.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199741/23910087. ------ 1. ==[ start ]==> (a ((^a.(^a.a))(a (a (^a.a))))) 2. ==[ alpha ]==> (a ((^x.(^y.y))(a (a (^z.z))))) 3. ==[ beta ]==> (a (^y.y)) 4. ==[ alpha ]==> (a (^x.x)) REDUCED to normal form. ------ 199742/23910117. ------ 1. ==[ start ]==> ((^a.(a a))(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((^y.((^z.z)(^x1.(^y1.y1))))(^y.((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.(^y2.y2))))) 5. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 6. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 7. ==[ beta ]==> (^y.(^z.z)) 8. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199743/23910585. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 199744/23911035. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199745/23911467. ------ 1. ==[ start ]==> ((^a.((a a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))(^y.(a (a (^z.z))))) 3. ==[ beta ]==> (((^y.(a (a (^z.z))))(^y.(a (a (^z.z)))))(^y.(a (a (^z.z))))) 4. ==[ alpha ]==> (((^x.(a (a (^y.y))))(^z.(a (a (^x1.x1)))))(^y1.(a (a (^z1.z1))))) 5. ==[ beta ]==> ((a (a (^y.y)))(^y1.(a (a (^z1.z1))))) 6. ==[ alpha ]==> ((a (a (^x.x)))(^y.(a (a (^z.z))))) REDUCED to normal form. ------ 199746/23921115. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.((^z1.z1)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199747/23921565. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199748/23922045. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a)))) c) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z)))) c) REDUCED to normal form. ------ 199749/23922063. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a (^a.a)))) a) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a (^z.z)))) a) 3. ==[ beta ]==> ((^y.y) a) 4. ==[ alpha ]==> ((^x.x) a) 5. ==[ beta ]==> a REDUCED to normal form. ------ 199750/23922069. ------ 1. ==[ start ]==> ((^a.a)((^a.(^a.a))(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)((^y.(^z.z))(a (a (^x1.x1))))) 3. ==[ beta ]==> ((^y.(^z.z))(a (a (^x1.x1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(a (a (^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199751/23922096. ------ 1. ==[ start ]==> ((^a.(a a))((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((^y.y)((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.(^y1.y1))))((^y.y)((^z.z)(^x1.(^y1.y1))))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))((^y1.y1)((^z1.z1)(^x2.(^y2.y2))))) 5. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))((^y1.y1)((^z1.z1)(^x2.(^y2.y2))))) 6. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))((^x1.x1)((^y1.y1)(^z1.(^x2.x2))))) 7. ==[ beta ]==> ((^y.(^z.z))((^x1.x1)((^y1.y1)(^z1.(^x2.x2))))) 8. ==[ alpha ]==> ((^x.(^y.y))((^z.z)((^x1.x1)(^y1.(^z1.z1))))) 9. ==[ beta ]==> (^y.y) 10. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199752/23922099. ------ 1. ==[ start ]==> ((a (a a))(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))(^x.((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))(^x.(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199753/23922123. ------ 1. ==[ start ]==> ((^a.b)((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((^x.b)((^y.(^z.(^x1.x1)))(^y1.y1))) 3. ==[ beta ]==> b REDUCED to normal form. ------ 199754/23922393. ------ 1. ==[ start ]==> ((^a.((^a.a) a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y) x))((^z.b)(^x1.(^y1.(^z1.z1))))) 3. ==[ eta ]==> ((^y.y)((^z.b)(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)((^y.b)(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> ((^y.b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((^x.b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> b REDUCED to normal form. ------ 199755/23922564. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(a ((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 199756/23922567. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^a.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.((^z.z)(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^x.(x x)))(^y.(^x1.(^y1.y1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.x1)))) REDUCED to normal form. ------ 199757/23922888. ------ 1. ==[ start ]==> ((^a.(^b.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))(((^x1.x1)(^y1.y1))((^z1.z1) b))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199758/23923014. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.z)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199759/23923017. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 199760/23923446. ------ 1. ==[ start ]==> ((^a.((a a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))((^y.y)(a (a (^z.z))))) 3. ==[ beta ]==> ((((^y.y)(a (a (^z.z))))((^y.y)(a (a (^z.z)))))((^y.y)(a (a (^z.z))))) 4. ==[ alpha ]==> ((((^x.x)(a (a (^y.y))))((^z.z)(a (a (^x1.x1)))))((^y1.y1)(a (a (^z1.z1))))) 5. ==[ beta ]==> (((a (a (^y.y)))((^z.z)(a (a (^x1.x1)))))((^y1.y1)(a (a (^z1.z1))))) 6. ==[ alpha ]==> (((a (a (^x.x)))((^y.y)(a (a (^z.z)))))((^x1.x1)(a (a (^y1.y1))))) 7. ==[ beta ]==> (((a (a (^x.x)))(a (a (^z.z))))((^x1.x1)(a (a (^y1.y1))))) 8. ==[ alpha ]==> (((a (a (^x.x)))(a (a (^y.y))))((^z.z)(a (a (^x1.x1))))) 9. ==[ beta ]==> (((a (a (^x.x)))(a (a (^y.y))))(a (a (^x1.x1)))) 10. ==[ alpha ]==> (((a (a (^x.x)))(a (a (^y.y))))(a (a (^z.z)))) REDUCED to normal form. ------ 199761/23923449. ------ 1. ==[ start ]==> ((a ((a a) a))(^b.(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))(^x.(a (a (^y.y))))) REDUCED to normal form. ------ 199762/23923881. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))(^b.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (a a)) a)(^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (a a)) a)(^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 199763/23924553. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((^z.b)((a a)(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((^z.b)((a a)(^x1.x1)))((^z.b)((a a)(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.b)((a a)(^z.z)))((^x1.b)((a a)(^y1.y1))))) 5. ==[ beta ]==> (((^y.b)((a a)(^z.z)))((^x1.b)((a a)(^y1.y1)))) 6. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))((^z.b)((a a)(^x1.x1)))) 7. ==[ beta ]==> (b ((^z.b)((a a)(^x1.x1)))) 8. ==[ alpha ]==> (b ((^x.b)((a a)(^y.y)))) 9. ==[ beta ]==> (b b) REDUCED to normal form. ------ 199764/23925906. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^b.(b (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(y (^z.z)))) 3. ==[ beta ]==> (((a b) a)(^y.(y (^z.z)))) 4. ==[ alpha ]==> (((a b) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 199765/23925984. ------ 1. ==[ start ]==> ((^a.(b a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((^x.(b x))((^y.y)(^z.a))) 3. ==[ eta ]==> (b ((^y.y)(^z.a))) 4. ==[ alpha ]==> (b ((^x.x)(^y.a))) 5. ==[ beta ]==> (b (^y.a)) 6. ==[ alpha ]==> (b (^x.a)) REDUCED to normal form. ------ 199766/23926293. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(^a.(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(^x1.(b (^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(^x1.(b (^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(^y.(b (^z.z)))) 5. ==[ beta ]==> (^y.(b (^z.z))) 6. ==[ alpha ]==> (^x.(b (^y.y))) REDUCED to normal form. ------ 199767/23926533. ------ 1. ==[ start ]==> ((^a.(^a.(^a.(^a.a))))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(((^y1.y1)(^z1.z1))((a a)(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199768/23926821. ------ 1. ==[ start ]==> ((^a.(a (^a.(^a.a))))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((^x.(x (^y.(^z.z))))((^x1.(a a))((a a) a))) 3. ==[ beta ]==> (((^x1.(a a))((a a) a))(^y.(^z.z))) 4. ==[ alpha ]==> (((^x.(a a))((a a) a))(^y.(^z.z))) 5. ==[ beta ]==> ((a a)(^y.(^z.z))) 6. ==[ alpha ]==> ((a a)(^x.(^y.y))) REDUCED to normal form. ------ 199769/23927424. ------ 1. ==[ start ]==> ((^a.(^b.b))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.y))((a (^z.(^x1.x1)))(a (^y1.y1)))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199770/23927739. ------ 1. ==[ start ]==> ((^a.((^a.a) b))((^b.b)(a a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))((^z.z)(a a))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 199771/23928030. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)(^c.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)(^z.(^x1.x1))) REDUCED to normal form. ------ 199772/23928687. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(^a.(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(^x1.(^y1.y1))) REDUCED to normal form. ------ 199773/23929578. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(^a.(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (((a a)(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 199774/23929818. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((^z.(^x1.x1))((a a)(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199775/23930370. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))(^z.((a a)(^x1.x1)))) 3. ==[ beta ]==> (b (^z.((a a)(^x1.x1)))) 4. ==[ alpha ]==> (b (^x.((a a)(^y.y)))) REDUCED to normal form. ------ 199776/23930631. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))(^b.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 199777/23930874. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (a a)))(^b.(^c.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (a a)))(^z.(^x1.(^y1.y1)))) REDUCED to normal form. ------ 199778/23931558. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (b (^z.((^x1.x1)(z z)))) 4. ==[ alpha ]==> (b (^x.((^y.y)(x x)))) 5. ==[ beta ]==> (b (^x.(x x))) REDUCED to normal form. ------ 199779/23931954. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^b.(a b))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(a x))) 3. ==[ eta ]==> ((((a a) a)(b a)) a) REDUCED to normal form. ------ 199780/23932143. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))(^b.(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))(^y.(^z.y))) 3. ==[ beta ]==> ((((a a)(a a)) a)(^y.(^z.y))) 4. ==[ alpha ]==> ((((a a)(a a)) a)(^x.(^y.x))) REDUCED to normal form. ------ 199781/23932665. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^a.((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.((z z) z))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.((z z) z))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.((y y) y))) REDUCED to normal form. ------ 199782/23933094. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(a ((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199783/23933097. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^a.((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(^x1.(^z1.z1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.y1))) REDUCED to normal form. ------ 199784/23933223. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(^a.(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(^x1.(^y1.(^z1.z1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(^x1.(^y1.(^z1.z1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(^z.(^x1.(^y1.y1)))) 5. ==[ beta ]==> (((^y.y) b)(^z.(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x) b)(^y.(^z.(^x1.x1)))) 7. ==[ beta ]==> (b (^y.(^z.(^x1.x1)))) 8. ==[ alpha ]==> (b (^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199785/23933331. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))(^b.(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))(^z.(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))(^z.(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))(^y.(a (a a)))) REDUCED to normal form. ------ 199786/23933439. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))(^b.(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(^y.(y y)))) REDUCED to normal form. ------ 199787/23933544. ------ 1. ==[ start ]==> ((^a.((^a.a)(^a.(^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(^z.(^x1.x1))))(a (^y1.(y1 y1)))) 3. ==[ beta ]==> ((^y.y)(^z.(^x1.x1))) 4. ==[ alpha ]==> ((^x.x)(^y.(^z.z))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199788/23933547. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(^x1.(^y1.(y1 y1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.(^x1.(x1 x1)))) REDUCED to normal form. ------ 199789/23933718. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(^a.((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.((^z1.z1) y1))) 3. ==[ eta ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^z1.z1)) 4. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(^y1.y1)) 5. ==[ beta ]==> (b (^y1.y1)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199790/23933970. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)(^c.(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)(^y.(^z.z))) REDUCED to normal form. ------ 199791/23934015. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a))))(^a.(a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))(^y1.(y1 y1))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(^y1.(y1 y1))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(x1 x1))) 5. ==[ beta ]==> ((^y.(^z.z))(^x1.(x1 x1))) 6. ==[ alpha ]==> ((^x.(^y.y))(^z.(z z))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199792/23934024. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a))))(^b.a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))(^x1.a)) REDUCED to normal form. ------ 199793/23934042. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a (^a.a))))(^a.a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a (^z.z))))(^x1.x1)) 3. ==[ beta ]==> ((^y.y)(^x1.x1)) 4. ==[ alpha ]==> ((^x.x)(^y.y)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199794/23934054. ------ 1. ==[ start ]==> ((a a)((^a.(^a.a))(a (a (^a.a))))) 2. ==[ alpha ]==> ((a a)((^x.(^y.y))(a (a (^z.z))))) 3. ==[ beta ]==> ((a a)(^y.y)) 4. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 199795/23934072. ------ 1. ==[ start ]==> (((^a.a) a)((a a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x) a)((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (a ((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (a ((a a)(^x.(^y.(^z.z))))) REDUCED to normal form. ------ 199796/23934081. ------ 1. ==[ start ]==> ((a (a a))((^a.a)((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (a a))((^x.x)((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (a a))((^y.y)(^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (a a))((^x.x)(^y.(^z.z)))) 5. ==[ beta ]==> ((a (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((a (a a))(^x.(^y.y))) REDUCED to normal form. ------ 199797/23934099. ------ 1. ==[ start ]==> (((a a) a)(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> (((a a) a)(((^x.x)(^y.(^z.z))) a)) 3. ==[ beta ]==> (((a a) a)((^y.(^z.z)) a)) 4. ==[ alpha ]==> (((a a) a)((^x.(^y.y)) a)) 5. ==[ beta ]==> (((a a) a)(^y.y)) 6. ==[ alpha ]==> (((a a) a)(^x.x)) REDUCED to normal form. ------ 199798/23934108. ------ 1. ==[ start ]==> ((a b)((^b.(^a.(^a.a)))(^a.a))) 2. ==[ alpha ]==> ((a b)((^x.(^y.(^z.z)))(^x1.x1))) 3. ==[ beta ]==> ((a b)(^y.(^z.z))) 4. ==[ alpha ]==> ((a b)(^x.(^y.y))) REDUCED to normal form. ------ 199799/23934126. ------ 1. ==[ start ]==> (((a a)(^a.a))((a (a (^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.x))((a (a (^y.y))) b)) REDUCED to normal form. ------ 199800/23934153. ------ 1. ==[ start ]==> (((^a.a) b)(((^a.(^a.a)) a) c)) 2. ==[ alpha ]==> (((^x.x) b)(((^y.(^z.z)) a) c)) 3. ==[ beta ]==> (b (((^y.(^z.z)) a) c)) 4. ==[ alpha ]==> (b (((^x.(^y.y)) a) c)) 5. ==[ beta ]==> (b ((^y.y) c)) 6. ==[ alpha ]==> (b ((^x.x) c)) 7. ==[ beta ]==> (b c) REDUCED to normal form. ------ 199801/23934378. ------ 1. ==[ start ]==> ((a ((^a.a) a))((^a.b)(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x) a))((^y.b)(^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a a)((^y.b)(^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a a)((^x.b)(^y.(^z.(^x1.x1))))) 5. ==[ beta ]==> ((a a) b) REDUCED to normal form. ------ 199802/23934549. ------ 1. ==[ start ]==> ((a (^a.(a a)))(a ((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(a ((^y.y)(^z.(^x1.x1))))) 3. ==[ beta ]==> ((a (^x.(x x)))(a (^z.(^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.(x x)))(a (^y.(^z.z)))) REDUCED to normal form. ------ 199803/23934657. ------ 1. ==[ start ]==> (((^a.a)(^a.(a a)))(((a a)(a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(y y)))(((a a)(a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(y y))(((a a)(a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(x x))(((a a)(a a))(a (a a)))) 5. ==[ beta ]==> ((((a a)(a a))(a (a a)))(((a a)(a a))(a (a a)))) REDUCED to normal form. ------ 199804/23934684. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.a))(((^a.a) b)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.a))(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1) b)((^y1.y1)(^z1.z1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y) b)((^z.z)(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)((^z.z)(^x1.x1))) 6. ==[ alpha ]==> (((^x.x) b)((^y.y)(^z.z))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199805/23934738. ------ 1. ==[ start ]==> (((^a.(a a))(^a.a))((b a)(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((b a)(a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((b a)(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((b a)(a b))) 5. ==[ beta ]==> ((^y.y)((b a)(a b))) 6. ==[ alpha ]==> ((^x.x)((b a)(a b))) 7. ==[ beta ]==> ((b a)(a b)) REDUCED to normal form. ------ 199806/23934765. ------ 1. ==[ start ]==> (((^a.a)(a (a a)))(((a a)(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(a (a a)))(((a a)(^y.y))((^z.z)(a a)))) 3. ==[ beta ]==> ((a (a a))(((a a)(^y.y))((^z.z)(a a)))) 4. ==[ alpha ]==> ((a (a a))(((a a)(^x.x))((^y.y)(a a)))) 5. ==[ beta ]==> ((a (a a))(((a a)(^x.x))(a a))) REDUCED to normal form. ------ 199807/23934792. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a) a))(((^a.a)(a a))((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z) a))(((^x1.x1)(a a))((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)(((^x1.x1)(a a))((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(a a))((a a)(^z.z)))) 5. ==[ beta ]==> (((^y.y)(a a))((a a)(^z.z))) 6. ==[ alpha ]==> (((^x.x)(a a))((a a)(^y.y))) 7. ==[ beta ]==> ((a a)((a a)(^y.y))) 8. ==[ alpha ]==> ((a a)((a a)(^x.x))) REDUCED to normal form. ------ 199808/23934846. ------ 1. ==[ start ]==> (((^a.(a a))(a a))(((a a) a)(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(x x))(a a))(((a a) a)(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a a)(a a))(((a a) a)(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a a)(a a))(((a a) a)(a (^x.(^y.y))))) REDUCED to normal form. ------ 199809/23934873. ------ 1. ==[ start ]==> ((a (^b.(^a.a)))(((^a.a)(^a.a))((^a.a) b))) 2. ==[ alpha ]==> ((a (^x.(^y.y)))(((^z.z)(^x1.x1))((^y1.y1) b))) 3. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1)((^y1.y1) b))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z)((^x1.x1) b))) 5. ==[ beta ]==> ((a (^x.(^y.y)))((^x1.x1) b)) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.z) b)) 7. ==[ beta ]==> ((a (^x.(^y.y))) b) REDUCED to normal form. ------ 199810/23934972. ------ 1. ==[ start ]==> (((a (a a))(a a))(b (^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))(a a))(b (^x.(x (^y.y))))) REDUCED to normal form. ------ 199811/23934999. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.a)))(a (^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.y)))(a (^z.(^x1.(^y1.y1))))) 3. ==[ beta ]==> ((a (^y.y))(a (^z.(^x1.(^y1.y1))))) 4. ==[ alpha ]==> ((a (^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 199812/23935098. ------ 1. ==[ start ]==> (((a (a a)) b)(((a a)(a a))(^a.(a a)))) 2. ==[ alpha ]==> (((a (a a)) b)(((a a)(a a))(^x.(x x)))) REDUCED to normal form. ------ 199813/23935125. ------ 1. ==[ start ]==> ((((^a.a)(^a.a)) a)(((^a.a) b)(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y)) a)(((^z.z) b)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y) a)(((^z.z) b)(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x) a)(((^y.y) b)(^z.(^x1.x1)))) 5. ==[ beta ]==> (a (((^y.y) b)(^z.(^x1.x1)))) 6. ==[ alpha ]==> (a (((^x.x) b)(^y.(^z.z)))) 7. ==[ beta ]==> (a (b (^y.(^z.z)))) 8. ==[ alpha ]==> (a (b (^x.(^y.y)))) REDUCED to normal form. ------ 199814/23935152. ------ 1. ==[ start ]==> (((a a)(^b.(^a.a)))((a (^a.(^a.a)))(^c.a))) 2. ==[ alpha ]==> (((a a)(^x.(^y.y)))((a (^z.(^x1.x1)))(^y1.a))) REDUCED to normal form. ------ 199815/23935179. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a a)))((b a)(^a.b))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y y)))((b a)(^z.b))) REDUCED to normal form. ------ 199816/23935206. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.a))(((a a)(^a.a))(^b.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.a))(((a a)(^z.z))(^x1.(a a)))) 3. ==[ beta ]==> ((a (^y.a))(((a a)(^z.z))(^x1.(a a)))) 4. ==[ alpha ]==> ((a (^x.a))(((a a)(^y.y))(^z.(a a)))) REDUCED to normal form. ------ 199817/23935323. ------ 1. ==[ start ]==> (((a (^a.a))(a (a a)))((^b.(^a.a))((^a.a) b))) 2. ==[ alpha ]==> (((a (^x.x))(a (a a)))((^y.(^z.z))((^x1.x1) b))) 3. ==[ beta ]==> (((a (^x.x))(a (a a)))(^z.z)) 4. ==[ alpha ]==> (((a (^x.x))(a (a a)))(^y.y)) REDUCED to normal form. ------ 199818/23935350. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) a))((^a.(a a))((a a)(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) a))((^z.(z z))((a a)(a a)))) 3. ==[ beta ]==> ((a ((^y.y) a))((^z.(z z))((a a)(a a)))) 4. ==[ alpha ]==> ((a ((^x.x) a))((^y.(y y))((a a)(a a)))) 5. ==[ beta ]==> ((a a)((^y.(y y))((a a)(a a)))) 6. ==[ alpha ]==> ((a a)((^x.(x x))((a a)(a a)))) 7. ==[ beta ]==> ((a a)(((a a)(a a))((a a)(a a)))) REDUCED to normal form. ------ 199819/23935377. ------ 1. ==[ start ]==> (((a (a a))(a (^a.a)))((^b.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.x)))((^y.a)(b (^z.z)))) 3. ==[ beta ]==> (((a (a a))(a (^x.x))) a) REDUCED to normal form. ------ 199820/23935404. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a a))((^a.(^a.a))((^a.(^a.a)) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (((^y.y)(a a))((^z.(^x1.x1))((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (((^x.x)(a a))((^y.(^z.z))((^x1.(^y1.y1)) a))) 5. ==[ beta ]==> ((a a)((^y.(^z.z))((^x1.(^y1.y1)) a))) 6. ==[ alpha ]==> ((a a)((^x.(^y.y))((^z.(^x1.x1)) a))) 7. ==[ beta ]==> ((a a)(^y.y)) 8. ==[ alpha ]==> ((a a)(^x.x)) REDUCED to normal form. ------ 199821/23935431. ------ 1. ==[ start ]==> ((a ((a a) a))((^a.a)(a (a (^a.a))))) 2. ==[ alpha ]==> ((a ((a a) a))((^x.x)(a (a (^y.y))))) 3. ==[ beta ]==> ((a ((a a) a))(a (a (^y.y)))) 4. ==[ alpha ]==> ((a ((a a) a))(a (a (^x.x)))) REDUCED to normal form. ------ 199822/23935863. ------ 1. ==[ start ]==> (((a (a a))((^a.a) a))((^a.a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((a (a a))((^x.x) a))((^y.y)(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (((a (a a)) a)((^y.y)(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (((a (a a)) a)((^x.x)(^y.(y (^z.z))))) 5. ==[ beta ]==> (((a (a a)) a)(^y.(y (^z.z)))) 6. ==[ alpha ]==> (((a (a a)) a)(^x.(x (^y.y)))) REDUCED to normal form. ------ 199823/23935953. ------ 1. ==[ start ]==> (((^a.a)(^a.b))(((a a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.b))(((a a)(a a))((^z.z) a))) 3. ==[ beta ]==> ((^y.b)(((a a)(a a))((^z.z) a))) 4. ==[ alpha ]==> ((^x.b)(((a a)(a a))((^y.y) a))) 5. ==[ beta ]==> b REDUCED to normal form. ------ 199824/23936034. ------ 1. ==[ start ]==> (((^a.(a a))(^a.(a a)))((b a)((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b a)((a a) a))) 3. ==[ beta ]==> (((^y.(y y))(^y.(y y)))((b a)((a a) a))) 4. ==[ alpha ]==> (((^x.(x x))(^y.(y y)))((b a)((a a) a))) IRREDUCIBLE: cycle. ------ 199825/23936115. ------ 1. ==[ start ]==> (((^a.b)(^a.a))((a b)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(^y.y))((a b)((a a)(^z.z)))) 3. ==[ beta ]==> (b ((a b)((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((a b)((a a)(^x.x)))) REDUCED to normal form. ------ 199826/23936142. ------ 1. ==[ start ]==> (((^a.a)(a b))(((a a) a)(b a))) 2. ==[ alpha ]==> (((^x.x)(a b))(((a a) a)(b a))) 3. ==[ beta ]==> ((a b)(((a a) a)(b a))) REDUCED to normal form. ------ 199827/23936169. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a) a))(((^a.a)(^a.a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a) a))(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(((^z.z)(^x1.x1))(a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a (^x1.(^y1.y1))))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a (^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a (^z.(^x1.x1)))) 7. ==[ beta ]==> ((^y.y)(a (^z.(^x1.x1)))) 8. ==[ alpha ]==> ((^x.x)(a (^y.(^z.z)))) 9. ==[ beta ]==> (a (^y.(^z.z))) 10. ==[ alpha ]==> (a (^x.(^y.y))) REDUCED to normal form. ------ 199828/23936223. ------ 1. ==[ start ]==> (((^a.(a a))(a (a a)))(((^a.a) a)((a a)(a a)))) 2. ==[ alpha ]==> (((^x.(x x))(a (a a)))(((^y.y) a)((a a)(a a)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(((^y.y) a)((a a)(a a)))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(((^x.x) a)((a a)(a a)))) 5. ==[ beta ]==> (((a (a a))(a (a a)))(a ((a a)(a a)))) REDUCED to normal form. ------ 199829/23936313. ------ 1. ==[ start ]==> (((a b)(^a.a))(((^a.(^a.a)) a)(^a.a))) 2. ==[ alpha ]==> (((a b)(^x.x))(((^y.(^z.z)) a)(^x1.x1))) 3. ==[ beta ]==> (((a b)(^x.x))((^z.z)(^x1.x1))) 4. ==[ alpha ]==> (((a b)(^x.x))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a b)(^x.x))(^z.z)) 6. ==[ alpha ]==> (((a b)(^x.x))(^y.y)) REDUCED to normal form. ------ 199830/23936403. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a)(^a.a)))((^b.b)(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y)(^z.z)))((^x1.x1)(a (a a)))) 3. ==[ beta ]==> ((a ((^y.y)(^z.z)))((^x1.x1)(a (a a)))) 4. ==[ alpha ]==> ((a ((^x.x)(^y.y)))((^z.z)(a (a a)))) 5. ==[ beta ]==> ((a (^y.y))((^z.z)(a (a a)))) 6. ==[ alpha ]==> ((a (^x.x))((^y.y)(a (a a)))) 7. ==[ beta ]==> ((a (^x.x))(a (a a))) REDUCED to normal form. ------ 199831/23936430. ------ 1. ==[ start ]==> (((a (a a))(a (a a)))((^a.(^a.(^a.a)))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (a a)))((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (a a)))(^y.(^z.z))) 4. ==[ alpha ]==> (((a (a a))(a (a a)))(^x.(^y.y))) REDUCED to normal form. ------ 199832/23936502. ------ 1. ==[ start ]==> (((^a.b) b)(((^a.a)(a a))(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b) b)(((^y.y)(a a))(^z.(a a)))) 3. ==[ beta ]==> (b (((^y.y)(a a))(^z.(a a)))) 4. ==[ alpha ]==> (b (((^x.x)(a a))(^y.(a a)))) 5. ==[ beta ]==> (b ((a a)(^y.(a a)))) 6. ==[ alpha ]==> (b ((a a)(^x.(a a)))) REDUCED to normal form. ------ 199833/23936511. ------ 1. ==[ start ]==> (((a b)(a a))((^b.(a a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(a a))((^x.(a a))((^y.y)(a a)))) 3. ==[ beta ]==> (((a b)(a a))(a a)) REDUCED to normal form. ------ 199834/23936538. ------ 1. ==[ start ]==> ((a ((^a.a)(a a)))((^a.b)((a a)(^a.a)))) 2. ==[ alpha ]==> ((a ((^x.x)(a a)))((^y.b)((a a)(^z.z)))) 3. ==[ beta ]==> ((a (a a))((^y.b)((a a)(^z.z)))) 4. ==[ alpha ]==> ((a (a a))((^x.b)((a a)(^y.y)))) 5. ==[ beta ]==> ((a (a a)) b) REDUCED to normal form. ------ 199835/23936718. ------ 1. ==[ start ]==> (((a b) b)(((^a.(^a.a)) a) a)) 2. ==[ alpha ]==> (((a b) b)(((^x.(^y.y)) a) a)) 3. ==[ beta ]==> (((a b) b)((^y.y) a)) 4. ==[ alpha ]==> (((a b) b)((^x.x) a)) 5. ==[ beta ]==> (((a b) b) a) REDUCED to normal form. ------ 199836/23936745. ------ 1. ==[ start ]==> ((((^a.a)(a a)) a)((b (^a.a)) b)) 2. ==[ alpha ]==> ((((^x.x)(a a)) a)((b (^y.y)) b)) 3. ==[ beta ]==> (((a a) a)((b (^y.y)) b)) 4. ==[ alpha ]==> (((a a) a)((b (^x.x)) b)) REDUCED to normal form. ------ 199837/23936772. ------ 1. ==[ start ]==> (((a a)(^b.(a a)))(((a a)(a a)) c)) 2. ==[ alpha ]==> (((a a)(^x.(a a)))(((a a)(a a)) c)) REDUCED to normal form. ------ 199838/23936997. ------ 1. ==[ start ]==> (((a a)((^a.a)(a a)))((^b.(^a.a))(^a.(^a.(^a.a))))) 2. ==[ alpha ]==> (((a a)((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((a a)(a a))((^y.(^z.z))(^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((a a)(a a))((^x.(^y.y))(^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(a a))(^y.y)) 6. ==[ alpha ]==> (((a a)(a a))(^x.x)) REDUCED to normal form. ------ 199839/23937024. ------ 1. ==[ start ]==> (((a (^a.a))(a b))((^a.(a a))(^b.b))) 2. ==[ alpha ]==> (((a (^x.x))(a b))((^y.(y y))(^z.z))) 3. ==[ beta ]==> (((a (^x.x))(a b))((^z.z)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))(a b))((^y.y)(^z.z))) 5. ==[ beta ]==> (((a (^x.x))(a b))(^z.z)) 6. ==[ alpha ]==> (((a (^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 199840/23937051. ------ 1. ==[ start ]==> ((((^a.a) a)((a a) a))((^b.a)(^c.(a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a) a))((^y.a)(^z.(a a)))) 3. ==[ beta ]==> ((a ((a a) a))((^y.a)(^z.(a a)))) 4. ==[ alpha ]==> ((a ((a a) a))((^x.a)(^y.(a a)))) 5. ==[ beta ]==> ((a ((a a) a)) a) REDUCED to normal form. ------ 199841/23937150. ------ 1. ==[ start ]==> (((^a.b) c)((^d.(^a.a)) b)) 2. ==[ alpha ]==> (((^x.b) c)((^y.(^z.z)) b)) 3. ==[ beta ]==> (b ((^y.(^z.z)) b)) 4. ==[ alpha ]==> (b ((^x.(^y.y)) b)) 5. ==[ beta ]==> (b (^y.y)) 6. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199842/23937249. ------ 1. ==[ start ]==> (((^a.(^a.a))(^b.(a a)))((b a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))(^z.(a a)))((b a)((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((^y.y)((b a)((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.x)((b a)((^y.y)(^z.z)))) 5. ==[ beta ]==> ((b a)((^y.y)(^z.z))) 6. ==[ alpha ]==> ((b a)((^x.x)(^y.y))) 7. ==[ beta ]==> ((b a)(^y.y)) 8. ==[ alpha ]==> ((b a)(^x.x)) REDUCED to normal form. ------ 199843/23937384. ------ 1. ==[ start ]==> (((^a.b)(^b.a))(((^a.a)(^a.a))(b a))) 2. ==[ alpha ]==> (((^x.b)(^y.a))(((^z.z)(^x1.x1))(b a))) 3. ==[ beta ]==> (b (((^z.z)(^x1.x1))(b a))) 4. ==[ alpha ]==> (b (((^x.x)(^y.y))(b a))) 5. ==[ beta ]==> (b ((^y.y)(b a))) 6. ==[ alpha ]==> (b ((^x.x)(b a))) 7. ==[ beta ]==> (b (b a)) REDUCED to normal form. ------ 199844/23937465. ------ 1. ==[ start ]==> (((^a.a)((a a)(^a.a)))((a (^a.a))((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))((a (^z.z))((a a)(a a)))) 3. ==[ beta ]==> (((a a)(^y.y))((a (^z.z))((a a)(a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))((a (^y.y))((a a)(a a)))) REDUCED to normal form. ------ 199845/23937492. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.a)(a a)))((a a)(b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.z)(a a)))((a a)(b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)((a a)(b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)((a a)(b (^y.y)))) 5. ==[ beta ]==> ((a a)(b (^y.y))) 6. ==[ alpha ]==> ((a a)(b (^x.x))) REDUCED to normal form. ------ 199846/23937528. ------ 1. ==[ start ]==> ((((^a.a) a)(^a.b))((b (^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)(^y.b))((b (^z.z))(^x1.x1))) 3. ==[ beta ]==> ((a (^y.b))((b (^z.z))(^x1.x1))) 4. ==[ alpha ]==> ((a (^x.b))((b (^y.y))(^z.z))) REDUCED to normal form. ------ 199847/23937582. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(^b.(^a.a)))(((^a.a) b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(^z.(^x1.x1)))(((^y1.y1) b)(^z1.a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(((^y1.y1) b)(^z1.a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(((^x1.x1) b)(^y1.a))) 5. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(^y1.a))) 6. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(^x1.a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199848/23937609. ------ 1. ==[ start ]==> ((((a a) a)(^a.(a a)))((a (^a.(^a.a)))(^a.(a a)))) 2. ==[ alpha ]==> ((((a a) a)(^x.(x x)))((a (^y.(^z.z)))(^x1.(x1 x1)))) REDUCED to normal form. ------ 199849/23937636. ------ 1. ==[ start ]==> (((a b)(^b.a))((b a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.a))((b a)(^y.(^z.z)))) REDUCED to normal form. ------ 199850/23937690. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.a))(((^a.a)(a a))(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))(((^z.z)(a a))(^x1.b))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.y))((a a)(^x1.b))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((a a)(^z.b))) REDUCED to normal form. ------ 199851/23937726. ------ 1. ==[ start ]==> (((a a)((a a)(^a.a)))((^a.b)((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.b)((^z.z)(a a)))) 3. ==[ beta ]==> (((a a)((a a)(^x.x))) b) REDUCED to normal form. ------ 199852/23937780. ------ 1. ==[ start ]==> ((((^a.a) a)(a b))((^b.(^a.a))(b a))) 2. ==[ alpha ]==> ((((^x.x) a)(a b))((^y.(^z.z))(b a))) 3. ==[ beta ]==> ((a (a b))((^y.(^z.z))(b a))) 4. ==[ alpha ]==> ((a (a b))((^x.(^y.y))(b a))) 5. ==[ beta ]==> ((a (a b))(^y.y)) 6. ==[ alpha ]==> ((a (a b))(^x.x)) REDUCED to normal form. ------ 199853/23937807. ------ 1. ==[ start ]==> (((a (a a))((a a) a))((^a.(a a))(a (^a.(^a.a))))) 2. ==[ alpha ]==> (((a (a a))((a a) a))((^x.(x x))(a (^y.(^z.z))))) 3. ==[ beta ]==> (((a (a a))((a a) a))((a (^y.(^z.z)))(a (^y.(^z.z))))) 4. ==[ alpha ]==> (((a (a a))((a a) a))((a (^x.(^y.y)))(a (^z.(^x1.x1))))) REDUCED to normal form. ------ 199854/23937834. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a)(^a.a)))((^b.a)((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z)(^x1.x1)))((^y1.a)((^z1.z1) b))) 3. ==[ beta ]==> (((^y.y)((^z.z)(^x1.x1)))((^y1.a)((^z1.z1) b))) 4. ==[ alpha ]==> (((^x.x)((^y.y)(^z.z)))((^x1.a)((^y1.y1) b))) 5. ==[ beta ]==> (((^y.y)(^z.z))((^x1.a)((^y1.y1) b))) 6. ==[ alpha ]==> (((^x.x)(^y.y))((^z.a)((^x1.x1) b))) 7. ==[ beta ]==> ((^y.y)((^z.a)((^x1.x1) b))) 8. ==[ alpha ]==> ((^x.x)((^y.a)((^z.z) b))) 9. ==[ beta ]==> ((^y.a)((^z.z) b)) 10. ==[ alpha ]==> ((^x.a)((^y.y) b)) 11. ==[ beta ]==> a REDUCED to normal form. ------ 199855/23937861. ------ 1. ==[ start ]==> ((((a a) a)(a (a a)))((^a.(^a.a))((a a)(a a)))) 2. ==[ alpha ]==> ((((a a) a)(a (a a)))((^x.(^y.y))((a a)(a a)))) 3. ==[ beta ]==> ((((a a) a)(a (a a)))(^y.y)) 4. ==[ alpha ]==> ((((a a) a)(a (a a)))(^x.x)) REDUCED to normal form. ------ 199856/23937888. ------ 1. ==[ start ]==> (((a b)((^a.a) a))((^a.a)(b (^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))((^y.y)(b (^z.z)))) 3. ==[ beta ]==> (((a b) a)((^y.y)(b (^z.z)))) 4. ==[ alpha ]==> (((a b) a)((^x.x)(b (^y.y)))) 5. ==[ beta ]==> (((a b) a)(b (^y.y))) 6. ==[ alpha ]==> (((a b) a)(b (^x.x))) REDUCED to normal form. ------ 199857/23937969. ------ 1. ==[ start ]==> ((a (b a))((^b.b)(^b.a))) 2. ==[ alpha ]==> ((a (b a))((^x.x)(^y.a))) 3. ==[ beta ]==> ((a (b a))(^y.a)) 4. ==[ alpha ]==> ((a (b a))(^x.a)) REDUCED to normal form. ------ 199858/23938248. ------ 1. ==[ start ]==> (((^a.a)(b a))(b ((a a)(a a)))) 2. ==[ alpha ]==> (((^x.x)(b a))(b ((a a)(a a)))) 3. ==[ beta ]==> ((b a)(b ((a a)(a a)))) REDUCED to normal form. ------ 199859/23938275. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(^a.a)))(a (b (^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(^z.z)))(a (b (^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(a (b (^x1.x1)))) 4. ==[ alpha ]==> ((^x.x)(a (b (^y.y)))) 5. ==[ beta ]==> (a (b (^y.y))) 6. ==[ alpha ]==> (a (b (^x.x))) REDUCED to normal form. ------ 199860/23938311. ------ 1. ==[ start ]==> ((((^a.a) a)(^b.(a a)))((^c.(a a)) b)) 2. ==[ alpha ]==> ((((^x.x) a)(^y.(a a)))((^z.(a a)) b)) 3. ==[ beta ]==> ((a (^y.(a a)))((^z.(a a)) b)) 4. ==[ alpha ]==> ((a (^x.(a a)))((^y.(a a)) b)) 5. ==[ beta ]==> ((a (^x.(a a)))(a a)) REDUCED to normal form. ------ 199861/23938329. ------ 1. ==[ start ]==> (((^a.(a a))(a b))(((^a.a) b)(a (^a.a)))) 2. ==[ alpha ]==> (((^x.(x x))(a b))(((^y.y) b)(a (^z.z)))) 3. ==[ beta ]==> (((a b)(a b))(((^y.y) b)(a (^z.z)))) 4. ==[ alpha ]==> (((a b)(a b))(((^x.x) b)(a (^y.y)))) 5. ==[ beta ]==> (((a b)(a b))(b (a (^y.y)))) 6. ==[ alpha ]==> (((a b)(a b))(b (a (^x.x)))) REDUCED to normal form. ------ 199862/23938338. ------ 1. ==[ start ]==> (((a (a a))(^a.b))((^b.b) c)) 2. ==[ alpha ]==> (((a (a a))(^x.b))((^y.y) c)) 3. ==[ beta ]==> (((a (a a))(^x.b)) c) REDUCED to normal form. ------ 199863/23938410. ------ 1. ==[ start ]==> (((^a.b)(a (a a)))(((a a)(^a.a))((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)(a (a a)))(((a a)(^y.y))((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (b (((a a)(^y.y))((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (b (((a a)(^x.x))((^y.y)(^z.z)))) 5. ==[ beta ]==> (b (((a a)(^x.x))(^z.z))) 6. ==[ alpha ]==> (b (((a a)(^x.x))(^y.y))) REDUCED to normal form. ------ 199864/23938518. ------ 1. ==[ start ]==> ((a (^a.(^a.(^a.a))))(((^a.a)(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(((^x1.x1)(^y1.y1))((a a)(^z1.z1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((^y1.y1)((a a)(^z1.z1)))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((^x1.x1)((a a)(^y1.y1)))) 5. ==[ beta ]==> ((a (^x.(^y.(^z.z))))((a a)(^y1.y1))) 6. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))((a a)(^x1.x1))) REDUCED to normal form. ------ 199865/23938617. ------ 1. ==[ start ]==> (((a (a a))(a b))(b (^c.(a a)))) 2. ==[ alpha ]==> (((a (a a))(a b))(b (^x.(a a)))) REDUCED to normal form. ------ 199866/23938698. ------ 1. ==[ start ]==> (((a b)(a (a a)))((^b.b)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a (a a)))((^x.x)(a (^y.y)))) 3. ==[ beta ]==> (((a b)(a (a a)))(a (^y.y))) 4. ==[ alpha ]==> (((a b)(a (a a)))(a (^x.x))) REDUCED to normal form. ------ 199867/23938725. ------ 1. ==[ start ]==> ((((^a.a)(a a))((^a.a) a))((^a.(^a.(^a.a)))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((^y.y) a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 3. ==[ beta ]==> (((a a)((^y.y) a))((^z.(^x1.(^y1.y1)))((^z1.z1) a))) 4. ==[ alpha ]==> (((a a)((^x.x) a))((^y.(^z.(^x1.x1)))((^y1.y1) a))) 5. ==[ beta ]==> (((a a) a)((^y.(^z.(^x1.x1)))((^y1.y1) a))) 6. ==[ alpha ]==> (((a a) a)((^x.(^y.(^z.z)))((^x1.x1) a))) 7. ==[ beta ]==> (((a a) a)(^y.(^z.z))) 8. ==[ alpha ]==> (((a a) a)(^x.(^y.y))) REDUCED to normal form. ------ 199868/23938806. ------ 1. ==[ start ]==> ((a (a (^a.(^a.a))))((^b.(a a))((a a) a))) 2. ==[ alpha ]==> ((a (a (^x.(^y.y))))((^z.(a a))((a a) a))) 3. ==[ beta ]==> ((a (a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 199869/23939382. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a a))(((^a.a) b)(a a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a a))(((^x1.x1) b)(a a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^x1.x1) b)(a a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z) b)(a a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199870/23939391. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.a))((^b.b) b)) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.x1) b)) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) b) REDUCED to normal form. ------ 199871/23939409. ------ 1. ==[ start ]==> ((a (^b.b))((a (^a.(^a.a)))(a (^a.a)))) 2. ==[ alpha ]==> ((a (^x.x))((a (^y.(^z.z)))(a (^x1.x1)))) REDUCED to normal form. ------ 199872/23939724. ------ 1. ==[ start ]==> ((a ((^a.a) b))((^b.b)(a a))) 2. ==[ alpha ]==> ((a ((^x.x) b))((^y.y)(a a))) 3. ==[ beta ]==> ((a b)((^y.y)(a a))) 4. ==[ alpha ]==> ((a b)((^x.x)(a a))) 5. ==[ beta ]==> ((a b)(a a)) REDUCED to normal form. ------ 199873/23940012. ------ 1. ==[ start ]==> (((a (^a.(^a.a))) b)((a a)(^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y))) b)((a a)(^z.z))) REDUCED to normal form. ------ 199874/23940039. ------ 1. ==[ start ]==> ((((^a.a) b) a)(((^a.a) b) a)) 2. ==[ alpha ]==> ((((^x.x) b) a)(((^y.y) b) a)) 3. ==[ beta ]==> ((b a)(((^y.y) b) a)) 4. ==[ alpha ]==> ((b a)(((^x.x) b) a)) 5. ==[ beta ]==> ((b a)(b a)) REDUCED to normal form. ------ 199875/23940066. ------ 1. ==[ start ]==> (((a a)(^b.b))((a (^a.(^a.a))) b)) 2. ==[ alpha ]==> (((a a)(^x.x))((a (^y.(^z.z))) b)) REDUCED to normal form. ------ 199876/23940093. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(^a.(^a.a))))((b a) c)) 2. ==[ alpha ]==> (((a (^x.x))(^y.(^z.(^x1.x1))))((b a) c)) REDUCED to normal form. ------ 199877/23940327. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(a (^a.a)))(b (a (^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(a (^x1.x1)))(b (a (^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.(^z.z))(b (a (^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.(^y.y))(b (a (^z.(^x1.x1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199878/23940363. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))((^b.b) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))((^z.z) a)) 3. ==[ beta ]==> ((b (^y.y))((^z.z) a)) 4. ==[ alpha ]==> ((b (^x.x))((^y.y) a)) 5. ==[ beta ]==> ((b (^x.x)) a) REDUCED to normal form. ------ 199879/23940669. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(a (^a.a)))(a (^b.b))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.z)))(a (^x1.x1))) REDUCED to normal form. ------ 199880/23940696. ------ 1. ==[ start ]==> ((((^a.a) b)(a a))((^a.(^a.(^a.a)))(a a))) 2. ==[ alpha ]==> ((((^x.x) b)(a a))((^y.(^z.(^x1.x1)))(a a))) 3. ==[ beta ]==> ((b (a a))((^y.(^z.(^x1.x1)))(a a))) 4. ==[ alpha ]==> ((b (a a))((^x.(^y.(^z.z)))(a a))) 5. ==[ beta ]==> ((b (a a))(^y.(^z.z))) 6. ==[ alpha ]==> ((b (a a))(^x.(^y.y))) REDUCED to normal form. ------ 199881/23941038. ------ 1. ==[ start ]==> ((((^a.a) b) b)(((a a)(^a.a)) c)) 2. ==[ alpha ]==> ((((^x.x) b) b)(((a a)(^y.y)) c)) 3. ==[ beta ]==> ((b b)(((a a)(^y.y)) c)) 4. ==[ alpha ]==> ((b b)(((a a)(^x.x)) c)) REDUCED to normal form. ------ 199882/23941245. ------ 1. ==[ start ]==> (((^a.b)(a b))(b (b a))) 2. ==[ alpha ]==> (((^x.b)(a b))(b (b a))) 3. ==[ beta ]==> (b (b (b a))) REDUCED to normal form. ------ 199883/23941353. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a) a))(((^a.a)(a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1) a))(((^y1.y1)(a a))((^z1.z1) a))) 3. ==[ beta ]==> ((^y.(^z.z))(((^y1.y1)(a a))((^z1.z1) a))) 4. ==[ alpha ]==> ((^x.(^y.y))(((^z.z)(a a))((^x1.x1) a))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199884/23941560. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((a a)(^a.a)))(a (^a.(^a.(^a.a))))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((a a)(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (((^y.y)((a a)(^z.z)))(a (^x1.(^y1.(^z1.z1))))) 4. ==[ alpha ]==> (((^x.x)((a a)(^y.y)))(a (^z.(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a a)(^y.y))(a (^z.(^x1.(^y1.y1))))) 6. ==[ alpha ]==> (((a a)(^x.x))(a (^y.(^z.(^x1.x1))))) REDUCED to normal form. ------ 199885/23941614. ------ 1. ==[ start ]==> (((a b)(a b))((^c.(^a.a))(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(a b))((^x.(^y.y))(a (^z.z)))) 3. ==[ beta ]==> (((a b)(a b))(^y.y)) 4. ==[ alpha ]==> (((a b)(a b))(^x.x)) REDUCED to normal form. ------ 199886/23941641. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a) a))((^b.(a a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a) a))((^y.(a a))((^z.z) a))) 3. ==[ beta ]==> (((a a)((a a) a))((^y.(a a))((^z.z) a))) 4. ==[ alpha ]==> (((a a)((a a) a))((^x.(a a))((^y.y) a))) 5. ==[ beta ]==> (((a a)((a a) a))(a a)) REDUCED to normal form. ------ 199887/23941668. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(^a.a)))((^a.b)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(^z.z)))((^x1.b)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(^z.z))((^x1.b)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.y))((^z.b)(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(^y.y)) b) REDUCED to normal form. ------ 199888/23941722. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a) a))((^b.(^a.a))((a a) a))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z) a))((^x1.(^y1.y1))((a a) a))) 3. ==[ beta ]==> (((a (^x.(^y.y))) a)((^x1.(^y1.y1))((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y))) a)((^z.(^x1.x1))((a a) a))) 5. ==[ beta ]==> (((a (^x.(^y.y))) a)(^x1.x1)) 6. ==[ alpha ]==> (((a (^x.(^y.y))) a)(^z.z)) REDUCED to normal form. ------ 199889/23941749. ------ 1. ==[ start ]==> ((((^a.a) b)(a (^a.a)))((^a.(a a))(a b))) 2. ==[ alpha ]==> ((((^x.x) b)(a (^y.y)))((^z.(z z))(a b))) 3. ==[ beta ]==> ((b (a (^y.y)))((^z.(z z))(a b))) 4. ==[ alpha ]==> ((b (a (^x.x)))((^y.(y y))(a b))) 5. ==[ beta ]==> ((b (a (^x.x)))((a b)(a b))) REDUCED to normal form. ------ 199890/23941776. ------ 1. ==[ start ]==> ((((a a)(a a))(a a))((^b.a)((^a.a)(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a a))((^x.a)((^y.y)(a a)))) 3. ==[ beta ]==> ((((a a)(a a))(a a)) a) REDUCED to normal form. ------ 199891/23941803. ------ 1. ==[ start ]==> ((a (b (^a.a)))((^a.(^a.a))((a a)(^a.a)))) 2. ==[ alpha ]==> ((a (b (^x.x)))((^y.(^z.z))((a a)(^x1.x1)))) 3. ==[ beta ]==> ((a (b (^x.x)))(^z.z)) 4. ==[ alpha ]==> ((a (b (^x.x)))(^y.y)) REDUCED to normal form. ------ 199892/23942082. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.(a a)))(b ((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.(x1 x1)))(b ((a a)(^y1.y1)))) 3. ==[ beta ]==> ((^y.(^z.z))(b ((a a)(^y1.y1)))) 4. ==[ alpha ]==> ((^x.(^y.y))(b ((a a)(^z.z)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199893/23942118. ------ 1. ==[ start ]==> ((((^a.a) b) c)((^d.a) a)) 2. ==[ alpha ]==> ((((^x.x) b) c)((^y.a) a)) 3. ==[ beta ]==> ((b c)((^y.a) a)) 4. ==[ alpha ]==> ((b c)((^x.a) a)) 5. ==[ beta ]==> ((b c) a) REDUCED to normal form. ------ 199894/23942145. ------ 1. ==[ start ]==> ((((a a)(a a)) b)((^c.(^a.a)) b)) 2. ==[ alpha ]==> ((((a a)(a a)) b)((^x.(^y.y)) b)) 3. ==[ beta ]==> ((((a a)(a a)) b)(^y.y)) 4. ==[ alpha ]==> ((((a a)(a a)) b)(^x.x)) REDUCED to normal form. ------ 199895/23942190. ------ 1. ==[ start ]==> (((^a.a)(b (^a.a)))((a b)((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(b (^y.y)))((a b)((^z.z) a))) 3. ==[ beta ]==> ((b (^y.y))((a b)((^z.z) a))) 4. ==[ alpha ]==> ((b (^x.x))((a b)((^y.y) a))) 5. ==[ beta ]==> ((b (^x.x))((a b) a)) REDUCED to normal form. ------ 199896/23942217. ------ 1. ==[ start ]==> (((^a.(^a.a))((a a)(a a)))(((a a) a)(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.y))((a a)(a a)))(((a a) a)(a (a a)))) 3. ==[ beta ]==> ((^y.y)(((a a) a)(a (a a)))) 4. ==[ alpha ]==> ((^x.x)(((a a) a)(a (a a)))) 5. ==[ beta ]==> (((a a) a)(a (a a))) REDUCED to normal form. ------ 199897/23942271. ------ 1. ==[ start ]==> (((^a.(a a))(a (^a.(^a.a))))((a (a a))((a a) a))) 2. ==[ alpha ]==> (((^x.(x x))(a (^y.(^z.z))))((a (a a))((a a) a))) 3. ==[ beta ]==> (((a (^y.(^z.z)))(a (^y.(^z.z))))((a (a a))((a a) a))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(a (^z.(^x1.x1))))((a (a a))((a a) a))) REDUCED to normal form. ------ 199898/23942352. ------ 1. ==[ start ]==> (((^a.b)((^a.a)(a a)))((a a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((^x.b)((^y.y)(a a)))((a a)((a a)(^z.z)))) 3. ==[ beta ]==> (b ((a a)((a a)(^z.z)))) 4. ==[ alpha ]==> (b ((a a)((a a)(^x.x)))) REDUCED to normal form. ------ 199899/23942388. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^a.b))(((a a)(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.b))(((a a)(^z.z))(^x1.x1))) 3. ==[ beta ]==> (((a a)(^y.b))(((a a)(^z.z))(^x1.x1))) 4. ==[ alpha ]==> (((a a)(^x.b))(((a a)(^y.y))(^z.z))) REDUCED to normal form. ------ 199900/23942469. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))(^a.(a a)))(((a a) a)(^a.(a a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.(z z)))(((a a) a)(^x1.(x1 x1)))) REDUCED to normal form. ------ 199901/23942496. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.a))(((^a.a)(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 3. ==[ beta ]==> ((b (^y.a))(((^z.z)(^x1.x1))(^y1.(^z1.z1)))) 4. ==[ alpha ]==> ((b (^x.a))(((^y.y)(^z.z))(^x1.(^y1.y1)))) 5. ==[ beta ]==> ((b (^x.a))((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> ((b (^x.a))((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> ((b (^x.a))(^z.(^x1.x1))) 8. ==[ alpha ]==> ((b (^x.a))(^y.(^z.z))) REDUCED to normal form. ------ 199902/23942586. ------ 1. ==[ start ]==> (((a a)(b (^a.a)))((^a.(^a.a))((^a.a)(a a)))) 2. ==[ alpha ]==> (((a a)(b (^x.x)))((^y.(^z.z))((^x1.x1)(a a)))) 3. ==[ beta ]==> (((a a)(b (^x.x)))(^z.z)) 4. ==[ alpha ]==> (((a a)(b (^x.x)))(^y.y)) REDUCED to normal form. ------ 199903/23942613. ------ 1. ==[ start ]==> (((a (^a.a))((a a)(a a)))((^a.a)((a a)(^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((^y.y)((a a)(^z.z)))) 3. ==[ beta ]==> (((a (^x.x))((a a)(a a)))((a a)(^z.z))) 4. ==[ alpha ]==> (((a (^x.x))((a a)(a a)))((a a)(^y.y))) REDUCED to normal form. ------ 199904/23942640. ------ 1. ==[ start ]==> ((((^a.a) a)((^a.a) b))((^c.(^a.a))(^a.a))) 2. ==[ alpha ]==> ((((^x.x) a)((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> ((a ((^y.y) b))((^z.(^x1.x1))(^y1.y1))) 4. ==[ alpha ]==> ((a ((^x.x) b))((^y.(^z.z))(^x1.x1))) 5. ==[ beta ]==> ((a b)((^y.(^z.z))(^x1.x1))) 6. ==[ alpha ]==> ((a b)((^x.(^y.y))(^z.z))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 199905/23942667. ------ 1. ==[ start ]==> (((a (a a))(a (^a.(^a.a))))((^b.(a a))(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (a a))(a (^x.(^y.y))))((^z.(a a))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (a a))(a (^x.(^y.y))))(a a)) REDUCED to normal form. ------ 199906/23942694. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(b a))((^a.b)(^b.a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(b a))((^z.b)(^x1.a))) 3. ==[ beta ]==> (((^y.y)(b a))((^z.b)(^x1.a))) 4. ==[ alpha ]==> (((^x.x)(b a))((^y.b)(^z.a))) 5. ==[ beta ]==> ((b a)((^y.b)(^z.a))) 6. ==[ alpha ]==> ((b a)((^x.b)(^y.a))) 7. ==[ beta ]==> ((b a) b) REDUCED to normal form. ------ 199907/23942748. ------ 1. ==[ start ]==> (((a b)((^a.a)(a a)))((^b.(^a.a))(^b.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x)(a a)))((^y.(^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a b)(a a))((^y.(^z.z))(^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((a b)(a a))((^x.(^y.y))(^z.(^x1.x1)))) 5. ==[ beta ]==> (((a b)(a a))(^y.y)) 6. ==[ alpha ]==> (((a b)(a a))(^x.x)) REDUCED to normal form. ------ 199908/23942775. ------ 1. ==[ start ]==> ((((^a.a)(a a))(a b))((^a.(a a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x)(a a))(a b))((^y.(y y))(^z.a))) 3. ==[ beta ]==> (((a a)(a b))((^y.(y y))(^z.a))) 4. ==[ alpha ]==> (((a a)(a b))((^x.(x x))(^y.a))) 5. ==[ beta ]==> (((a a)(a b))((^y.a)(^y.a))) 6. ==[ alpha ]==> (((a a)(a b))((^x.a)(^y.a))) 7. ==[ beta ]==> (((a a)(a b)) a) REDUCED to normal form. ------ 199909/23942802. ------ 1. ==[ start ]==> ((((a a)(^a.a))((a a) a))((^b.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(^x.x))((a a) a))((^y.a)(^z.b))) 3. ==[ beta ]==> ((((a a)(^x.x))((a a) a)) a) REDUCED to normal form. ------ 199910/23943054. ------ 1. ==[ start ]==> (((^a.(a a))(^b.b))((a (^a.a))(a b))) 2. ==[ alpha ]==> (((^x.(x x))(^y.y))((a (^z.z))(a b))) 3. ==[ beta ]==> (((^y.y)(^y.y))((a (^z.z))(a b))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a (^z.z))(a b))) 5. ==[ beta ]==> ((^y.y)((a (^z.z))(a b))) 6. ==[ alpha ]==> ((^x.x)((a (^y.y))(a b))) 7. ==[ beta ]==> ((a (^y.y))(a b)) 8. ==[ alpha ]==> ((a (^x.x))(a b)) REDUCED to normal form. ------ 199911/23943360. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a) a)((a b) b)) 2. ==[ alpha ]==> ((((^x.(^y.y)) a) a)((a b) b)) 3. ==[ beta ]==> (((^y.y) a)((a b) b)) 4. ==[ alpha ]==> (((^x.x) a)((a b) b)) 5. ==[ beta ]==> (a ((a b) b)) REDUCED to normal form. ------ 199912/23943540. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(a ((^a.a)(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(a ((^z.z)(a a)))) 3. ==[ beta ]==> (b (a ((^z.z)(a a)))) 4. ==[ alpha ]==> (b (a ((^x.x)(a a)))) 5. ==[ beta ]==> (b (a (a a))) REDUCED to normal form. ------ 199913/23943549. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))((^b.(a a)) a)) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))((^z.(a a)) a)) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(a a)) REDUCED to normal form. ------ 199914/23943576. ------ 1. ==[ start ]==> ((((^a.a)(a a))(^b.(a a)))((^a.b) b)) 2. ==[ alpha ]==> ((((^x.x)(a a))(^y.(a a)))((^z.b) b)) 3. ==[ beta ]==> (((a a)(^y.(a a)))((^z.b) b)) 4. ==[ alpha ]==> (((a a)(^x.(a a)))((^y.b) b)) 5. ==[ beta ]==> (((a a)(^x.(a a))) b) REDUCED to normal form. ------ 199915/23943603. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^a.b))((^c.a) c)) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.b))((^z.a) c)) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.b)) a) REDUCED to normal form. ------ 199916/23943648. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))((^a.a)(^a.a)))((a (a a))(a (a a)))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))((^x1.x1)(^y1.y1)))((a (a a))(a (a a)))) 3. ==[ beta ]==> ((^y.(^z.z))((a (a a))(a (a a)))) 4. ==[ alpha ]==> ((^x.(^y.y))((a (a a))(a (a a)))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199917/23943765. ------ 1. ==[ start ]==> ((((^a.(^a.a)) a)(^a.a))((a b)(^a.a))) 2. ==[ alpha ]==> ((((^x.(^y.y)) a)(^z.z))((a b)(^x1.x1))) 3. ==[ beta ]==> (((^y.y)(^z.z))((a b)(^x1.x1))) 4. ==[ alpha ]==> (((^x.x)(^y.y))((a b)(^z.z))) 5. ==[ beta ]==> ((^y.y)((a b)(^z.z))) 6. ==[ alpha ]==> ((^x.x)((a b)(^y.y))) 7. ==[ beta ]==> ((a b)(^y.y)) 8. ==[ alpha ]==> ((a b)(^x.x)) REDUCED to normal form. ------ 199918/23943828. ------ 1. ==[ start ]==> (((a (^a.a))(b (^a.a)))((^b.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a (^x.x))(b (^y.y)))(^x1.x1)) 4. ==[ alpha ]==> (((a (^x.x))(b (^y.y)))(^z.z)) REDUCED to normal form. ------ 199919/23943855. ------ 1. ==[ start ]==> ((((^a.a) a)((a a)(a a)))((^a.(a a))(a (a a)))) 2. ==[ alpha ]==> ((((^x.x) a)((a a)(a a)))((^y.(y y))(a (a a)))) 3. ==[ beta ]==> ((a ((a a)(a a)))((^y.(y y))(a (a a)))) 4. ==[ alpha ]==> ((a ((a a)(a a)))((^x.(x x))(a (a a)))) 5. ==[ beta ]==> ((a ((a a)(a a)))((a (a a))(a (a a)))) REDUCED to normal form. ------ 199920/23943882. ------ 1. ==[ start ]==> (((a (a a))((^a.a) b))((^b.a)((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((a (a a))((^x.x) b))((^y.a)((^z.z)(^x1.x1)))) 3. ==[ beta ]==> (((a (a a)) b)((^y.a)((^z.z)(^x1.x1)))) 4. ==[ alpha ]==> (((a (a a)) b)((^x.a)((^y.y)(^z.z)))) 5. ==[ beta ]==> (((a (a a)) b) a) REDUCED to normal form. ------ 199921/23943909. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))(a (^a.(^a.a))))((^a.(^a.a))((a a) a))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))(a (^z.(^x1.x1))))((^y1.(^z1.z1))((a a) a))) 3. ==[ beta ]==> (((^y.y)(a (^z.(^x1.x1))))((^y1.(^z1.z1))((a a) a))) 4. ==[ alpha ]==> (((^x.x)(a (^y.(^z.z))))((^x1.(^y1.y1))((a a) a))) 5. ==[ beta ]==> ((a (^y.(^z.z)))((^x1.(^y1.y1))((a a) a))) 6. ==[ alpha ]==> ((a (^x.(^y.y)))((^z.(^x1.x1))((a a) a))) 7. ==[ beta ]==> ((a (^x.(^y.y)))(^x1.x1)) 8. ==[ alpha ]==> ((a (^x.(^y.y)))(^z.z)) REDUCED to normal form. ------ 199922/23943936. ------ 1. ==[ start ]==> ((((a a) a)(b a))((^a.a)(a b))) 2. ==[ alpha ]==> ((((a a) a)(b a))((^x.x)(a b))) 3. ==[ beta ]==> ((((a a) a)(b a))(a b)) REDUCED to normal form. ------ 199923/23943963. ------ 1. ==[ start ]==> (((a b)((a a)(^a.a)))((^a.b)(^a.a))) 2. ==[ alpha ]==> (((a b)((a a)(^x.x)))((^y.b)(^z.z))) 3. ==[ beta ]==> (((a b)((a a)(^x.x))) b) REDUCED to normal form. ------ 199924/23944017. ------ 1. ==[ start ]==> ((((a a)(^a.a))(a b))((^b.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(a b))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(a b))(^z.z)) 4. ==[ alpha ]==> ((((a a)(^x.x))(a b))(^y.y)) REDUCED to normal form. ------ 199925/23944071. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((^a.a)(^a.a)))((^b.a)(^b.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((^z.z)(^x1.x1)))((^y1.a)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))(^x1.x1))((^y1.a)(^z1.(^x2.x2)))) 4. ==[ alpha ]==> (((a (^x.(^y.y)))(^z.z))((^x1.a)(^y1.(^z1.z1)))) 5. ==[ beta ]==> (((a (^x.(^y.y)))(^z.z)) a) REDUCED to normal form. ------ 199926/23944098. ------ 1. ==[ start ]==> ((((^a.a) b)(a (a a)))((^a.(^a.a))(^c.a))) 2. ==[ alpha ]==> ((((^x.x) b)(a (a a)))((^y.(^z.z))(^x1.a))) 3. ==[ beta ]==> ((b (a (a a)))((^y.(^z.z))(^x1.a))) 4. ==[ alpha ]==> ((b (a (a a)))((^x.(^y.y))(^z.a))) 5. ==[ beta ]==> ((b (a (a a)))(^y.y)) 6. ==[ alpha ]==> ((b (a (a a)))(^x.x)) REDUCED to normal form. ------ 199927/23944125. ------ 1. ==[ start ]==> ((((a a)(a a))((^a.a) a))((^a.a)(^a.b))) 2. ==[ alpha ]==> ((((a a)(a a))((^x.x) a))((^y.y)(^z.b))) 3. ==[ beta ]==> ((((a a)(a a)) a)((^y.y)(^z.b))) 4. ==[ alpha ]==> ((((a a)(a a)) a)((^x.x)(^y.b))) 5. ==[ beta ]==> ((((a a)(a a)) a)(^y.b)) 6. ==[ alpha ]==> ((((a a)(a a)) a)(^x.b)) REDUCED to normal form. ------ 199928/23944197. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) a)((^b.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) a)((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((a (^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((a (^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((a (^x.x))(^z.z)) 6. ==[ alpha ]==> ((a (^x.x))(^y.y)) REDUCED to normal form. ------ 199929/23944215. ------ 1. ==[ start ]==> (((^a.a)(^a.(a (^a.a))))((a (a a))((^a.a) a))) 2. ==[ alpha ]==> (((^x.x)(^y.(y (^z.z))))((a (a a))((^x1.x1) a))) 3. ==[ beta ]==> ((^y.(y (^z.z)))((a (a a))((^x1.x1) a))) 4. ==[ alpha ]==> ((^x.(x (^y.y)))((a (a a))((^z.z) a))) 5. ==[ beta ]==> (((a (a a))((^z.z) a))(^y.y)) 6. ==[ alpha ]==> (((a (a a))((^x.x) a))(^y.y)) 7. ==[ beta ]==> (((a (a a)) a)(^y.y)) 8. ==[ alpha ]==> (((a (a a)) a)(^x.x)) REDUCED to normal form. ------ 199930/23944620. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.a))(b ((^a.a)(^a.a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.z))(b ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> (((^z.z)(^y.y))(b ((^x1.x1)(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)(^y.y))(b ((^z.z)(^x1.x1)))) 5. ==[ beta ]==> ((^y.y)(b ((^z.z)(^x1.x1)))) 6. ==[ alpha ]==> ((^x.x)(b ((^y.y)(^z.z)))) 7. ==[ beta ]==> (b ((^y.y)(^z.z))) 8. ==[ alpha ]==> (b ((^x.x)(^y.y))) 9. ==[ beta ]==> (b (^y.y)) 10. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199931/23944647. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(a ((a a) a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(a ((a a) a))) 3. ==[ beta ]==> ((a (a (^y.y)))(a ((a a) a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(a ((a a) a))) REDUCED to normal form. ------ 199932/23944674. ------ 1. ==[ start ]==> (((^a.(^a.a))((^a.(^a.a)) a))(((^a.a)(^a.a))(a a))) 2. ==[ alpha ]==> (((^x.(^y.y))((^z.(^x1.x1)) a))(((^y1.y1)(^z1.z1))(a a))) 3. ==[ beta ]==> ((^y.y)(((^y1.y1)(^z1.z1))(a a))) 4. ==[ alpha ]==> ((^x.x)(((^y.y)(^z.z))(a a))) 5. ==[ beta ]==> (((^y.y)(^z.z))(a a)) 6. ==[ alpha ]==> (((^x.x)(^y.y))(a a)) 7. ==[ beta ]==> ((^y.y)(a a)) 8. ==[ alpha ]==> ((^x.x)(a a)) 9. ==[ beta ]==> (a a) REDUCED to normal form. ------ 199933/23944728. ------ 1. ==[ start ]==> (((^a.(a a))((a a)(a a)))(((^a.a) a)((^a.a) a))) 2. ==[ alpha ]==> (((^x.(x x))((a a)(a a)))(((^y.y) a)((^z.z) a))) 3. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(((^y.y) a)((^z.z) a))) 4. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(((^x.x) a)((^y.y) a))) 5. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a ((^y.y) a))) 6. ==[ alpha ]==> ((((a a)(a a))((a a)(a a)))(a ((^x.x) a))) 7. ==[ beta ]==> ((((a a)(a a))((a a)(a a)))(a a)) REDUCED to normal form. ------ 199934/23944872. ------ 1. ==[ start ]==> ((((a a)(^a.a))(^b.(a a)))(((^a.a) a)(^b.a))) 2. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(((^z.z) a)(^x1.a))) 3. ==[ beta ]==> ((((a a)(^x.x))(^y.(a a)))(a (^x1.a))) 4. ==[ alpha ]==> ((((a a)(^x.x))(^y.(a a)))(a (^z.a))) REDUCED to normal form. ------ 199935/23944953. ------ 1. ==[ start ]==> ((((^a.a) b)(^b.(^a.a)))(((^a.a)(^a.a)) a)) 2. ==[ alpha ]==> ((((^x.x) b)(^y.(^z.z)))(((^x1.x1)(^y1.y1)) a)) 3. ==[ beta ]==> ((b (^y.(^z.z)))(((^x1.x1)(^y1.y1)) a)) 4. ==[ alpha ]==> ((b (^x.(^y.y)))(((^z.z)(^x1.x1)) a)) 5. ==[ beta ]==> ((b (^x.(^y.y)))((^x1.x1) a)) 6. ==[ alpha ]==> ((b (^x.(^y.y)))((^z.z) a)) 7. ==[ beta ]==> ((b (^x.(^y.y))) a) REDUCED to normal form. ------ 199936/23944980. ------ 1. ==[ start ]==> ((((a a)(a a))(^a.(a a)))((a (a a)) b)) 2. ==[ alpha ]==> ((((a a)(a a))(^x.(x x)))((a (a a)) b)) REDUCED to normal form. ------ 199937/23945052. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(a a))(b (a (a a)))) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(a a))(b (a (a a)))) 3. ==[ beta ]==> (((a a)(^y.y))(b (a (a a)))) 4. ==[ alpha ]==> (((a a)(^x.x))(b (a (a a)))) REDUCED to normal form. ------ 199938/23945079. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(a ((^a.a)(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a ((^x1.x1)(^y1.y1)))) 3. ==[ beta ]==> ((a (^x.(^y.(^z.z))))(a (^y1.y1))) 4. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(a (^x1.x1))) REDUCED to normal form. ------ 199939/23945151. ------ 1. ==[ start ]==> ((((^a.a) a)(b (^a.a)))(c (^b.a))) 2. ==[ alpha ]==> ((((^x.x) a)(b (^y.y)))(c (^z.a))) 3. ==[ beta ]==> ((a (b (^y.y)))(c (^z.a))) 4. ==[ alpha ]==> ((a (b (^x.x)))(c (^y.a))) REDUCED to normal form. ------ 199940/23945178. ------ 1. ==[ start ]==> (((a (a a))((a a)(a a)))(b (^a.(a a)))) 2. ==[ alpha ]==> (((a (a a))((a a)(a a)))(b (^x.(x x)))) REDUCED to normal form. ------ 199941/23945205. ------ 1. ==[ start ]==> ((((^a.a)(^a.a))((^a.a) b))(a (^b.(^a.a)))) 2. ==[ alpha ]==> ((((^x.x)(^y.y))((^z.z) b))(a (^x1.(^y1.y1)))) 3. ==[ beta ]==> (((^y.y)((^z.z) b))(a (^x1.(^y1.y1)))) 4. ==[ alpha ]==> (((^x.x)((^y.y) b))(a (^z.(^x1.x1)))) 5. ==[ beta ]==> (((^y.y) b)(a (^z.(^x1.x1)))) 6. ==[ alpha ]==> (((^x.x) b)(a (^y.(^z.z)))) 7. ==[ beta ]==> (b (a (^y.(^z.z)))) 8. ==[ alpha ]==> (b (a (^x.(^y.y)))) REDUCED to normal form. ------ 199942/23945232. ------ 1. ==[ start ]==> ((((a a) a)(a (^a.(^a.a))))((^a.(a a))(a a))) 2. ==[ alpha ]==> ((((a a) a)(a (^x.(^y.y))))((^z.(z z))(a a))) 3. ==[ beta ]==> ((((a a) a)(a (^x.(^y.y))))((a a)(a a))) REDUCED to normal form. ------ 199943/23945259. ------ 1. ==[ start ]==> (((a b)(b a))((^b.a)(a (^a.a)))) 2. ==[ alpha ]==> (((a b)(b a))((^x.a)(a (^y.y)))) 3. ==[ beta ]==> (((a b)(b a)) a) REDUCED to normal form. ------ 199944/23945286. ------ 1. ==[ start ]==> ((((^a.a)(a a))((a a)(^a.a)))((^a.(^a.a))((^a.a) a))) 2. ==[ alpha ]==> ((((^x.x)(a a))((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 3. ==[ beta ]==> (((a a)((a a)(^y.y)))((^z.(^x1.x1))((^y1.y1) a))) 4. ==[ alpha ]==> (((a a)((a a)(^x.x)))((^y.(^z.z))((^x1.x1) a))) 5. ==[ beta ]==> (((a a)((a a)(^x.x)))(^z.z)) 6. ==[ alpha ]==> (((a a)((a a)(^x.x)))(^y.y)) REDUCED to normal form. ------ 199945/23945313. ------ 1. ==[ start ]==> ((((a a)(^a.a))((^a.a)(a a)))((^a.a)(a (a a)))) 2. ==[ alpha ]==> ((((a a)(^x.x))((^y.y)(a a)))((^z.z)(a (a a)))) 3. ==[ beta ]==> ((((a a)(^x.x))(a a))((^z.z)(a (a a)))) 4. ==[ alpha ]==> ((((a a)(^x.x))(a a))((^y.y)(a (a a)))) 5. ==[ beta ]==> ((((a a)(^x.x))(a a))(a (a a))) REDUCED to normal form. ------ 199946/23945367. ------ 1. ==[ start ]==> (((a (^a.(^a.a)))((a a) a))((^b.a)(^a.(^a.a)))) 2. ==[ alpha ]==> (((a (^x.(^y.y)))((a a) a))((^z.a)(^x1.(^y1.y1)))) 3. ==[ beta ]==> (((a (^x.(^y.y)))((a a) a)) a) REDUCED to normal form. ------ 199947/23945394. ------ 1. ==[ start ]==> ((((^a.a) b)((^a.a)(^a.a)))((^a.(^a.a))(^b.a))) 2. ==[ alpha ]==> ((((^x.x) b)((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 3. ==[ beta ]==> ((b ((^y.y)(^z.z)))((^x1.(^y1.y1))(^z1.a))) 4. ==[ alpha ]==> ((b ((^x.x)(^y.y)))((^z.(^x1.x1))(^y1.a))) 5. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1))(^y1.a))) 6. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z))(^x1.a))) 7. ==[ beta ]==> ((b (^x.x))(^z.z)) 8. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 199948/23945421. ------ 1. ==[ start ]==> ((((a a)(a a))(a (a a)))((^a.a)(^a.(a a)))) 2. ==[ alpha ]==> ((((a a)(a a))(a (a a)))((^x.x)(^y.(y y)))) 3. ==[ beta ]==> ((((a a)(a a))(a (a a)))(^y.(y y))) 4. ==[ alpha ]==> ((((a a)(a a))(a (a a)))(^x.(x x))) REDUCED to normal form. ------ 199949/23945493. ------ 1. ==[ start ]==> (((^a.(a (^a.a))) b)((^a.(^a.a)) c)) 2. ==[ alpha ]==> (((^x.(x (^y.y))) b)((^z.(^x1.x1)) c)) 3. ==[ beta ]==> ((b (^y.y))((^z.(^x1.x1)) c)) 4. ==[ alpha ]==> ((b (^x.x))((^y.(^z.z)) c)) 5. ==[ beta ]==> ((b (^x.x))(^z.z)) 6. ==[ alpha ]==> ((b (^x.x))(^y.y)) REDUCED to normal form. ------ 199950/23945502. ------ 1. ==[ start ]==> (((a (a (^a.a)))(a a))(b (^b.a))) 2. ==[ alpha ]==> (((a (a (^x.x)))(a a))(b (^y.a))) REDUCED to normal form. ------ 199951/23945529. ------ 1. ==[ start ]==> ((a ((^a.a)(^a.(^a.a))))(a (^a.(a a)))) 2. ==[ alpha ]==> ((a ((^x.x)(^y.(^z.z))))(a (^x1.(x1 x1)))) 3. ==[ beta ]==> ((a (^y.(^z.z)))(a (^x1.(x1 x1)))) 4. ==[ alpha ]==> ((a (^x.(^y.y)))(a (^z.(z z)))) REDUCED to normal form. ------ 199952/23945700. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.(^a.a))))(a ((^a.a) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.(^x1.x1))))(a ((^y1.y1) a))) 3. ==[ beta ]==> (b (a ((^y1.y1) a))) 4. ==[ alpha ]==> (b (a ((^x.x) a))) 5. ==[ beta ]==> (b (a a)) REDUCED to normal form. ------ 199953/23945808. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a)))(^a.b))(b b)) 2. ==[ alpha ]==> (((^x.(^y.(^z.z)))(^x1.b))(b b)) 3. ==[ beta ]==> ((^y.(^z.z))(b b)) 4. ==[ alpha ]==> ((^x.(^y.y))(b b)) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199954/23945943. ------ 1. ==[ start ]==> (((^a.(a (^a.a)))(^a.(^a.a)))(b a)) 2. ==[ alpha ]==> (((^x.(x (^y.y)))(^z.(^x1.x1)))(b a)) 3. ==[ beta ]==> (((^z.(^x1.x1))(^y.y))(b a)) 4. ==[ alpha ]==> (((^x.(^y.y))(^z.z))(b a)) 5. ==[ beta ]==> ((^y.y)(b a)) 6. ==[ alpha ]==> ((^x.x)(b a)) 7. ==[ beta ]==> (b a) REDUCED to normal form. ------ 199955/23945952. ------ 1. ==[ start ]==> (((a (a (^a.a))) b)((a a)(^a.a))) 2. ==[ alpha ]==> (((a (a (^x.x))) b)((a a)(^y.y))) REDUCED to normal form. ------ 199956/23945979. ------ 1. ==[ start ]==> ((((^a.a)(^a.(^a.a))) a)((a a) a)) 2. ==[ alpha ]==> ((((^x.x)(^y.(^z.z))) a)((a a) a)) 3. ==[ beta ]==> (((^y.(^z.z)) a)((a a) a)) 4. ==[ alpha ]==> (((^x.(^y.y)) a)((a a) a)) 5. ==[ beta ]==> ((^y.y)((a a) a)) 6. ==[ alpha ]==> ((^x.x)((a a) a)) 7. ==[ beta ]==> ((a a) a) REDUCED to normal form. ------ 199957/23945997. ------ 1. ==[ start ]==> (((^a.a)((^a.a)(^a.(^a.a))))(a (a a))) 2. ==[ alpha ]==> (((^x.x)((^y.y)(^z.(^x1.x1))))(a (a a))) 3. ==[ beta ]==> (((^y.y)(^z.(^x1.x1)))(a (a a))) 4. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(a (a a))) 5. ==[ beta ]==> ((^y.(^z.z))(a (a a))) 6. ==[ alpha ]==> ((^x.(^y.y))(a (a a))) 7. ==[ beta ]==> (^y.y) 8. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199958/23946006. ------ 1. ==[ start ]==> (((a a)(^b.(^a.(^a.a))))((^a.a) a)) 2. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((^x1.x1) a)) 3. ==[ beta ]==> (((a a)(^x.(^y.(^z.z)))) a) REDUCED to normal form. ------ 199959/23946024. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a (^a.a))))(a a)) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a (^z.z))))(a a)) 3. ==[ beta ]==> ((^y.y)(a a)) 4. ==[ alpha ]==> ((^x.x)(a a)) 5. ==[ beta ]==> (a a) REDUCED to normal form. ------ 199960/23946032. ------ 1. ==[ start ]==> (^a.((a (^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (^x.((x (^y.y))(^z.(z (^x1.x1))))) REDUCED to normal form. ------ 199961/23946033. ------ 1. ==[ start ]==> (a ((a (^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> (a ((a (^x.x))(^y.(y (^z.z))))) REDUCED to normal form. ------ 199962/23946531. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))(^z.(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 199963/23957061. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))(^y1.(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199964/23958009. ------ 1. ==[ start ]==> (((^a.(^a.a))(a (a (^a.a)))) b) 2. ==[ alpha ]==> (((^x.(^y.y))(a (a (^z.z)))) b) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 199965/23958018. ------ 1. ==[ start ]==> (((a (^a.a))(^a.(a (^a.a)))) a) 2. ==[ alpha ]==> (((a (^x.x))(^y.(y (^z.z)))) a) REDUCED to normal form. ------ 199966/23958024. ------ 1. ==[ start ]==> ((^a.a)((a (^a.a))(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.x)((a (^y.y))(^z.(z (^x1.x1))))) 3. ==[ beta ]==> ((a (^y.y))(^z.(z (^x1.x1)))) 4. ==[ alpha ]==> ((a (^x.x))(^y.(y (^z.z)))) REDUCED to normal form. ------ 199967/23958033. ------ 1. ==[ start ]==> ((^a.(^a.a))((^a.(^a.a))(a (a (^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.y))((^z.(^x1.x1))(a (a (^y1.y1))))) 3. ==[ beta ]==> (^y.y) 4. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199968/23958051. ------ 1. ==[ start ]==> ((^a.(a a))((a a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(x x))((a a)(^y.(^z.(^x1.x1))))) 3. ==[ beta ]==> (((a a)(^y.(^z.(^x1.x1))))((a a)(^y.(^z.(^x1.x1))))) 4. ==[ alpha ]==> (((a a)(^x.(^y.(^z.z))))((a a)(^x1.(^y1.(^z1.z1))))) REDUCED to normal form. ------ 199969/23958063. ------ 1. ==[ start ]==> (((^a.a)(^a.a))(^b.((^a.a)(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.y))(^z.((^x1.x1)(^y1.(^z1.z1))))) 3. ==[ beta ]==> ((^y.y)(^z.((^x1.x1)(^y1.(^z1.z1))))) 4. ==[ alpha ]==> ((^x.x)(^y.((^z.z)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (^y.((^z.z)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (^x.((^y.y)(^z.(^x1.x1)))) 7. ==[ beta ]==> (^x.(^z.(^x1.x1))) 8. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199970/23958078. ------ 1. ==[ start ]==> ((^a.b)(((^a.a)(^a.(^a.a))) a)) 2. ==[ alpha ]==> ((^x.b)(((^y.y)(^z.(^x1.x1))) a)) 3. ==[ beta ]==> b REDUCED to normal form. ------ 199971/23958114. ------ 1. ==[ start ]==> ((^a.(^a.(^a.a)))((^a.(a (^a.a)))(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.z)))((^x1.(x1 (^y1.y1)))(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.z)) 4. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form. ------ 199972/23958519. ------ 1. ==[ start ]==> ((^a.(^a.(a a)))((^a.a)(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((^x.(^y.(y y)))((^z.z)(^x1.(^y1.(^z1.z1))))) 3. ==[ beta ]==> (^y.(y y)) 4. ==[ alpha ]==> (^x.(x x)) REDUCED to normal form. ------ 199973/23958522. ------ 1. ==[ start ]==> ((a (^a.(a a)))(^b.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> ((a (^x.(x x)))(^y.(^z.(^x1.(^y1.y1))))) REDUCED to normal form. ------ 199974/23958981. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.a)))(^a.(^b.(^a.(^a.a))))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.z)))(^x1.(^y1.(^z1.(^x2.x2))))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.(^y1.(^z1.(^x2.x2))))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.(^x1.(^y1.(^z1.z1))))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199975/23959401. ------ 1. ==[ start ]==> ((^a.((a a) a))((a a)(^a.(a (^a.a))))) 2. ==[ alpha ]==> ((^x.((x x) x))((a a)(^y.(y (^z.z))))) 3. ==[ beta ]==> ((((a a)(^y.(y (^z.z))))((a a)(^y.(y (^z.z)))))((a a)(^y.(y (^z.z))))) 4. ==[ alpha ]==> ((((a a)(^x.(x (^y.y))))((a a)(^z.(z (^x1.x1)))))((a a)(^y1.(y1 (^z1.z1))))) REDUCED to normal form. ------ 199976/23959734. ------ 1. ==[ start ]==> ((^a.(^a.b))((^b.(^a.a))(^b.b))) 2. ==[ alpha ]==> ((^x.(^y.b))((^z.(^x1.x1))(^y1.y1))) 3. ==[ beta ]==> (^y.b) 4. ==[ alpha ]==> (^x.b) REDUCED to normal form. ------ 199977/23960277. ------ 1. ==[ start ]==> (((^a.b)(a a))(^a.(^a.(a (^a.a))))) 2. ==[ alpha ]==> (((^x.b)(a a))(^y.(^z.(z (^x1.x1))))) 3. ==[ beta ]==> (b (^y.(^z.(z (^x1.x1))))) 4. ==[ alpha ]==> (b (^x.(^y.(y (^z.z))))) REDUCED to normal form. ------ 199978/23960508. ------ 1. ==[ start ]==> ((^a.((^a.a)(a a)))((a b)(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.((^y.y)(x x)))((a b)(^z.(^x1.x1)))) 3. ==[ beta ]==> ((^y.y)(((a b)(^z.(^x1.x1)))((a b)(^z.(^x1.x1))))) 4. ==[ alpha ]==> ((^x.x)(((a b)(^y.(^z.z)))((a b)(^x1.(^y1.y1))))) 5. ==[ beta ]==> (((a b)(^y.(^z.z)))((a b)(^x1.(^y1.y1)))) 6. ==[ alpha ]==> (((a b)(^x.(^y.y)))((a b)(^z.(^x1.x1)))) REDUCED to normal form. ------ 199979/23960682. ------ 1. ==[ start ]==> (((^a.b)(^a.(^a.a)))(^b.((^a.(^a.a)) a))) 2. ==[ alpha ]==> (((^x.b)(^y.(^z.z)))(^x1.((^y1.(^z1.z1)) a))) 3. ==[ beta ]==> (b (^x1.((^y1.(^z1.z1)) a))) 4. ==[ alpha ]==> (b (^x.((^y.(^z.z)) a))) 5. ==[ beta ]==> (b (^x.(^z.z))) 6. ==[ alpha ]==> (b (^x.(^y.y))) REDUCED to normal form. ------ 199980/23961474. ------ 1. ==[ start ]==> (((a (^a.a))(^b.(a a)))(^c.(b (^a.a)))) 2. ==[ alpha ]==> (((a (^x.x))(^y.(a a)))(^z.(b (^x1.x1)))) REDUCED to normal form. ------ 199981/23961861. ------ 1. ==[ start ]==> (((a b)((^a.a) a))(^c.(^d.(^a.a)))) 2. ==[ alpha ]==> (((a b)((^x.x) a))(^y.(^z.(^x1.x1)))) 3. ==[ beta ]==> (((a b) a)(^y.(^z.(^x1.x1)))) 4. ==[ alpha ]==> (((a b) a)(^x.(^y.(^z.z)))) REDUCED to normal form. ------ 199982/23961939. ------ 1. ==[ start ]==> ((^a.(b a))(((^a.a) b) c)) 2. ==[ alpha ]==> ((^x.(b x))(((^y.y) b) c)) 3. ==[ eta ]==> (b (((^y.y) b) c)) 4. ==[ alpha ]==> (b (((^x.x) b) c)) 5. ==[ beta ]==> (b (b c)) REDUCED to normal form. ------ 199983/23963661. ------ 1. ==[ start ]==> (((^a.(^a.(^a.a))) b)(^c.((^a.a) b))) 2. ==[ alpha ]==> (((^x.(^y.(^z.z))) b)(^x1.((^y1.y1) b))) 3. ==[ beta ]==> ((^y.(^z.z))(^x1.((^y1.y1) b))) 4. ==[ alpha ]==> ((^x.(^y.y))(^z.((^x1.x1) b))) 5. ==[ beta ]==> (^y.y) 6. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199984/23963694. ------ 1. ==[ start ]==> ((^a.((^a.a) b))(((^a.a) b)(^a.a))) 2. ==[ alpha ]==> ((^x.((^y.y) b))(((^z.z) b)(^x1.x1))) 3. ==[ beta ]==> ((^y.y) b) 4. ==[ alpha ]==> ((^x.x) b) 5. ==[ beta ]==> b REDUCED to normal form. ------ 199985/23964336. ------ 1. ==[ start ]==> ((((^a.a) b)(^a.a))(^a.((^a.a) b))) 2. ==[ alpha ]==> ((((^x.x) b)(^y.y))(^z.((^x1.x1) b))) 3. ==[ beta ]==> ((b (^y.y))(^z.((^x1.x1) b))) 4. ==[ alpha ]==> ((b (^x.x))(^y.((^z.z) b))) 5. ==[ beta ]==> ((b (^x.x))(^y.b)) REDUCED to normal form. ------ 199986/23964693. ------ 1. ==[ start ]==> ((^a.((a a)(a a)))((b a)(^a.(^a.a)))) 2. ==[ alpha ]==> ((^x.((x x)(x x)))((b a)(^y.(^z.z)))) 3. ==[ beta ]==> ((((b a)(^y.(^z.z)))((b a)(^y.(^z.z))))(((b a)(^y.(^z.z)))((b a)(^y.(^z.z))))) 4. ==[ alpha ]==> ((((b a)(^x.(^y.y)))((b a)(^z.(^x1.x1))))(((b a)(^y1.(^z1.z1)))((b a)(^x2.(^y2.y2))))) REDUCED to normal form. ------ 199987/23965773. ------ 1. ==[ start ]==> ((^a.(b (^a.a)))((a (^a.a))(^c.(^a.a)))) 2. ==[ alpha ]==> ((^x.(b (^y.y)))((a (^z.z))(^x1.(^y1.y1)))) 3. ==[ beta ]==> (b (^y.y)) 4. ==[ alpha ]==> (b (^x.x)) REDUCED to normal form. ------ 199988/23966091. ------ 1. ==[ start ]==> ((((^a.a) b) c)(^a.(b a))) 2. ==[ alpha ]==> ((((^x.x) b) c)(^y.(b y))) 3. ==[ eta ]==> ((((^x.x) b) c) b) 4. ==[ beta ]==> ((b c) b) REDUCED to normal form. ------ 199989/23966334. ------ 1. ==[ start ]==> (((a b)(^b.(a a)))(^c.((a a)(^a.a)))) 2. ==[ alpha ]==> (((a b)(^x.(a a)))(^y.((a a)(^z.z)))) REDUCED to normal form. ------ 199990/23967513. ------ 1. ==[ start ]==> (((^a.b)((a a)(^a.a)))(^b.(^b.(a a)))) 2. ==[ alpha ]==> (((^x.b)((a a)(^y.y)))(^z.(^x1.(a a)))) 3. ==[ beta ]==> (b (^z.(^x1.(a a)))) 4. ==[ alpha ]==> (b (^x.(^y.(a a)))) REDUCED to normal form. ------ 199991/23967522. ------ 1. ==[ start ]==> (((a b)(^c.(^a.a)))(^a.((^a.a)(a a)))) 2. ==[ alpha ]==> (((a b)(^x.(^y.y)))(^z.((^x1.x1)(z z)))) 3. ==[ beta ]==> (((a b)(^x.(^y.y)))(^z.(z z))) REDUCED to normal form. ------ 199992/23967753. ------ 1. ==[ start ]==> ((^a.(^a.(a (^a.a))))((^a.b)(a a))) 2. ==[ alpha ]==> ((^x.(^y.(y (^z.z))))((^x1.b)(a a))) 3. ==[ beta ]==> (^y.(y (^z.z))) 4. ==[ alpha ]==> (^x.(x (^y.y))) REDUCED to normal form. ------ 199993/23967909. ------ 1. ==[ start ]==> ((((a a) a)(b a))(^c.(^a.b))) 2. ==[ alpha ]==> ((((a a) a)(b a))(^x.(^y.b))) REDUCED to normal form. ------ 199994/23968176. ------ 1. ==[ start ]==> ((^a.(a (a (^a.a))))((^b.(^a.a)) c)) 2. ==[ alpha ]==> ((^x.(x (x (^y.y))))((^z.(^x1.x1)) c)) 3. ==[ beta ]==> (((^z.(^x1.x1)) c)(((^z.(^x1.x1)) c)(^y.y))) 4. ==[ alpha ]==> (((^x.(^y.y)) c)(((^z.(^x1.x1)) c)(^y1.y1))) 5. ==[ beta ]==> ((^y.y)(((^z.(^x1.x1)) c)(^y1.y1))) 6. ==[ alpha ]==> ((^x.x)(((^y.(^z.z)) c)(^x1.x1))) 7. ==[ beta ]==> (((^y.(^z.z)) c)(^x1.x1)) 8. ==[ alpha ]==> (((^x.(^y.y)) c)(^z.z)) 9. ==[ beta ]==> ((^y.y)(^z.z)) 10. ==[ alpha ]==> ((^x.x)(^y.y)) 11. ==[ beta ]==> (^y.y) 12. ==[ alpha ]==> (^x.x) REDUCED to normal form. ------ 199995/23968620. ------ 1. ==[ start ]==> (((^a.a)(a (a (^a.a))))(^b.(^c.a))) 2. ==[ alpha ]==> (((^x.x)(a (a (^y.y))))(^z.(^x1.a))) 3. ==[ beta ]==> ((a (a (^y.y)))(^z.(^x1.a))) 4. ==[ alpha ]==> ((a (a (^x.x)))(^y.(^z.a))) REDUCED to normal form. ------ 199996/23968629. ------ 1. ==[ start ]==> (((a a)(^a.(a (^a.a))))(^a.((a a) a))) 2. ==[ alpha ]==> (((a a)(^x.(x (^y.y))))(^z.((z z) z))) REDUCED to normal form. ------ 199997/23968782. ------ 1. ==[ start ]==> (((^a.b)(b a))(^a.(^c.a))) 2. ==[ alpha ]==> (((^x.b)(b a))(^y.(^z.y))) 3. ==[ beta ]==> (b (^y.(^z.y))) 4. ==[ alpha ]==> (b (^x.(^y.x))) REDUCED to normal form. ------ 199998/23969049. ------ 1. ==[ start ]==> ((^a.(^b.(^a.(^a.a))))((^a.a)(^b.(^a.a)))) 2. ==[ alpha ]==> ((^x.(^y.(^z.(^x1.x1))))((^y1.y1)(^z1.(^x2.x2)))) 3. ==[ beta ]==> (^y.(^z.(^x1.x1))) 4. ==[ alpha ]==> (^x.(^y.(^z.z))) REDUCED to normal form. ------ 199999/23969052. ------ 1. ==[ start ]==> ((a (^b.(^a.(^a.a))))(^b.(^b.(^a.a)))) 2. ==[ alpha ]==> ((a (^x.(^y.(^z.z))))(^x1.(^y1.(^z1.z1)))) REDUCED to normal form. ------ 200000/23969511. ------ 1. ==[ start ]==> (((^a.a)(^b.(^a.(^a.a))))(^a.(^a.(a a)))) 2. ==[ alpha ]==> (((^x.x)(^y.(^z.(^x1.x1))))(^y1.(^z1.(z1 z1)))) 3. ==[ beta ]==> ((^y.(^z.(^x1.x1)))(^y1.(^z1.(z1 z1)))) 4. ==[ alpha ]==> ((^x.(^y.(^z.z)))(^x1.(^y1.(y1 y1)))) 5. ==[ beta ]==> (^y.(^z.z)) 6. ==[ alpha ]==> (^x.(^y.y)) REDUCED to normal form.